Ut:'iiA'i
Cornell University Library
MT
40.M39 1854
3 1924 022 480 267
Stlfata,
BJem fork
BENNO LOEWY LIBRARY COLLECTED BY
BENNO LOEWY 1854.1919
BEQUEATHED TO CORNELL UNIVERSITY
Cornell University Library
The tlie
original of
tliis
book
is in
Cornell University Library.
There are no known copyright
restrictions in
the United States on the use of the text.
http://www.archive.org/details/cu31924022480267
THEORY AND
PRACTICE
MUSICAL COMPOSITION BY
ADOLPH BERNHARD MARX, DOCTOB OF MUSIC, MUSICAL DIBECIOB Or THE tTHITEBSITT OF BERLIN,
ETC.
TRANSLATED FEOM THE THIRD GERMAN EDITION, AND EDITED BY
HEERMAlSr
S.
SAKONI.
FIFTH AMEEIOAN EDJTION,
WITH AN APPENDIX AND NOTES, BY EMILIUS GIEAC, OP THE
CONSERVATORY
OP PARIS.
NEW YOEK: PUBLISHED BY MASON BROTHEES. 23 PARK ROW.
Entered, according to Act of Congress, in the year 1851, by
MASON & LAW, In the Clerk's Offlce of the District Court for the Southern Distiict of
''
New
York.
Entered, according to Act of Congress, in the year 1854,
bf
MASON BROTHERS, In the Clerk's Office of the District Court for the Southern District of
New
York,
PUBLISHERS' ADVERTISEMENT.
A. B.
Marx
holds such high rank in
Gennany
upon
as a writer
the subject of Musical Composition, that any recommendation of his
great
work
to those
who
are at all acquainted with the musical
rature of the land which
be superfluous.
thoroughly
work of
It is
scientific,
is
emphatically the
home
lite-
of music, would
without a rival as a treatise upon this subject,
and yet adapted to popular comprehension.
this character in the English
language has been so
A
much
sought after in vain, as to lead to the present translation, which embraces two books,
Book
Book
I.
viz.
The Elements
II.
of Musical Composition.
The Accompaniment of a given Melody
reference to Chorals
The
:
and
People's Songs.
translation has been
edition,
made from
closely as possible, securing, at the
American student,
pared by the Editor.
with especial
(Volkslied.)
the third improved
and great care has been taken
tion to the
;
to
German
follow the original as
same time, the necessary adapta-
—and an Introduction has
been pre-
Ilxtraot
of a Letter recevoed from JiB.. A. B. Maex, ly the PiibUshers. Berlin, June 23, 1852.
Gentlemen,
Your
my
communication, and the copy of a translation of
polite
work on Mubical Composition, have been received through
*****
Messrs.T- Edwards,
thanks.
Sandford,
&
Co., for
which accept
I find that your translator (as far as I
am
my
warmest
able to judge from
a somewhat imperfect acquaintance with the English language) has done his work very ^jrac&aWy and successfully; and I beg
you to express honored
my
to him, as also to the eminent
work with
their approval,
my
men who have
sincerest thanks,
and
also yourselves to accept the same, for the very elegant style of the edition.
AUTHOR'S PREFACE.
The
true problem of a treatise on
Art may be thus expressed
TJiat it should transmute the most thorough
knowledge of Art into
and immediately
pil,
the consciousness
him
incite
and
and comprehensive
sensibilities
of the pu-
to artistic activity.
Neither abstract knowledge nor technioaHnstruotion can ever secure
artistic culture,
or even prepare the
opposed to the essence of Art
and
;
way
for
it
;
both are
the fault of the old
it is
teachers, as I have elsewhere proved, that they have not risen
above
As
this unartistie
tendency, or been willing to depart from
the achievement of the
vaded mind,
is
artist,
bom' of
his
own
not an abstract thougHt, but an embodied
spirit,
united in as intimate and inseparable a unity as the soul and of man, so
must the
most
and impressive
way
living
to bolder
science of
Art continually
truths,
from which
it
and more joyous achievements.
it.
free, truth-per-
body
strive after the
should lead the Both, however,
should be accompanied with that certainty, reposing on the convictions of experience,
and that ardent
ments and progress, which,
in
characteristics of a true artistic
my
desire for
new
achieve-
opinion, are the conditions
and
life.
This principle, in connection with contemplation on the essence
by observation and artistic activity from an early youth, strengthened by a view of the historical deve-
of Art, matured
period of
lopment of telligent
in
my
art,
and by the growing approbation of the most
and continually enlarging experience,
first
and second
treatises, is still
my
—
law.
in-
this principle, as
That the
inter-
author's preface.
6 change of theory and sence, of traries,
law and
practice, of
though
mated, and
liberty, of
form and es-
formerly, — —may become more
melody and harmony
as
still,
in reality united,
fertile of results,
my
was
principal
aim
called conliving, ani-
in the present
In this view, notwithstanding the gap in the formal, or
work.
rather merely nominal separation of the Elements from their ac-
companiments, I consider
an essential improvement to have
it
placed the further development of passes and harmonic figuration after the
and not before and
all
where they are immediately applied,
choral,
and more copious treatment of the secular melodies,
for the freer
This, however,
where they are not needed.
it,
further improvements are to be tested
by the
intelligence of
the professor, and the experience of teachers and pupils.
I would gladly
ofiFer
to
younger teachers, or to such as have
not yet had opportunity for extensive experience, an intimation of
my
method of teaching
;
certainly not with the presumption of
being able to say any thing
new
or important, but, as a duty, un-
assumingly to impart what I have to others.
however,
is
the insuflSciency of
all
immediate intuition most strongly cates
and only when
;
Precisely here,
writing to supply the place of
Not books, but
felt.
edu-
life,
quickened and wrought on by
life is
can books perform their mightiest and most beneficent namely, to unite the experience and intelligence of
many
life,
office,
lives
;
to
give support and a rallying-point, so that every isolated existence
—always most whole
—may
limited in
its
immediate activity in relation to the
not forever perish
;
that every worker, unadvised
and unquestioned by the mute Past and Present, may not be forced either to begin his task anew, or follow in the gloomy path
of transmitted usage, in order to be not wholly without support.
Often and long enough has the want of this reciprocal action of doctrine and felt.
Even
own
ers attempting with seurs, while their
the least
skill for
able composers
made itself most painfully we been obliged to see teach-
in our artistic science
life
in our
times have
words and books
to
form
own examples proved them composition
who
;
artists or connois-
to
be wanting in
and, on the other hand, there are
venture to neglect,
if
not to treat with dis-
dain, every pedagogic, psychological, or other assistance, even to
own
explain the science of their
are easily recognized prejudice
is
by
The former
execution.
skill in
their deficiency
The
not so the latter.
;
only too widely diffused, that an able or even a dis-
tinguished composer, must of necessity, and without further pains,
be also an able teacher
;
while yet the indispensableness of fur-
ther qualifications in a teacher
is
so easily seen, that pedagogic
science long since offered to explain,
proved, (as in the cases of that artistic ability
W. A.
and experience has often
Mozart and L. V. Beethoven,)
and the capacity
to teach are not so often or
may
so necessarily united, that the one
The teacher
the greatness of the other.
be safely inferred from should, indeed, possess
—should
the cultivation, the spirit, and the soul of an artist,
himself an
artist,
—
but, besides this,
he should not be wanting
be in
the full vocation, the dexterity, the experience, and the capacity
of the pedagogue.
found or attained,
Seldom
as this many-sided fitness
make us
reflection will not fail to
either
is
confess
its
necessity.
My the
method of
first
teaching, both in theory and practice, has from
verbal instruction only so
much
is
to acquaint the scholar with the
him
Of pure
been directed in conformity with these views. at first premised as
method of
to the point of artistic effort.
From
his teacher, perceives
what
While the scholar who to observe
and what
is
less gifted
—
will
its
to miss in the
—thus pre-
almost of themselves grasp
the next necessary, or next possible point, or understand
The
out diflaculty from the course of lectures.
kept from the beginning in his future
life.
artistic activity,
The teacher
peculiar
familiar with
form of the tune, the more able and diligent scholars pared among the
of notes,
first series
(the major diatonic scale,) the instruction assumes
and permanent character.
and direct
instruction,
the
necessary
is
—
in the
also remains fresh
with-
it
scholar
thus
is
atmosphere of
and
active,
has no longer cause, either in his work or his meditations, to
and fear'
the old disheartening dissension between Art and Science.
With
single scholars, or even with
teacher's side,
two or more, who
and watch the movements of
his pen, or
sit
at the
who
often
8
author's preface.
unexpectedly take the pen into their own hands,-^-to
must give
teacher
advice, or instruct
a work already begun
;
how
instruction has
—
sooner he
is
—the
more
pecially in the greater tasks of the
corrected at leisure, thus enabling
him
may
be taken up and
at once to perceive the
discrepancy of his error with some part of his work.
where
individuality
and
tion give the last decision in the it
its
my
scholar, es-
fugue and sonata forms, pro-
vided they have but one tenable position,
He
of
—the
successful, in
The mistakes of the
opinion, is the teacher's work.
not hold
fertile
anticipate the teacher,
able of himself to discover an explanation or an ex-
pedient-^to accelerate his progress
science,
the
for all these purposes this sys-
been proved most agreeable and
The more the scholar can
results.
whom
to proceed with
to explain, to improve, or to avoid
such and such a dubious point,
tem of
them how
subjective sensation
moment
In
artistic
and
voli-
of artistic creation, I do
advisable that the scholar should wholly avoid errors.
should be thoroughly tried and tested, and have opportunity
to conquer himself
progress
;
by
his
own
might.
A vanquished
error is a
an error merely suppressed threatens a return.
TABLE OF CONTENTS. MUSICAL NOTATION". PAOa IHTRODUCTIOK
.
.
15
PAKT FIRST.—TONES AND NOTES. Chaptee Chaptee Chapter Chapter Chapter Chapter Chapter Chapter
II.
The Tone System The Note System
III.
Abbreviations and other accidental Characters in Music
IV.
Elevation and Depression
V.
The Measuring of Tone- relations The Tone Species, Sexes, or Modes The Keys
I.
VI. VII.
VIII. Relation of
18 19
Keys
.
.
.
24 38
.
.36
.... .... .
41
44 46
BOOK FIRST. ELEMENTS OF MtTSICAL COMPOSITION. PART FIRST.—COMPOSITION FOR SINGLE PARTS (MONOPHONIC COMPOSITION), Chapter
ulation,
:
;
3.
II.
;
III.
Retrospection, 59.
Invention of Monophonic Phrases, 61;
Formation of Passages, 63
Chapter
;
;
ation of the Tone-chain, 66
Chapter
63.
The first Formations 1. The Tone-chain, with its Species, 63 ; Tone Reg54 The Major Scale, ih. Analysis of the Scale, 66 3. Rhythmical form-
I.
;
Discovery of New
1.
The Design and
Formation of Phrases, 64 Means, 67.
3.
;
4.
its
Efficacy, iS.^
Periods, 66.
PART SECOND.—COMPOSITION FOR TWO PARTS CDUOPHONIC COMPOSITION). Chapter Chapter
I.
II.
The Duophonic Composition, derived from the Monophonic, 73. The Duophonic Composition, derived from Natural Harmony, 74 77; Melodic Application,
ner of arriving at
it, ii.
Application,
Harmonic Designs, 78
dence,
Chapter
ib.
;
3.
;
3. Application,
;
ib.
III.
The Duophonic Composition,
81.
4.
The Cadmce,
79
;
6.
ii.
;
I. ManHarmonic
The
;
Half-Ca-
10
TABLE OF COin^KTS;
Chapter IV.
Compositions of two and three parts, 84
Retrospection, 87
;
Compo^
;
tiona of threo parts, 89.
The Double Duophonic
Chapter V.
Composition, 90
PART THIKD.—HARMONY OF
Application, 93.
;
THE.
MAJOR
SCALE.
Chapter I. Discovery of the necessary Harmonies, 94, Chapter H. Examination and Justification of the Harmony, 99 A. The Four Voices*, ifi. ; B. The Connection of Chords, 100; C. Harmonic Besi^ns^ ib: ;~ D. Faulty Pro-;
gressions, 101;
1.
Octave Succession (Consecutive Octaves),
Succession (Consecutive Fifths), 102 of the Dominant, 105.
;
E.
ib.
The Dominant Chord,
2.
;
103
Quint or Fifth F.
;
The Triad
Chapter TIL The Accompaniment of given Melodies, 107 j A. Limitation to those means which were found in the Ascending Scale, ib.] B. The Descending Scale, 109.
PART FOXJRTH.—THE FREER USE OF THE CHORDS IN OUR POSSESSION,
113.
I. Harmonic Designs, 114 A. Development of a Single Chord, ib. ; H, Combination of Major Triads, 115 1. Designs of Nearest Connection, ib. 3. Designs Of Remote Connection, ib. C. The Combination of Minor Triads, and of Minor and Major Triads, 116 D. Harmonic Designs froiA adding the Dominant Chords 117; 1. The Dominant Chord preparing the end, ib. 2. Other Chords in connection with the Dominant Chord, 118; E. Extension of the Harmonic Designs by means of Rhythm, 118 F. Formation of Harmonic Passages or Sequences, 119 Prelude, 120. Chapter II. Freer Harmonization of given Melodies, 122 A. Freer use of Triads B. Free introduction of the Donunant Chord, 125 ib. Freer Treatment of the Dominant Chord, 127 Doubling of intervals in the Dominant Chord, 128 Covered
Chapter
;
;
;
;
;
;
;
;
;
;
;
;
Octaves and Fifths,
;
129.
PART FIFTH.—INVERSION OF CHORDS, Chapter Chapter
I.
II.
Enumeration and Appellation of the Inversions, 132 Free use of the Inversions, 136
New
A.
;
131.
;
Figuring, 134.
Designs and Passages,
B. Combination of Inversions with Fundamental Chords, 133
;
C. Preludes
t&.
and Final
Cadences, 140; D, Avoiding faulty progressions, 141; E. The Diminished Triads, Chapter III. Employment of Inversions, &c., 143. Chapter IV. Close and dispersed Harmony, 144 Retrospection Modulation, 147
ib.
—
;
PART SIXTH.— HAHMONT OF THE MINOR SCALE. Chapter Chapter
I.
II.
Formation of the Minor Scale, 149. Harmonization of the Minor Scale, 151
;
Nona-Chord (Chord of the
Ninth), 152.
Chapter HI. Nona-Chord, ished Septime Chord,
continVfed,
Chapter IV. Freer use of the Melodies,
i5.
;
3.
154; Inversions of the Nona-Chord, 155
163
;
2.
Dimin-
New
Chords, 157
;
1.
Major Melodies, 158
;
3.
Minor
Licenses of the Dominant Chord, 160.
PART SEVENTH.—MODULATION INTO FOREIGN KEYS, Chapter
;
ib.
161.
Modulation from one Key into another, 162 1. The Dominant Chord, The Nona-Chords, 168 3. The Septime Chord, ib. ; 4. The Diminished
I.
;
;
TABLE OF CONTENTS. Septimo Chord, 169;
The Minor
7.
Cmaftek
5.
The Diminished
tft.
;
6.
The Dominant
Triad, 170
;
Triad, 171.
new means
Introduction of
II.
Triad,
11
Ascertainment of Digressive Melody, ternal Characteristics, 174
;
to the Harmonization of Melodies, 173 ib.
1.
;
External Characteristics,
B. Discovery of all eligihle Chords, 175
;
t£.
;
2.
;
A. In
C. Application
of these means to Indigenous or Digressive Melodies, 177.
Chapter
III.
Formation of new passages with the aid of Foreign Chords, 186 1. Pas2. Indigenous Passage, 190 3. Successions of Nona;
sages of Dominant Chords, 189
Chords, 191;
4.
;
;
Indigenous Passage of Nona-Chords, 192
Septime Chords, 192. Chapter IV. Variable modulations, 196 B.
The Dominant Chord,
A.
;
;
5.
Successions of derived
The Diminished
Septime. Chord,
ib.
;
199.
Chapter V. General Order of Construction, 201 A. The first perfect Construction of a two-part Composition, ib, ; B. Second two-part Construction, 303 C. Further ex;
;
tension of Modulation, 304
The
D.
;
Interrupted Cadence, 305.
Chapter VI. Abrhpt Modulation, 207. Chapter VII. Order of Modulation for more extended Compositions,
21Ij Passages of
Phrases, 313.
Chapter VIII. The Pedal-point, Chapter IX. Hetrospection, 220
215. ;
A. Development of Harmony,
ib.
PART EIGHTH. -DISPLACEMENT OF CHORDS,
228.
Chapter I. Suspensions from above, 228 Suspensions of fundamental Tones, 334. Chapter II. Suspensions from below, 236 A means of Connection, 238 Fifths niiti gated by Suspensions, 244 Octaves covered by Suspensions, 245. Chapter III. Anticipated Tones, 346. ;
;
;
;
PART NINTH.—THE Chapter Chapter B.
The
Chapter
The
I.
PASS,
248.
Diatonic Pass, 249 Participant Tone, 360. Chromatic Passes and Assistant-tones, 263; A. The Chromatic
II.
;
Pass,
I'A.
Assistant-tone, 256.
The
III.
results of Passes, 358
The Superfluous
;
Triad, 260.
PART TENTH.—THE TREATMENT OF MORE OR LESS THAN" FOUR VOICES, Chapter Chapter tion,
ib.
I.^
II. ;
266.
Triphonic, Duophonic, and Monophonic Compositions, 366.
More-than-tetraphonic Compositions, 271; A.
B.
The
The Polyphonic Composi-
Double-choired, or Poly-choired Composition, 376.
BOOK SECOND. THE ACCOMPANIMENT OF GIVEN MELODIES. iNTRODUCTIOIf, 381.
PART FIRST.—THE ACCOMPANIMENT OF THE CHORAL, 283. Chapter
I.
General Conception of the Melody, 285
the principal points of Modulation,
Chapter
It.
Disposition of the
ib.
;
Harmony,
B.
;
A. Confirmation of the Key and of Cadences, 390.
Summary
297.
TABLE OF CONTENTS.
12
Chapter III. Simple treatment of the Choral, 305. Chapteu IV. Higher treatment of the Choral, 310 B. Application to the Choral, 314 tion,
ib.
B. Fhrase-repetition,
;
ib.
;
;
1.
;
Technical
A. Character of the Toicei, 311 Difficulties, 318
;
aim of Choral treatment,
3. Artistic
j
A. Tone-repeti310.
Chapter V. The Canlus Firmua in other Voices, 831 A. The Cantus Firmua in the Alto, 322 B. The Cantus Firmus in the Tenor, 333 G. The Cantus Firmus in the ;
;
;
Bass, 334.
Chapter VI. More and
less
than four Voices,
less
treatment, 328
;
voiced treatment of the Choral, 327 1.
i6. j
The Duophonic
treatment,
The Choral with more than four Voices,
B.
A. The Choral with
;
ii.
;
2.
The fTriphonio
330.
How to acquire facility in the Harmonization of the Choral,
331.
PART SECOND.—CHORALS IN THK ECCLESIASTICAL KEYS,
338.
Chapter VII.
r.HAPTER
monic
The
I.
Point, 342
foreign Tones,
A. The Melodic Point, a.; B. The HarC. The Essential Tones of every Key, 344 D. Admissibility ot £. Transposition and Signature, i&. F. Modulation into other
Ecclesiastical Keys, 341;
;
;
ib.
;
;
Keys, 346.
Chapter Chapter Chapter Chapter Chapter Chapter
The Ionian Key, 34T. The Mixolydian Key, 349. IV. The Dorian Key, 350. V. The aiolian Key, 352. VI. The Phrygian Key, 354. VIL The Lydian Key, 35S. II.
IIL
PART THIRD.—THE SECULAR NATIONAL SONG, Chapter ib,
2.
;
General Conception of the Melody, SdO
I.
Character of Keys,
;
1.
358.
Consideration of Voice-region,
ib.
Chapter II. Plan of the Harmony, 381; 1. The Measure or the Quantity of the Harmony, ib. 2. Number of accompanying Voices, 364 ; 3. The Form of the Harmony, 366. Chapter III. Harmonic Figuration, 367 Discovery of its Designs, t&. ;1. Monophonic Designs, ib. 3. Duophonic and Polyphonic Designs, 363. Chapter IV. Execution of the Harmonic Figuration, 370 ; A. The Harmonic Point of 1. Retarded Resolution, ib. ; 3. Octave and Quint-Succession, 371; View, ib. B. The Melodic Point of View, ib. 1. Consistency of Execu3. Passing-tones, 373 2. Firm Connection, ib. tion, 373 Chapter V. The Exercise of Harmonic Figuration in Passages and given Melodies, 375 1. Passages rediiced to Harmonic Figuration, t&. ; 2. Accompaniment of given ;
;
;
;
;
;
I
;
Melodies, 377.
Chapter VI. Passing-Tone and Bye-Tone, 379 382
;
;
Help Tones,
381; Trills, Turns,
8ic.,
Passing or Transient Chords, 384.
Chapter VII. Introduction of Passes and Help-tones into Figuration, 385 A. FiguraB. Figuration of the Bass, 387 C. Figuration of a tion of the Upper Voice, ib. ;
;
;
Middle Voice, 389
Chapter
;
Application, 390.
VIII. Application of these
means
to Artistic
APPBITDIX, The Figural
Prelude, 401.
Accompaniments,
392.
ELEMENTS OE MUSICAL NOTATION. Br THE
TRANSLATOB.
PREFACE TO THE ELEMENTARY PART.
The
indefiniteness of the English language, in everything
concerning Music, makes
it
a task of extreme
difficulty to
write an Elementary Treatise, corresponding to a theoretical
work of any
foreign,
and particularly German author.
German musicians have made Music that
is
it
absolutely impossible to do
lating their
The
so thorough a study,
them
justice in trans-
works with general terms, which at every step
are subject to modifications and contradictions. It is this consideration
of this tise,
work
which has induced the Translator
to prepare the student
the chief object of which
such terms as
may
by an Elementary Trea-
is to
give exact definitions of
occur in this or other works of the same
author, and the exact meaning of which
it is
absolutely ne-
cessary for the student to know.
In order to avoid the introduction of indefinite terms, or
arguments upon them, as much as possible, the Translator has thought
it
best to convey the necessary information in regu-
lar didactic
form ; and
if
comparisons and arguments cannot
be absolutely avoided, they will be possible.
made
at least as brief as
INTRODUCTION.
" Music ear,"
is
is
the art of combining sounds agreeable to tbe
the general definition given of the word.
Not every sound, however agreeable cal sound
;
nor
It follows, then, that
sic.
to the ear, is a musi-
a combination of such sounds always
is
our
first
Mu-
task must be to distin-
guish musical sounds, or sounds agreeable to the ear, from
such sounds as constitute Music.
We know that the afiected
by Music.
ear
is
the organ which
Every vibration of means,
lision of bodies, or other
air
is
most directly
caused by a col-
sufficient to affect the ear,
we designate by the general name of
SOUND.
We
know,
also, that
voice, as well as
Music
is
produced by the human
by instruments of various kinds
—
Flutes,
These instruments distinguish
Trumpets, Violins, &c.
themselves from each other by the quality of their sounds. Finally,
we
perceive on one and the same instrument, that
the sounds produced upon
it
vary in regard to pitch.
Thus,
for instance, are the sounds produced on the shorter strings
of a
Harp more
string. call it
When we
acute than those produced on a longer consider a sound in this respect,
we must
16
TONE.
We
have, therefore,
many
the longer or thicker strings are called low shorter or thinner strings are called high. voices,
The
different tones. ;
tones of
those of the
Thus of human
we say that the tones of a man's voice, in general,
are lower than those of a boy's or girl's voice
the Flute, Violin, Trumpet,
we
;
the tones of
say, are higher than those
of the Bassoon, Double-bass, and Horn.
We
say " in ge-
neral ;" for since every voice and every instrument can pro-
duce many tones,
man's
it
can occur that the highest tones of a
voice, for instance, are higher than the lowest tones
of a girl's voice, &c.
Every tone or sound
to
be produced, must be produced
within a certain time, therefore must
fill
a certain space of
time,—^a longer or shorter space, definite or indefinite.
This time, or space of time, accorded to a tone or sound,
is
called its
DURATION.
We
say, therefore, of a tone
:
it
has a definite or inde
finite duration.
If
we cause
the gradual production of a series of tones or
sounds of certain duration, according to some regulating law, in any fixed and continued, i.e. repeated, time-mo-
ments, we call this regulation of time-succession,
RHYTHM. Where such regulation
does not take place, the tones have
either
no certain duration, or follow in no regular succes-
sion
we say
A
;
that such tone-succession
succession of toneS; which
is
is
unrhythmical.
formed according
to
any
17 particular plan, and at the
same time rhythmically regulated,
(whether agreeably, expressively, &c., or not,)
is
called a
MELODY.*
A piece of is
Music can
consist of a single tone-series,
—
it
then called
Monophonic,
Or
it
one voice.)
(for
can consist of two, three, four, or more, simulta-
neously progressing tone-series
Duophonic Tetraphonic
(for (for
two voices)
then called
Triphonic (for three voices)
;
four voices)
it is
;
or Polyphonic (for
;
many
voices.)
Each
series of tones, however,
upon some instrument,
is
called
a
TOICE The simultaneously-meeting
whether sung or produced
.
tones of different voices
must
stand to each other in some reasonable, corresponding relation.
This relation
is
called
HARMONY And
of all these essentials
:
.
tones and sounds, tone-suc-
cession and rhythm, melody and harmony, does
MUSIC consist.
*
A mve concise definition of Melody will be given at a later porioc'.
FIRST PAET.
TONES AND NOTES. CHAPTEE
I.
THE TONE SYSTEM. Tone
is
a sound of certain height or depth, (pitch.)
We know
already that there are
of the various tone-gradations
Music, however, not
A
of.
all
is
many
tones
;
the mass
absolutely innumerable.
these tone-gradations are
In
made use
part merely of these tones are actually and fixedly
employed.
These tones constitute what
is
called the
TONE SYSTEM. This tone-system contains above one hundred tones.
would have occasioned much
name
for each of
them
;
and
classification of these tones
difficulty to fix
this
It
a particular
has been the cause of the
under seven
DEGREES. These degrees have been named
C—D—E— F—G— A—B. And
all tones
them.
have one of these names, or one derived from
CHAPTEE
II.
THE NOTE SYSTEM. For
the designation of tones,
we make use
of a series of
characters, called
NOTES. It
would be tedious for us
eical Notation.
We
Mu-
must content ourselves with communi-
cating the facts, that after five lines
to enter into the history of
many changes and
modifications,
have been fixed upon, on which, or between which,
the tones are indicated
by open or
filled circles,
or ovals, ac-
cording to their pitch and duration. 1.
Where
these five lines are not sufiBcient, additional lines,
called
LEGER LINES are introduced, which, not being continuous, are easily distinguished from the lines of the stave.
2.
Here
^=1=1=4
^
-
4 j 4
w« have introduced
the leger lines, in order to designate
20 those high or low tones, which are above the highest or the
lowest tones capable of being designated within the stave.
We
might now read and write
all
we
notes, if
what meaning to attach to any particular note. words,
we must
sponding
to
fix
only
knew
In other
upon some point, or some note corre-
a certain tone, by which we can be guided in the
designation of the others.
For
this
purpose we have certain characters, called
CtEF s, Of such clefs
which indicate the tone represented by them. there are three in use
The
G-clef, or Treble-clef
The
C-clef,
The
F-clef, or Bass-clef.
1.
has this form,
:
—THE
;
and
G-CLEF
fc
and indicates that upon the the tonei g, (the lowest
g
line inclosed
by
lower circle,
its
of the Oboe, or the fourth
/f
of a
six-octave Piano-forte, counting from the left to the right,) shall be represented.
French composers of former times,
placed this clef upon the it
first line
of the stave, thus
imperative to consider the note upon
tive of the tone g.
At
it
making
as the representa-
present the G-clef
is
invariably
placed upon the second line of the stave, and the notes pre-
ceded by
il
it
would accordingly be named thus
s^s gab
:
m
FGAB CDEFGAB CDEFG
21
By means many
of additional leger-lines,
upon
additional tones
this stave
we migtt
;
designate
but since the read-
ing of such notes would be a very troublesome task, another
character has been invented, in the shape of a wave, or dotted line
:
8-
which, with the figure 8 before
indicates that the passage thus
sung an octave higher than
The
and the
it,
it is
marked
succeeding
it,
to be played or
written-
leger lines below the stave can be avoided, if neces-
by substituting another cM.
sary,
is
S
More of
this,
however,
anon.
THE C-CLEF,
2Its
most usual form
fold one.
is
Indicatiag the tone
A,
B
* A
and
:,
'(jj^)
upon the
names of the notes succeeding
'
,
use
its
it is
is
a
three-
used
as Soprano-clef;
in which case it is placed
the
this
first line it
of the stave, and
are fixed accordingly
DEFGAB CDEFGABC
B
B, as Alto- clef.
As such
it is
placed upon the third line of the stave, and
the notes succeeding
,jmm.
it
are called
:
^^B
3 V
-iD
z E
^ «
^ =
CDEFGAB CDE
22 C, as Tenor-clef.
As
sueli it IS
placed apbn the fourth line of the stave, and
the notes succeeding
it
are called
^
:
.^wi-it^
6."
m
1^
A It is
m CDEFGAB DEFGAB
^-f?
B
hardly necessary to add, that additional leger-lines
can be employed in the C-clef, as
3 It
.
—T HE
-well as in the
G or i^-clef.
F-CLEF.
has generally this ^f;, or some other similar form,
and indicates the tone
exclusively
f$
upon the fourth
.
line of the stave,
to the notes succeeding it the following
now placed
It is
names
and thus gives :
23 8.
3: The above appear 6hus
^
=£
passage, if written in the Treble-clef, would
CHAPTEE m. ABBBETEATIONS AOT) OTHER ACCrDEIITAL CHAEACTEES rw MUSIC.
We
have already mentioned the character which trans-
The same
poses a tone-series to the octave above. ter is
charac-
used for the transposition of a passage into a lower ocIn such case the wave-line
tave.
to be transposed.
is
placed below the notes
For single notes the
figure
8 will be
suffi-
cient.
A
similar facilitation consists in
employing the words
alV-ott«va, or aZZ'S^*, which, if placed above the notes, indicates that the higher octave is to be added to the notes
thus marked intended.
m
;
if
Thus
placed below the notes, the lower octave ia the following passages.
12.
:c
m
:•:
$
-$
might be expressed in
this
manner : all'Sva.
m
13.
all'Sya.
,
m
fcti:
25
Other abbreviations,
like alia
3za
(ter^£), alia
6S
{sista),
&c., will need no further explanation. Finally, there are certain characters intended to save the
notation of a passage partly. If a passage is to be repeated two, three, or four timeSj it
written but once, and the words
is
his,
are placed above to
it.
— —quater, ter,
In addition to the above, the passages
be repeated are often inclosed by curves, or dots
n
X4.^
:
26 If a passage
is
to be repeated, the
end of which expe-
riences an alteration in its repeat, the part to be altered is
enclosed by a curve, and the words
placed above
marked
volta), are
In the repetition of such part, the passage
it.
1^ is omitted, and the player has to pass on beyond
the repeat, where the words to guide
1= (prima
him.
2S
(seconda), should be placed
The words prima
volta,
and seconda
volta,
stand here for 1st and 2d, time, and thus explain the mystery.
The words Da similar meaning,
capo, (D. i. e.,
"
C,
or
B. c,
or d.
c.,)
have a
to repeat."
If the repetition goes merely to a certain point, where the piece
is to
be ended, the point
is
marked by the word
Fine, (end,)
and
is
for the sake of clearness
a pause
placed above the end note
;
:
and instead of the simple
D. C, the words D. C. aljine (from the commencement
to
the end), are placed at the point where the repetition is to
take place. If the repetition is to begin at a certain point in the dle of the piece, that point is
and instead of sign, are used.
d.
mid-
marked thus
c, the words
d. s., (dal segno,)
from the
27
There are in use facilitation,
still
we might
more characters of abbreviation and
say,
but these not being absolutely ne-
cessary for our immediate purpose, vre shall give their meaning -ffhen they occur.
CHAPTER
IV.
ELEVATION Aim) DEPEESSION.
When we
compare our notes and tones, as far as we know
them at present, with the key-board of a Piano-forte, we find that
we do not know yet
the tones of our system,
all
and that consequently we cannot represent them by notes.
We have
reference to the upper keys, or black keys of the
Piano-forte.
We
have permitted
this
pleteness, in order to obtain a basis sily arrive at the
Our
wanting tones and characters.
tones, thus far, if succeeding each other in regular
rotation, are
by no means equidistant from each
Beginning from
c,
for instance,
we
between the two, however, there
The same a and
A
temporary incom-
from which we can ea-
relation exists
other.
arrive at the next tone is
room
d;
for another tone.
between d and c,/ and g,
g and a,
b.
diagram of these relations
achieving our object. c as the first tone its octave, will
;
will
We have here
aid us materially in
accidentally mentioned
and on examination the
series
from c to
be found so satisfactory to the ear, that we
shall adopt it at once as the
normal tone-series for our ana-
lysis, being, in addition to
the above, the only one of the
seven tone-series at present within our reach, which pletely satisfactory.
Here, then,
possible intermediate tones are
is
is
com-
a diagram in which the
marked by a mere
dot, for
29
we have no other means
the simple reason that, at present,
of designating them
C—d—ef—g—a—b
We
repeat, again, that this succession of tones ;
we
c to the other,
der, or to use
for
will call the
perfectly it
were,
whole diagram a lad-
a technical expression derived from the Latin
" Ladder,"
(^scala,)
we
will call it
A SCALE
.
Having once adopted the term " scale," that
is
and since we ascend, as
satisfactory to the ear
from one
word
c
we should
call the
it is
but natural
intermediate tones
DEGREES, and the distances from tone to
tone, or
from degree to de-
gree,
STEPS When we now
compare the
.
different steps,
we
find that
those admitting of an intermediate tone are larger, must be larger, than those
tone.
We
which do not admit of an intermediate
will distinguish these different species of steps
by the terms " whole steps," or " steps," and " half steps."
We find, further,
that our scale contains five steps, and
two half steps, distributed in such a manner, that from the first to
the second, from the second to the third, from the
fourth to the fifth, from the fifth to the sixth, and from the sixth to the seventh degree, are steps to the fourth,
and from the seventh
half steps, as in the following diagram 1
16, c
;
:
—e-f—g—a— 1
d
i
1
and from the third
to the eighth degree, are
1
1
J
h-c.
30
We
stated In a former paragraph that ottr taking c as the
basis of a scale,
We will
was merely accidental.
remember
that a succession of tones, in order to be a scale, must be a
regular succession, in which the steps and half steps are
And now we
distributed according to the above diagram. will
attempt to form a scale from any other tone.
We
take
accidental
;
g-,
which the student
may
again consider merely
the reason, whereof, however, will soon become
The regular
apparent to him.
when we take the degrees,
g—a,
succession
as they follow from
6, c, d,
e,/,
g
;
attended to
is
g
to g, thus
:
or thus,
,17.
i but on striking these notes on the Piano, and comparing them with our last diagram (No. 16), we soon discover that the steps
from the sixth to the seventh, and from the seventh to
The
the eighth degree, are different from our diagram.
and
g
are correct, but
the/
is
/ degree is necessary to make And now we we could
find
it
our scale complete.
There
the very tone
original/",
we
we need
being absolutely indis-
new tone upon
this
from the
is
The/ degree
g-.
we place
distinguish
e
Yet the
return to those intermediate tones, for which
no name.
between the/ and pensable,
we want.
not what
it
;
and
place this
in order to
mark
# before
it.
This character
is
called a
" sharp," and conveys
the idea, that the tone before the representative of which
it
31 is
as
placed, has been it
made more
sharpened,
acute, elevated
were.
The
scale of
G, with
amendment, would present the
this
following appearance
18.
i It is
now a
C in
the scale of It is
correct scale in every particular, differing from
but one point, that of pitch.
time now to give the reasons for taking the tone
experiment upon.
The student
the fifth tone of our ori-
ginal scale, and in taking again the fifth tone of our scale, d,
one more sharp will be
the scale of
dent
may
to
will perceive that one tone
G was
only required an alteration.
g
all that is requisite to
D correspond with that of
Thus
G.
new
make
the stu-
pursue his course, adding sharp to sharp, while we
begin at a different point, probably to meet him at some point where
We
sion.
we can
explain his doubts, or remove his indeci-
have simply
to add, that in the course of his la-
bors, if he pursues the plan
we
indicated,
suming his task from the fifth tone of the
i.
e.,
always re-
last scale, he will
soon discover tones which are not in our original scale;
but in following the above directions, he cannot
fail in
com-
pleting his scale.
We
have succeeded so well in constructing a scale up-
on g, the
fifth
tone above
c,
that
we are warranted by
at least, in attempting the formation of a scale fifth
tone below
it,
upon f, the
c.
Let us again write our degrees in regular succession, beginning
with^
32
19. rf;
^
J
J
r
Comparing the steps of
gram No. 16, we
f-r^
this tone-succession
with our dia-
find that while in the scale of
by
the seventh tone which required being replaced it is
now
the fourth tone which
demands a
we must
bear again in mind, that
from the original
h,
we
was
We
preserve the regular sue
course to the intermediate tone below it
it
another,
modification.
cession of the degrees, and b being too high,
tinguish
G,
it,
we have
and in order
re-
to dis-
place a
b before
This character
it.
is
called a
"
flat,"
and conveys
the idea, that the tone before the representative of which is
placed has been lowered, depressed—^aWewed, as
With
it
pearance
the scale of
F would
it
it
were.
present the following ap-
:
20.
m
*=
The elevated tones have
the word
as/ sharp, g sharp, &c. The depressed tones have them, as h
Taking
flat,
fifth
a
flat,
above
g the
" sharp"
afiSxed to
name "flat"
affixed
C, fifth
fifth
tone to construct our scales upon,
G,D,^,E,B,Fi, below
to
&c.
would give us the scales of
Taking
them,
fifth,
Cit,&c.
would give us the scales of
C,F,Bi>,E\>,Jl\>,Di,
Gk
33
That some of these
scales should be alike in sound, yet
different in appearance,
we know when
Enough
need not trouble us.
to use the one or the other,
that
and enough to
remember that we issued from the same point
two
in
differ-
ent directions, and that our impulse has carried us over
ground previously gone over from the other point.
ai.
il
FfaT.
iFLaTi
§FILOTini3
.l.fHfiilSI'.i
In order to avoid the unnecessary accumulation of characters in the notation of
a piece of music, the sharps or
flats
incident to the scale or key in which a composition has been written, are merely placed at the beginning of the piece, or
at the beginning of each stave, and are called the signature
of a scale or key.
by
This signature
certain characters, (of which
until another signature occurs.
of music, flats its
fied.
we have then
to
is
we
valid until shall
it is
recalled
speak directly,) or
During the course of a piece
remember how many sharps or
key requires, and what tones have been thus modi-
34
The
fact of there being in existence incidental flats
and
sharps, leads us to suppose that there are also accidental
sic,
These occur in almost every piece of mu-
and sharps.
flats
and
piece
is
arise
when the composer leaves the key in •which the
written, either temporarily or permanently, without
changing the signature, or when a tone of a foreign scale introduced without afiecting the regular key. the sharp or
good imtil
flat is
it is
is
In such case
always placed before the tone, and holds
recalled
—
i. e,',
until the modified tone ia re-
placed by the original one, or until the end of the measure ia
which the accidental occurs.
The
neutralizing a sharp or flat is called this
character used for
a " natural," and has
form H
It is placed before the note to
be neutralized, and holds
good to the end of the measure* in which
There are
also instances in
or depression of a tone
point of pitch.
is
it
occurs.
which the incident elevation
not sufficient to reach the desired
Double sharps (X) and double
have been introduced in such cases.
flats,
The former
elevates
the tone an additional half step, the latter depresses the same ratio. tural
(tlfc^)
is
We need hardly naention that
{hh,)
it
in
a double na-
required to neutralize the efiect of either.
If the intermediate tones of
which we have spoken, can
occur in the course of a composition, they can also occur in
a scale.
Here
* The word measure signifies a musical division marked by perpendicular " bars." More of thi» in the chapter on Rhythm.
lines, called
35
22.
^^^^^^^^p^^m is
the scale of C, with all
its
intermediate tones.
We have
written the ascending scale with sharps, and the descending scale with flats, in order to avoid the introduction of natu-
A better
rals.
reason for
it,
however, will be given in the
" Theory of Music."
A
scale, in
which the intermediate tones are introduced,
called a
is
Chromatic Scale. In contradistinction to
it
the original scale
is
called the
Diatonic Scale.
Tones which c
l"
,
ct
and d
differ in
b ,
cI
name but not
Enharmomc, More
in sound, like 6
and/, &c., are called
cf this hereafter.
and
CHAPTBE
V.
THE MEASUEING OP TONE-EELATIOKS. Since Music
know
is
a combination of tones,
it is
necessary to
the relations of these tones to each other.
We
can designate
one tone
is
it
superficially,
higher than another, for instance,
higher than the d of the same octave.
above each tone there are statement
is
by merely stating that
But
many lower and
^
or a
since under
is
and
higher ones, this
by no means as exact as we should
desire
it.
Counting the degrees would be already much more exact. Beginning from any one which we call the
next above
it
call the first degree,
the Latin numerals are used for this purpose
and English names.
Frequently
the second, third, &c.
they will occur even in our work,
we
will give
we
;
and since
both the Latin
There are then
The first degree, or First, or Prima. " Second, or Secunda. The second " Third, The third, or Tertia. " Fourth, or Qunrta. The fourth, " Fifth, The fifth, or Quinta. " Sixth, The sixth, or Sexta. " Seventh, op Septima. The seventh,
— — — — — —
And
in
some .instances
Thus we have
it is
necessary to go even further.
37
The eighth The ninth The tenth
degree,
" Ninth,
or
degree,
" Tenth,
or Decima.
The
degree,
" Eleventh,
or Undecima.
degree,
" Twelfth,
or Duodecima.
degree,
" Thirteenth, or
degree,
" Fourteenth, or Decima quarta.
degree, or Octave,
eleventh
The twelfth The thirteenth The fourteenth
We perceive
Nona.
Decima
tertia.
at once that Octave, Nintli, Tenth, &c., are
nothing but the
second, third, and fourth degree, in a
first,
higher octave. that there
or Octava.
Yet, at a later period^ we shall discover
a difference, sometimes, between these degrees.
is
When we now spective pitch,
This relation
compare two tones
we place them
is
in regard to their re-
in a relation to each other.
called
INTERVAL.
We
G
and
But even
know
^X,
this designation is not sufficiently exact, for
we
that each of our degrees embraces j/?De different tones.
Which mand,
C and D form together the interval of D the interval of a fifth, &c.
say, therefore,
a second,
of those five
is
now
in reality intended ?
for instance, the fifth of C, it
or ^1"
,
or g^^.
They
all
from C, and consequently are
If
may be g,ov
stand upon the
fifth
we deg'i
,
or
degree
all fifths.
We require, therefore, a more exact tone-measure, and for it
we take
the smallest measures of our tone-system, the
HALF-STEP, and the
STEP.
We
are
now enabled
tone-relations of
the steps and
to give
any possible
an exact statement of the
interval,
by merely counting
half-steps therein contained.
Thus the second
38 d, for instance, contains
c
d and
or c c
b
(i b
—
d and d
and
dit
But
— it
e,
—
d"
.
two half-steps,
The
third c
— —
e
or four half-steps, c
c
—
cS
and
c4
—
d,
contains two steps,
cS
,
cI
—
d,
rf
d
it
e.
would be too troublesome always to give the exact
measure of an interval in so many steps and half-steps, and have been distinguished four classes of
for this reason there intervals,
which in themselves at once express the exact
measure of the
Each
relation.
interval can be
Major, or Minor, or Diminished, or Superfluous.
Each minor
interval arises
jor one, or in other words,
same major
it is
a half-step smaller than the
interval.
Each diminished minor
from the diminution of a ma-
interval, or
interval is a half-step smaller than the
two half-steps smaller than the same ma-
jor interval.
Each superfluous
interval is a half-step larger than the
major interval.
When we
once know, therefore,
tervals are, it will be easy to
ished, or superfluous intervals. tion of the
major intervals
how
make
of
And
large the major in-
them minor, diminthe best representa-
is
ouK SCALE itself; for each tone in interval.
it
forms with the fundamental tone a major
Consequently
39 c
d
is
a major second,
c
e
"
a major
c—f c g c
a " a major sixth,
c
b "
c
a major seTenth,
— " —d "
c
an
c
The major second
— — — — — — — — —
it will
be easy
octave,
a major ninth;*
When we remember now
— — — — —
that
contains 1 step,
— — — — — — —
third fourth, fifth,
sixth,
seventh, octave,
ninth,
2
steps,
2
steps,
of
it
4
steps,
5 stops,
5 steps, and 2 half-steps,
6
the major fifth c
many
i. e.,
interval, it will be easy to
g
The minor
c
d
b,
e
i,
b
b, b, b, b,
g
to
from
intervals
c
for instance,
we wish
to change
a minor one, we must subtract a
change the
c
g^
.
C—g^
is
a minor
c are therefore
the minor second,
— — — — —
— — — — —
third,
fourth, fifth,
sixth,
seventh.
We must bear in mind that these intervals are merely major, as
to the fundamental tone of the scale
selves form various intervals is
half-steps,
half-steps (by depression or ele-
If,
into
c—f c—g c—a
*
and 2
steps,
a minor, diminished, or superfluous one, by add-
vation) as are requisite.
fifth.
1 half-step,
and 1 half-step, and 1 half-step, and 1 half-step,
measure the other intervals.
to
ing or subtracting as
half-step,
and
3 steps,
Having once obtained a major
make
third,
« a major fourth, " a major fifth,
no*
a major
fourth, &c.
;
thus
(c)
.
The
related
other degrees amongst them-
d—f and e—g are
not major thirds
;
f—b
40 In order to change c
must be elevated a jor seventh c
I
—
6
g
S
a minor seventh,
ct
—
the
of the
g
ma-
must be depressed
In order to make of the
.
h a diminished seventh, b must be de-
pressed an additional half-step
In this manner
venth.
"
b i
fifth,
make
In order to
a half-step, and must become 6
minor seventh
a superfluous
into
half-step.
it is
;
c
It
—
b
^
is
a diminished se-
very easy to represent any mi-
nor, diminished, or superfluous interval.
In the last chapter we
we
now
find
intervals,
made mention of enharmonic
tones
which though of equal height in re-
gard to the tones constituting them, have different names,
and which, therefore, are called
Enharmonic
Intervals.
Thus, for instance, the minor third with the superfluous second c c
g
S is
di
;
c
e
^
is
enharmonic
the superfluous fifth
enharmonic with the minor sixth
c
a
t ,
&c.
CHAPTER THE TONE
SPECIES, SEXES,
We have seen that grees,
VI.
Music has at
its
OE MODES. command seven
de-
upon which, however, can be constructed a great num-
ber of tones and tone-relations.
It
is
possible that
these tones and relations can occur in one composition.
work of art has certain
since every
tendency, since sensations,
it
is
it
limits of
all
But
design and
expresses a certain round of ideas and
natural that the tones and tone-relations
should be limited in the same manner
;
that for each composi-
tion there should be a certain circle of tones and relations,
within which the composition should exclusively or principally
move. This circumstance
facilitates the task of
intr^ucing the
student into the empire of tone-formations, without the risk of his losing himself in the infinity of manifold forms.
The seven
degrees, so lately mentioned, form the basis' of
every composition. five
But each degree can be represented
in
different manners, and thus there are innumerable pos-
sibilities
of combination.
But of
all
these possibilities, the system of
modern Music
has selected two as the only essential ones. called
Tone Species, or Modes, and are either major or minor.
They
are
42 distinguished In both are the seven degrees, and they are to each other from each other by the relation of the degrees degree iorms -with and by the size of the interval which each
the
first tone.
THE MAJOR MODE has exclusively major intervals.
we formed
Consequently all the scales
in the fourth chapter are major scales,
to the major
and belong
mode.
THE MINOR MODE contains also major intervals, with the exception of the
Third and Sixth, which are mmor. change major intervals into minor,
Since
We
the third and
to
be easy for us to
it will
change a major mode into a minor.
we know how
have but to depress
sixth to change C-major,
—e—f—g—a— — 6
d
c
c,
for instance, into C-minor,
—
d
c
Thus we
t
find that the
—f—g—
b
fit
—— b
e
1
i
c.
minor scale has the following steps
d— —f—g— a — b —
c
The most
e
^
I"
1"
1
n
i
conspicuous step in this scale,
to 6, a step of a superfluous second.
c.
i
is
Like
the one from a all
•>
other super-
fluous intervals, this progression in the course of the scale, afiects
us disagreeably.
,aa. -S^
^^^^
43 This, however,
is
not the case in every tone-succession
for instance, not in the following
23.
P
±>
>!.
:
V. !fe
w
•where the superfluous second has been avoided,
n and
it is
not
our object to obtain a mild tone-succession, but a firm basis for our compositions.
CHAPTEE Vn. THE KEYS. In the fourth chapter we have been taught the number of the
major
and how they can be formed.
scales or keys,
now form as many minor we hare
also learned
scales or keys.
what signature
scale or key.
The
different law.
Their signature
it,
We can
In the same chapter
to give to each
major
signatures of the minor keys follow a is
not as the scale demands
but each minor key has the signature of that major key
which
lies
The
a minor third above
signature of .^-minor
it.
is
npt, as one
would expect,
a sharp before g, nor does that of D-minor consist of a
and h
l"
; but ./2-minor has the signature of C-major,
ct
and
D-minor has the signature of 2^-major.
Here
D, G,
C,
y,
Bb,
Eb.
are the signatures of the most usual minor keys.
Two
keys, (a major and a minor key,) which have the
same signature, are
called
PARALLEL KEYS, Or PARALLEL TONES.
The
parallel-tone of a minor key, as
we have
seen, lies a
45 minor third above a major key
We
lies
it,
and, vice versa, the parallel-tone of
a minor third below
it.
can now more fully understand the object of the
nature.
It tells us
elevated
—
1,
what degrees are
2, it serves us as the
;
to be depressed or
token of the key in which
But we know
the composition has been written.
such signature can belong to two different keys der to ascertain exactly in what key a piece
must turn point,
we
to its
will
But
harmony.
if it
until
we
is
;
also that
and
in or-
we
written,
arrive
at that
remember that generally
THE LAST TONE and
sig-
of a picCe,
ends with a chord,
THE LOWEST TONE
of that chord,
in connection with the signature, will be a sure indicator of
the key.
If,
for instance, the signature consisted of
sharps, and the lowest tone of the last chord were p,
would know at once that the piece
is
composed
two
we
in B-minor,
the parallel tone of D-major.
But what of those degrees signature
is
not suitable 1
in the minor keys for which the
The
t
or
i"
belonging to them
is
placed before the respective notes as often as they occur, thus making these elevations or depressions almost accidental.
CHAPTER Vni. RELATION OP KEYS.
When
we compare the
find that each deviates
different
keys with each other, we
from the other to a greater or
Thus C-major and G-major
degree.
tonej/and/S
.
deviate but in one
Comparing, however, the scale of C-major
with U-major, we find that the two scales tones from each other has_/lt,
Two
c'i
,
less
;
C-major has
_/",
c,
differ
in four
g, d j J5J-major
gi, di
keys which have several tones in common are said to
be
RELATED.
We
have just now seen that this relationship can take
place in a greater or less degree, according to the tones which the two have in
common.
There
number of
are, conse-
quently, different
DEGREES OF RELATIONSHIP. Finally, tion
we have
between
in the
already seen several manners of connec-
different
keys
;
the major keys were connected
form of the Quint-circle
;
the minor keys, with the
parallel major keys, and with their own major keys. are, therefore, three kinds of relationship.
There
47 Relation of
1.
Here the Quint-Sircle
The keys
degrees.
Major Keys.
indicates the relationship with its
lying close together in the Quint-circle,
deviate from each other in but one tone, and stand in the f,rst
degree of relationship to each other.
the Quint-circle before us thus 4
6
spread
:
310133466 b
6
When we
3
»
Q^^Dh—A\,—E\>—B\,—F—C—G—D-~A—E-'B—F!i we
key has
find that each
bors to the right
and
its
two nearest relations as neigh-
to the left.
Relatives of the second degree are those which differ in
Thus X>-major on one
two tones.
side,
and
B
!>
-major on the
other, stand in the second degree of relationship to C-major. 2. Relationship
The
of Parallel Keys.
parallel keys are related to each other in the first
degree, for they differ
C-major and
from each other in but one tone.
./2-minor,
C-minor and
E
b
Thus
-major, are relatives
of the first degree.
When we we
combine
this
new kind
perceive a
kind of relationship with the other, of relationship between the keys.
We have found that each major key stands in relationship of
—
degree
the
first
its
Parallel
1, with its neighboring
key,
—
^for
JP-major, and .;2-minor.
instance,
major keys
;
2,
with
C-major with G-major,
But now the major keys
G
and
F
stand again in the first degree of relationship with their Paral lei tones,
E-minor and D-minor.
Consequently we can con
sider these minor tones as relatives of the second degree to
the first major key (C-major.) hibits to us
The
following diagram ex-
43 0-major, Ji'-major,
»
A-miaoi, G-major, as relatives of the
first
degree.
jK-minor, as relatives of the second degree.
l)-ininor,
We might pursue ther, but this Tvould
these degrees of relationship
much
far-
be but an unnecessary waste of time and
paper. 3.
Relationship of
Minor Keys with
Major Keys,
their
and amongst themselves.
We know grees from
we should
already that each minor key deviates in two de-
its
major key, in Third and Sixth.
consider
them as
Consequently
relatives of the second degree.
But a singular coincidence draws
this
bond of union closer
together.
The
fifth tone,)
and the Sub-dominant, (the fourth
Tonic, (the
scale are its principal
first tone,)
the Dominant, (the tone,) of each
moments, and these three moments be-
long to the major scale as well as to the minor
communism
of tones
later period,) that
is
we can
tone as relatives of the
And
finally
so influential, (as
we
;
and
consider the two modes of the
first
we consider
this
a
shall see at
same
degree.
those minor tones which stand in
the relation of Tonic, Dominant, and Sub-dominant to each other, as relatives of the first degree.
£-minor and D-minor as
D—e—f—g—a—bh—4—d—e—f c
d
to
two and three points
:
—
g —e—f—gl —aa— — —d h
e—fi—g
When we
consider
relatives of the first degree
.>3-minor, though their scales deviate in
a—h
Thus we
c
e
a~-b—c—di—e
combine these relationships with those found
49
under 2, we can form a similar diagram of relationships of first
and second degree. ^-minoi, iJ-minor, C-major, E-nunor.
F-major, It
Gr-inajor.
remains now for the student to form similar diagrams
«f other major and minor keys.
FIRST BOOK. ELEMENTS OF MUSICAL COMPOSITION.
First Part. Composition for Single Farts, {Monophonic Composition).
CHAPTER
I.
THE FIRST FORMATIONS. 1.
THE TONE-CHAIN, WITH
ITS SPECIES.
"i
A Musical composition consists
of one or
more
successions of
tones (tone-chains) which progress simultaneously, and which are
intended for one or more instruments
;
one or more voices
for
or for instruments and voices together.
Beginning with the most simple
have already to make a
—the
single tone-chain
Por a
distinction.
—we
tone-chain does not
contain merely sounds, which succeed each other, but that sue cession
is
hy
regulated
sound
is
(Rhythm), which indicate
certain laws
when one sound should succeed the
other,
and how long each
to continue.
But regardless of
all
rhythmical laws,
we
will, for
the present,
analyze the mere tonical contents of a tone-chain.
These tones can succeed each other in various manners.
They
can progress from low to high, from high to low, or these two
be mixed. We distinguish therefore ascending (a), and descending (b), tone-chains, and those, which both ascend and The repetidescend, and which we will designate as vague (c). tion of one and the same tone, too, might inappropriately be directions can
called a tone-chain (n)
other
by
;
and
finally the tones
regular degrees, as in a, b, and
c,
or
can succeed each
by irregular degrees
as in B.
A
^^ -•—#-
B
C
54 It is
effect
easily perceived that ascending tone-chains produce the
of exaltation, elevation, tension, while, on the contrary,
scending ones produce the effect of relaxation, or return
de-
to repose.
Vague tone-chains awalce neither the one nor the other sensation but with a certain indecision remain between the two
distinctly,
knd have a share of
either.
Yet with
all their
deviation in detail
they can, in general, belong to one of the two principal species,
-»^J^
^=='^iir'ir7Z i 3c:
i We have now only to is
more
restless,
add that the motion of " step by step' motion i»
quiet and even, while the skipping irregular
unsteady,
and nervous. But more of that anon.
Tone Eegulation. The vast resources which music has
command make
at its
it
absolutely necessary that, in our attempts to produce or invent
we should observe a certain order and limit, in ordei way amidst the enormous mass of tone-formations. We require foundation upon which we can construct our forma tions, and from which we can derive them. tone-chains,
to find our
s,
We will
select the diatonic scald- as our first foundation.
since even this scale has its different species,
them the
original
But
will select from
and most satisfactory one
The Major
The reasons
we
Scale.
for this choice will in a future chapter
become
ap-
parent of themselves.
The major
scale,
from
i Tonic,
its
Tonic to
its
octave, rests
-gs: =i=«=
moves thence through the remaining degrees {d to b), and upon the Tonic, or its octave. Al] perfectly agreeable to our feelings, and the more so -when
closes, satisfactorily, again
this is
upon the
we compare
it
to other tone-chains
;
for instance,
with
55
i
ir^r
or with imperfect tone-chains (not beginning, or not ending with
the Tonic).
m
-
w
.0.
We recognize The
the scale.
m
-
the Tonic, therefore, as the heginning and end of latter originates
from the Tonic and returns to
it.
—
moment of repose, the scale the moment of motion, Here we have discovered at is formed. last an antithesis which runs through the whole science of musi& Repose and Motion, Tonic and Scale. In juxtar-position to the Tonic
the
—
Analysis of the Scale.
When we that
it
examine the
scale in its
halves, exactly alike in steps
and one
;
i.
we
find
consists of
two
smgle progressions
contains Steps and half-steps, and that
it
each half containing two steps
e.
half-step.
E F
B
G one
one
A
G one
half
B one
C* half
* We suppose that every student of composition is familiar with tin major scales but in case of the student's not being able to represent to himself such a scale at once, we refer him to the above measurement of th« ;
scale for assistance.
We know that on
every tone of our tone-system we can construct a major they all progress like scales have like proportions
and that all major the above c major scale,
1 step,
1 step,
;
-J
step,
1 step,
1 step,
1 st«p,
-J
step.
In order then to construct a major Scale on any particular tone, we have but to write the seven degrees from it to the octave, and justify it afterwards, by means of flats or sharps, according to the above diagi-am. In constructing the scale on a, for instance, we first write the seven degrees
ABGDEFGA A
to b, a whole step, agrees with the diagram ought to be a whole step, and consequently will have to be enlarged by changing c into cj| c^io d is now a half-step, dto e a whole step both in accordance with our model eiof, however, is merely a half-step when consequently /has to be changed into/|, and, it ought to be a whole one for the same reason, g into g^.
and measure each
step.
6 to c
;
;
:
;
In constructing the scale oid\> major, thus:
Dh
we would
E F G A B
first
write the degrees
G Dh
and then regulate the distances from one degree sharps or flats, whichever is wanted.
to the other
by means
of
56
The one of these other leads to
tone-chains originates in
c,
the Tonic; the
the Tonic ; both find in c their centre and juno
c,
tional point.
G
£
A
O _^
B
C Even
we
in this formation of the scale
F
JS
find the
Tonic the
chief
point from which the other tones advance, to which they return,
and around which they move. ^Rhtthmioal Formation of the Tone-Chain.
2.
We have until now considered the tone-chain and scale, and
we have
another should resound.
after
happen
at equal
particularly, in a
ionical contents only of the
tacitly
and unequal intervals of time most infinitely varied manner.
fore begin again with the
;
and the
latter
We will there-
most simple, and imagine a regular
each tone of equal value;
cession,
admitted that one tone
This resounding, however, can
for instance,
suc-
the scale
in
crotchets (quarter-notes)
i? us,
because one tone like
the other passes by, without distinction.
The longer we would more fatiguing and
But
this
form does
not
satisfy
continue this chain of equi-long sounds, the confusing would
it
be to
us.
Our
feeling urges us to distinguish
and to regulate ; we must divide this chain to make Admitting the division by two as the conception.
would begin perhaps in «
and
ry
this r^
it
easier of
easiest,
we
manner A
f\
thus arrive at the simplest
regulation
of time.
Simple
Measure. This regulation, at present, exists only in our imagination, or
on paper ; but to make it reality we distinguish every first note of a measure (marked '^) by a stronger accentuation. This accent
makes every beginning of a measure
perceptible,
and by these
57
means we have introduced
into our scale a variety to -which de-
cided and absolute necessity has led us.
Our and
tone-chain appears
now
well regulated in regard to time,
been made perceptible by the alternate
this regulation has
change of strong and weak intonation rhythmical
A
in short, it has
;
been made
has received the Rhythm.
it
;
Rhythmical Tone-Chain
is called a Melody, and a melody is and simplest creation of art. Already in our first attempt we found it necessary to begin
the
first
and end with the Tonic as the most important pleteness and perfection
was
owing to
tone,
and
its
com-
and But now we have learned also to distiuguish rhythmically important and unimportant tones. If our melodies shall now be round and perfect, rhythmically as well as tonically, in fact
this beginning
ending thus.
we
have rhythmical chief
will find it desirable that they should
notes for the beginning and for the end.
We
experience an unsatisfactory feeling in the above melody,
because, though beginning on a principal part
portant one
;
and the melody
is lost,
as
it
ends on an unim-
were, because the end-
it
note has no weight.
We will therefore re-form
our scale in this manner
n 3.
The beginning has
lost its emphasis,
and the satisfactory end remunerate us
but the succeeding notes for
it.
But perhaps we prefer not being tied to this particular form of beginning it may be possible to have a beginning and ending ;
alike satisfactory.
And
here
is
all
appears to us imperfect in sible,
remember a
the time to
accompany us through
our labors. its
we should always retain
necessary
—
^let it
what
is
wanting."
we know,
Whenever a formation
parts, or not clear and comprehen-
of it whatever
be found wherever
In this instance
to supply
principle which should
"
that
it
it is
may
we have found good
—and
or
afterwards try
our object to place the be-
ginning and ending of our melody on an accented part of the also know, that the eight notes of our scale have measure.
We
58 to appear in four measures
part
it
—
at least
we know
at present
of no
Finally, if the last tone has to fall on an accented
other form.
either in the shape of a half-note, or a quarter-
must be
by a quarter-rest. down would give us a
note, succeeded
This noted
figure
something like the
fol-
lowing:
m
The
and we see at once clearly what has to be done.
three
wanting notes have to enter the vacant measure. The first of these can do so in the form of a quarter note; the other two have to
become eighth notes.
s
iw We have now arrived all
our demands. 1.
at a formation
which ccarresponds with
It is
In regard to tone-succession, beginning
and ending on
the Tonic. 2. It is
3. In
rhythmically well regulated,
regard to accentuation of beginning and end-note,
it is
and well closed off, and thus satisfactory. same time we have obtained But at the three species of notes half-notes, 4. A variety of rhythm and this variety proves quarter-notes, and eighth-notes distinct
—
itself at the 5.
same
;
—
titne-,
A means of promoting
our object:
for,
the end-note, the
aim of the whole, has the longest duration; and the eighth-notes,
immediately before
it,
serve to accelerate
movement towards it, and to make the end-note more characteristic. We have now a gradation of rhythm the
as well as of melody.
Thus
far
ascending.
we have inadvertently represented all our tone-chains as Nothing prevents us now from attempting a descending
one: 6.
P
s -&-
59 It
exhibits a steady and satisfactory return to repose
—the begin-
ning of all our tone movements.
But both formations have a very one-sided elevation
is all
;
the other
is
character.
exclusively relaxation.
The one Only the
combination of the two in a larger whole can in every respect satisfy us.
m
mm
^ m
We have now arrived at a tone
formation which, issuing from
rhythm to the Tonic of a higher octave, marks this point by a rhythmical pause, and then returns in We perthe same steady manner to the repose of the first tone. ceive also that this formation is composed of two halves (a and b) which, each by itself perfect, combine to make the perfect whole, a whole consisting of two subordinate wholes. But though each the Tonic, rises in pitch and
of these parts or phrases resembles the other in rhythmical formation and tone-contents, the direction in the tone succession of
each is exactly opposite ; the one forming the reversed counterpart of the other.
Such formation, consisting of two perfect phrases,
thesis
and
antithesis, is called a Period.
Formations which lack the satisfactory ending of a period or
8.
m
phrase are called passages. Retrospection.
We
have now conceived the first ideas of composition, and them in tones. They were
realized 1.
The
tone-chain,
with
its different
sions.
The
first
foundation of
all
directions
and progres-
—the
tone succession
diatonic
scale.
between repose and motion in the scale. and simplest rhythmical order, by the aid of which a mere tone-chain became a melody.
The The
distinction first
60 5.
The
fixed
division, 6.
and manifold valuation of sounds, mensural
and accent.
The melody strove
to acquire a rhythmical
marked point
of beginning and ending and became a phrase. 7.
This brought ns to a variety of rhythmical motion.
8.
The invented phrase (thesis) demanded a counterpart (antithesis), and the two together formed a Period.
9.
A
formation of a
new
—the
nature
passage
—
^was indi-
cated.
And
thus
we have
arrived at the three fundamental formations
of all musical constructions
Phrase
—Period—^Passage—
and have recognized the characteristics of their construction.
61
CHAPTER
II.
INTENTION OF MONOPHONIO PHRASES. THE DESIGN AND
1.
In order to arrive at
our
first
new
progressions
satisfactory phrase (No. 5).
different parts ; in the first
ITS EFFICACr.
we wiU
We
measures a
see
it
return
now
to
constructed of
series of quarter-notes
;
in
the latter quarter and eighth-notes, which lead to the final note.
Thus we can
distinguish various tone-groups
;
for instance,
a tone-
chain of quarter-notes.
'i w A group ending more satisfactorily is in the latter measures.
^
10. ».
If still
we
are willing to resign a satisfactory ending,
we
can select
more groups.
g
"•^w
Such forms which contain the germ and the impulse of longer Each junction of two or more notes
phrases are called designs.
can serve as a design. signs,
how
and
it is for
to apply them,
continually at
new
of these designs scale has given
Every composition
us to consider
how we
consists of such de-
are to nurse these germs,
and how to multiply them, in order to arrive
phrases, passages, and periods. is
us
already sufficiently prepared. six,
The invention The simple
and every new formation adds to that
number.
Every design can be applied by
itself
fi2
By
1.
repetition on the
By
repetition in a higher or lower range,
p^
i By
3.
repetition in opposite direction.
i By
4.
degrees,
^^^a
12.
2.
same
5
repetition in notes of longer or shorter duration (aug
mentation and diminution). Augmented.
Original design.
13.
DiminiBhcd.
^j-jS
5.
By
changing of i^esis (weak, unaccented part of a measure)
into arsis (accented part of a measure), or vice versa.
P^3
f By expanding
or contracting the design ; a smaller for a larger interval, or vice versa. '%6.
".^^^^^ 7.
By combining one
design with another, or
We need not mention
signs,
can already see is.
We
and leave
it
-&-
more to a phrase
that these different manners of applica^
tion can change with each other, or
formation
by changing
1^
iw We
i. e.,
how
combine to a greater whole.
inexhaustible the field of musical
need therefore only show a few of these deto the industry of the student to invent others.
^
63 But to
return again to our actual
task,
we
will begin
time with the most subordinate of our formations
We say most subordinUte, because
this
the passages.
they do not even end within
themselves.
2,
Each
FOKMATION OF PASSAGES.
repetition of a design produces a
repetition of the third design, in
No.
passage.
Thus the
11, gives us the following
•#-l
ffi The same design reversed would give us the following
$
16.
Were it we
our object to
could do so
measure
e
i make No. 15
still
g more
light
and
flighty,
by beginning with the unaccented part of the
(thesis).
i^g^s^
17.
beginning,
we
No. 15 and 18 would form an and consequently a new passage.
en-
Availing ourselves again of the
new ending and
would be led to the following
18.
1^
a3
i
A combination of designs tirely
new
design,
m
u
19.
The
further practice of these forms and designs remains
for the student. facility
The advantage of
now
this exercise consists in the
of winning from every formation a
and in the student's proper progression
—
new
^not
aspect or feature
confusedly, according
64
—
to his humor, design, and inclination
necessary, and not seizing the 3.
Here, too,
^but retaining
new without
the good and
absolute necessity.
^FOKMATION OF PHRASES.
\
we begin with
the third design in No. 11, because of most conspicuous. In No. 5 it appeared the third measure. But it might appear as well in any
the smaller ones
only in
it is
the
other measure.
W^
20.
^
We might now attempt to repeat the most animated part 21.
B
This would leave us only one tone to
and while the beginning of
this
fill
the third measure,
phrase would appear very ani-
mated, the latter part would be the more dragging.
new formation in which the would be more equally distributed.
us, then, to
notes
a
22.
This leads
different species
of
s
E
This phrase gives us something
new
to consider.
The
rhyth-
two different parts which are alike different from the phrases and from the halves of a period thesis and antithesis. But while their rhythmical formation is mical formation has divided
it
into
satisfactory, their tonical formation is not;
not begin or do not end in the tonic. ations Sections,
for either
We will
call
they do
these form-
and thus we have to distinguish in a period which
No. 22 would give us
a
23.
JJ
-m-
b
and
^
•
not only the thesis and antithesis a and c,
c
d, also.
b,
but the sections
a, 6,
65 Let us
now
24.
a
return to No. 21, and repeat the principal design:
^
S
^^
rhe same reversed would give us
^^
25 ^-
In the one
we have
^
-s>-
ascended above the Tonic, in the other
have descended below
it,
and
in thus starting
we
from and returning
to the Tonic, deviations from the general direction have appeared.
This can take place at any other point as well,
A
^P^g^
26.
and since we have
here, at a,
gone back one note, we might as
well go back two or three.
27.
But
i D
here, in
5
-#-
No. 27, we have already
out arriving at the Tonic. phrases this
;
we
take four
We
filled four
measures with-
find it necessary to enlarge our
more measures and
continue, perhaps in
manner:
^S^^^^g^^ 28.
We need not defend the slight variation in A
strict
the sixth measure.
adherence to the design would have led us beyond the
proposed number of measures.
The dragging of the above might
be corrected by the substitution of a short note
—p 29.
-^
1-
for a long one,
and
this
would lead us
end the above phrase perhaps like
to
this
^i^^ss^^ 30.
We have now arrived different parts
at a greater liberty
of
foi-mation.
The
need no longer be of the same length, but require
merely being balanced ; two sections of two measures each are succeeded by a third one which has four measures and deviates in
form by being more animated.
its
we have now abandoned the division by 2, we might tempt slow phrases of three equal sections or divisions. Since
31.
^
t 3±
:zz
We have introdu6ed this merely in order common law
able the
at-
is
:
to
show how unten-
that each phrase or period ought to
two or more measures. We shall give more instances for with the same right with which we have introduced the figure 3 here, we shall introduce other deviations from the consist of
in future
;
primitive proportions.
4.
PERIODS.
We have formed our first period
of thesis and antithesis, and
both parts were perfectly corresponding with each other, only that the tone-chains were conducted into opposite directions. This is but No. 30 teaches us to give to the antimore animated, different formation. Thus we might form No. 23 into a period by enlarging it thus
the simplest formation
;
thesis a
^
:
32.
It will
—the
3
be advisable to observe at first, in these important parts and antithesis equality in the number of measures,
thesis
—
and to accustom the mind to order and symmetry, before attempting other,
more
free formations.
67
CHAPTER DISCOVERY OF
We have now
discovered
all
III.
NEW
MEANS.
the fundamental forms of musical
The forms were
construction, together with their characteristics.
the Design,
the Section, the Phrase, the Passage, the Period—^with thesis and antithesis.
We will now again return to analyze
and
its
contents.
the third design of No. 11, and
It consists
—one
of three notes
twx) eighth notes, or together, a 2-4
quarter note
measure.
But the three notes might also have equal value, and in that we would be led to a new design which would give us the
case
following phrase,
33.
and with
The
£
Ep=lEj it
" the Triple
difference
Time."
between
former ones every
first
this
and former designs
same proportions can be represented means we obtain a new formation.
34.
is,
that in the
note was longer than the following.
^m^-
s
in Triple time,
and by
The this
:?2=
^-
first note was as long as the two fallowHere it is of twice the length. To give it thrice the length would lead us from Triple time to Common time, or
In our
first
design the
ing together.
from 4. to X-
35.
fe^a^^^
e,8
We might have
obtained the same result in
doubled the length of the
time, if
we had
note or contracted two measures
firs^
In the latter case
into one.
^
we
should have obtained period? of
ABA BAB
twice two measures, 36.
A
B
E closing with
what was once a chief
part,
but otherwise regularly
built.
But, pear, 1.
it
the difference between No.
little as
reveals to us
We perceivfe
what
in fiiture wjll
that No.
36 and
Na
7 may
36 not merely originated
but has also the same tonical content and the
No.
in
accented notes in No. 7, and have remained so in No. 36.
marked
a
b,
have at least been chief notes, and have here
than those marked
4-4
notes. A
it
2.
but more than
a,
all
We can, therefore, unhesitatingly change
one,
and a
a
one into a
of a small phrase should 36,
7,
same rhythm of
The notes here marked with a have beea chief notes or
notes.
cent
ap-
be very important.
will
We
still
be
Even
one.
upon a former
fall
sufficiently
2a
a if
Those less ac-
the remaining a
phrase into
the end note
chief part, as in
No.
marked.
perceive in the prolongation of the No. 33
—
strengthening of the accent in one and the same design,
35, a
by en
largement of the time species,
37.
Sk
in
i^ 3^^^
means of expression which vocal composition.
ted notes
many more 38.
will
It is clear
become that
particularly important
by means of ties and
dot-
gradations can be obtained.
^m m -&
When we now perceive that the
return to No. 34, and analyze the design,
first
note contains, or
is
equal
to,
two
consequently could be reduced into two quarter-notes
;
we
quarters,
69
i^i
3;
39.
il
we might
or
SiiEt
^ir^-^
continue the division
quarter-note into
two
m^
further,
still
and reduce
eacih
eightb-notes.
«-pg^#j.^^;E^
=p=f=
Here we
arrive at a class of
new
designs which consist of the
repetition of one note,
41.
Such designs
rhythmical nature, and serve to
are, of course, of
animate a phrase when
we
are limited to few tones.
But we return to No. 40.
we
If
frequent repetition of one and the
change
m
42.
it
for a neighboring
:J_/-#
P
one
are not pleased with the
same
tone,
we
can easily ex-
either the higher one,
;
Qm
-a^*-al-
zpi
or the lower one,
^^m^^^^H
43.'
Why have we
taken a\ intead of a ?
Because
1^
~^-
in all the
former
measures the interval from the third to the fourth note was only a half-step, and because this smaller interval of a half-step leads
more flowingly upward.
first time, have we introduced a foreign tone, and we have perceived at the same time that with the aid of such a one we can ascend more flowingly than with the whole step. We can now introduce the neighboring tone much sooner, and
Here, for the
introduce the assistant-note 44.
i
^S
m^ m.
We have to jepeat is
no room
still
later
:
± ¥--
the b in the third measure, because there
for an intermediate tone between b and
Perhaps the continual motion
in quarter-notes
c.
might appear
70
We can avoid
monotonous and trifling to us.
it
by
leaving out the
second assistant note
'^m^'^^^m^^
45.
If
we were
spicuous,
we might change
^^
46.
make
inclined to
=K-
it
this interruption still
con-
2: time.
into
^^^^m
two last phrases we arrive The tone-chain is divided by
In the tion.
more
at a
new
conspicuous forma
rests into small tone-groups.
They are not as important as the sections, but nevertheless of some consequence. We will call them Links. Such links might have been obtained much sooner by the prolonging of notes.
And
thus a period
might be divided, into
two
f, g, h,
and
Small
1,
into thesis
sections (a, b).
3,
and antithesis
(a, b.) 2,
the thesis
each section into two links,
(c, d, e,
i.)
as the results of Part
the works of our great masters,
I.
may
it
will
appear in comparison with
be
still
advisable for the
71 student not to disdain or neglect these
The
attempts.
first
ad-
vantages to be derived from them are many. First of logical
all,
mode
the student
-will
acquire that systematic and ana^
of proceeding which
is
so absolutely necessary to the
mastering of any subject.
He
will learn to limit himself,
and to derive from any given
most manifold developments and
subject the
how important
refer to the first Allegro of Beethoven's
To show we need but
results.
such faculties are to the composer,
Symphony
in
C
minor,
—
which grows almost entirely from a design of four notes, four notes which do not even distinctly indicate any particular key.
^^^^^ and yet these few notes have given will claim the
rise to
a composition which
admiration of centuries to come.
But these simple formations serve
also to facilitate the indis-
pensable acquirement of composing without the aid of any instru-
ment.
It
himself,
by
here where the student can learn to represent to
is
force of imagination only, tone-formations of
less completeness.
At
We warn the pupil, one
is
a later point,
it is
more
or
impossible.
however, to guard against two
The
faults.
the deserting of the analogous proceeding, so strenuously
recommended, and the other, the losing sight of his object. had produced No. 46 immediately after No. 31 or No. should probably have obtained a good phraSe ness of the
how and
wherefore,
;
If 5,
but the conscious-
and the inexhaustible source of
analogous and legitimate formations would have been lost to
The second
we we
us.
fault exhibits itself generally in the fact, that the
pupil, in consequence of impatience, or
having exhausted the
scale,
under the impression of
proceeds to harmonic formations
instance
;
for
A-ix.
i^^^^^
We finally
advise the pupil not to confine his exercises to the
key of c major, but
to attempt
them
in every
major key
;
and
if
he has once seized a design; never to rest until he has formed a Period or Phrase.
72
Second Part. Composition for
Two
Parts, (Duophonic Composition).
CHAPTEE
I.
THE DUOPHONIC COMPOSITION, DEKITED FEOM THE MONOPHONIC.
The more we extend our monophonic baseless
must they appear
;
tone-chains, the
more
not alone because, however interest-
mere tone-thread without volume,
ing their contents, they are a
but because the Tonic, as the
first
and
last note, offers too little
weight against the more richly developed
scale.
Let us attempt, therefore, the duophonic composition. It lies
nearest to add a similar tone-chain in a higher or lowei
No. 5 treated in
octave.
this
manner would give us the follow
ing:
^P^
49.
is duophonic, it employs The consequence of this is a
not to be denied that this phrase
It is
two voices
in different tone-regions.
broader tone-volume
larger,
—particularly appropriate
for
massive
effects.
But two such voices are mentally equal to one only ; for, thougL both have the same rhythm and
in different tone-regions, they
tone-succession.
Yet
this
phrases.
proceeding can form the basis of
We
many monophonic
can transfer the tone-chain of two voices to a single
one.
Thus No. 49 would give us the following phrase
50.
m
We
^m
:
divided the last half-note into eighths and quarter-notes,
73 because the transition from the sixteenth notes to quarter notes
would have heen too abrupt and
When we now melody (as
:
first
violent.
proceeding to this
new
basis for
combine the former designs with the octave-designs
i. e.,
we might
apply our
call the
present ones),
exhaustible source of formations.
we open
further details or gradual development
models, and leave
it
again a
new and
Without entering
we
will
in-
any give a few as into
to the student to practice others.
Three or four tone-chains in
different regions
might be treated
same manner, and give rise to many new such phrases would partake of such vagueness of
in the
designs.
But
character that
they could only be used in extraordinary cases, and do not require
any
special practising.
Finally,
we might
attempt to gain a species of pseudo-dTiophomc
composition by means of embellishing or circumscribing the one, or the other.
^ J
52
P^^^^fc ^
Such apparent polyphony will be particularly useful in orchescomposition and in the accompaniment of vocal music, but
tral
will not benefit us
much
at present.
74
CHAPTER
II.
THE DUOPHONIC COMPOSITION, DERIVED FROM NATURAL HARMONY.
1.
HowEVKE much signs,
MANNER OF ARRIVINO AT or
little
we
IT.
develope from these octave de-
our actual object, a real Duophony, in which each voice has
a different fundamental melody, cannot be obtained from them.
We require for this different voices,
another basis showing-us what sounds of two
according to the nature of the tone-world, ac-
tually belong together.
Let our ear be the other
;•
first
judge of a tone which agrees with an-
say, for instance, with the tonic
c.
It is
certainly not d.
But the following, e, answers our purpose. To these, again, we can only add g, and after that none will answer but the octave c.
WWhat we by the
have here accidentally discovered
science of acoustics.
The
is
fully confirmed
latter tells us that the following
sounds belong together
54.
The Tonic is the basis, fandamental tone, of the whole mass. The ear acknowledges in this combination the most perfect conWe will call such tone-mass " Harmony," or " Harmonic cord. mass," and its lowest tone we wUl call the fundamental tone. The above combination is therefore our first harmonic mass. Following the sounds which acoustics designate as the next succeeding,
we meet with
a sound not exactly belonging to oui
75 scale
;
we
shall
speak of
a part of the scale
makes
er,
its
—and immediately
aftei- it,
appearance.
P
55.
Of these,
in future
it
and g belong to the first mass do not agree with its fundamental tone. c, e,
exiled as they are from the
first
mass, unite very well with one
g —and form with
tone at least of it
d and f, howevThe two latter,
;
it
a second harmonic mass.
J^ 56.
E
^ I
Our
ear tells us that these belong together, and in the course
of our investigations
When we now
it
will
111 57.
BE
in another
1111 ^ t3H
1
i w^
3= -&-
1.
be proved
way.
consider our present tone-group
That only the
"we find
:
1
A
m
2
2
five last tones are in the regular succession
of the scale ; a and b and the higher
c,
are wanting
;
for
the six preceding notes have neither the form nor connection of the scale. 2.
That nine notes (those marked 1) belong to the first harmonic mass, but passing all repetitions, the latter consists only of the notes
c, e,
already chosen for us. ularly
—*aoh
and g ; the same which our ear has These notes are placed very reg-
one a third from the others.
The Tonic
is
the fundamental note. 3.
Five other notes (marked 2) form the second harmonic mass, which is not alone inferior in number of sounds con-
formed less regularly. The funmass is the thrice-repeated g ; n tone which we have discovered in our first mass. Addbut
is
also
damental note of
this
stituting
it,
ing to this fundamental tone the highest tone, /,
we
discov-
er the boundary -tones (p. 56) of the scale which
around the Tonic, and of which they are related to
it.
we know
move
already that
76
•
We have long designated the fundamental tone of the first mass by the word Tonic. We will now distinguish the fundamental tone of the second mass by the word Dominant. The why of calling this tone the Dominant will be shown at some For the present it deserves that name, if for nothing future time. the fact that
else, at least for
and
is
the basis of the second mass,
it is
two masses.
the junctional point of the
This tone, the " Dominant,"
is
in other words, the Tifth of the
the
fifth
note of every
scale, or
Tonic
Formerly we placed Tonic and Scale
m juxtaposition, because the former was the origin
of the
latter,
and was the beginning and end of the scale. Here we find the Tonic again in the same capacity ; but this time it is supported not only by octaves, but by the whole first mass, which latter we shall therefore call " tonical mass," or " tonical harmony."
mass we find, now, the second mass, And this first, whence it originated. The fundamental note of is done in the most simple manner. the second mass goes to that of the first (the tonic) ; if an ocOpposed to
which
this tonical
latter returns to the
tave of the dominant
is
existing
it
remains as the
fifth
of the to
mass /proceeds into the nearest tone of the first mass, e, and d can do nothing better than to follow this direction, and, nical
;
consequently, goes to
58.
c.
-^-^i=t^
mT
r
rt r
first becomes most prominent when the tone /is in existence. It is less prominent when the two others only, g, d, are used. For these two form a fifth exactly like one in the first mass (c g), and
This inclination of the second mass towards the
the
can partake, as
it
were, of the nature of the
a momentary point of repose. quite distant from the
first
The same/
as
first
mass, and form
we have
seen, is also
harmonic combination which nature
has given us (No. 57), and in which the interval of the seventh
(^
—/)
is
not contained.
n We can apply
\
APPLICATION.
2.
our present tone-group.
new
1.
Melodically, for
2.
Harmonically in the two masses, and upon the two together
we can base
tone-ohains.*
the composition of duophonic phrases.
Melodic Application. It is
not merely the
imperfect scale,
still
serve as a basis for our melody, but
of
all
c,
e,f, g,
rf,
which can
can also use the succession
tones belonging to one and the same mass.
^
m
59
we
^=
rplain that the
It is
struction and its
first
number of
mass, on account of tones, is
much more
its
regular con-
productive and
appropriate for a melodic foundation, than the second mass. in reality the
melody of
either
mass
But
consists of only three tones,
with their repetitions. In No. 59 these masses have been used in their regular order, i.
e.,
them
either ascending or descending. in vague directions
;
This leads us to attempt
for instance, the first
mass
:
60.
^^
Ml
But the limitedness of our tone-group
is
always in our way, and
we find that repetition of tone or design and the development of Rhythm will be necessary to produce variety of invention froir such insufficient means.
Harmonic Application. Having achieved thus much,
for the
proper estimation of our
means, nothing remains but to apply them in the formation of
duophonic phrases.
In this
we must
consider the upper voice as
the principal, and the lower as subordinate voice, or accompani* Our covered
foundation for melody was the MajorScale ; here we have dissecond foundation, the harmony, or the harmonic masses.
first
tine
78
ment ;
for,
tone-chain i.
by a
have a choice of several notes,
accompaniment
;
will
is
first,
mass we
since in either
always choose the nearest
^
M:
make
excep-
the fundamental form of
f?*
61.
In the
we
But
Below
Duophony.
ei
accompany each tone of our
reserving, however, the right to
whenever necessary.
tions
better connected (No. 57.).
second, lower tone, which agrees with the
belongs to the same mass.
e.,
for
much
therefore our present object to
It is
more
the higher sounds are, agreeably to their nature,
prominent, and are melodically
r first
eight
i-j-
~i^
accompaniments we see the alternate change
of first and second mass, and after this they belong exclusively to the
first
mass
—though the y
at the
end might belong also to the
second mass.
Why of
at
A have we not taken
Firstly, because
e ? it
voice
g had but
y, the nearest tone, instead
just
would have caused an unnecessary stoppage ;
secondly, because
e
of
been used, and the repetition in the second
in connection with c designate the first
mass much more distinctly than the g, which belongs to both masses. The repetition does take place in the very next moment, but then it happens at places where the first mass, under any circumstances, remains stationary, and where it can be done without injuring that change of masses which we had in view. Why have we commenced our accompaniment only with the eighth tone
?
Because then only
and because we have made
it
we
could safely decide upon
it,
our principle, always in doubtful
which is undoubted, and from this certainty was easy afterwards, (from a to the end) to regulate whatever was uncertain.
cases, to retain that it
3.
We recognize now
HARMONIC DESIGNS.
more
distinctly
what we can
ofTert
w
i'h (uir
79 present material.
now we have
Until
of designs and formations,
We can add
now
a third class,
known two
only
and rhythmical
viz., tonical
classesi
designs.
harmonic designs, which we
viz.,
can produce
mass
(a)
from the
(b)
from the second mass exclusively.
(c)
from the alternate
first
exclusively.
from the mixture of the two.
use, or
62.
-rrr 4.
THE CADENCE.
We have discovered already place of the Tonic, or the
principal tone of this mass,
We
voice.
shall
effect
that the
Moment and
mass has taken the The Tonic is the
first
of Repose.
is
most
effective in the
mass, and most appropriately in the position of
--^
r unless
we
We have, the
first
;
taposition
r-
resign the
Tonic, as at
T
harmony and
lead
both voices into the
b.
further, placed the second
exactly as ;
first
a.
^
^
63.
upper
our cadences, therefore, with the
we
mass
in juxtaposition to
formerly placed Tonic and Scale in jux-
and as formerly the
scale
moved
into the Tonic to
an ending (cadence), thus will the second mass move now The into the first (c), in order to accomplish the same object. third tone only is thereby inadmissible, because (d) it would preeffect
vent the resolving of the upper voice into the Tonic, in order to
end there. 5.
THE HALF CADENCE.
Simultaneously with the former
we
have, however, discovered
mass without its third tone We serve as a temporary point of repose.
that the second
longer limited to the single point of repose
is
appropriate to
are,
—the
therefore,
Tonic
—but
no we
80 have a second one, however imperfect,
This latter
we
will ap-
ply in the ending of the thesis,
64.
and
^ ir
call it
designated
g first will be appropriately Full Cadence, or simply " Cadence."
a Half-cadence, while the
by Whole
cadence,
81
CHAPTER
III.
THE DUOPHONIC COMPOSmOlf. Now, ject to
to us
at
last,-
we
can resume our actual work.
form tone-chains of the most perfect form
—
in the
First of
known
form of a Period.
all, let
us regulate our two masses into a Period.
d —-
^
-&
E
65.
our ob-
It is
at present
-=F
-f-
The beginning with the first mass lies probably nearest. The thesis (a) makes its cadence from the firsj into the second mass. The antithesis (b) makes its cadence from the second mass into the first. The vacant space can be filled out according to the general laws of Tone-succession, Progression, Harmony, and Phraseology which we have learned. And here begins again the practice, and with
it
the industry of
the student.
We might 66.
fill
the thesis with the notes with which
it
began,
m if=x^y-x^x=^-
r
f-r
but that would be insupportable monotony.
Therefore
we
will
retain for the present the first mass, but not the -same notes
perhaps in this manner
67.
S
E^
r-i This attempt acter of the
We
is
^
r-r
an improveriient upon, the
melody is vague, and the rhythm
intend to animate the
1
itter,
first
is
;
but the char-
very monotonous.
and the melody ought to have
82 a
more decided
direction, as
we have been
formations of Phrases and Periods.
taught in our
again the melodic gradations of thesis and antithesis,
probably form the following 68.
^
:
--;
first
In order, then, to produce
^
we
should
83 No.
68,
how
and
is
repeated
in.
the second measure.
the design of the third measure
(at least rhythmically).
is
We perceive, also
repeated in the
Were we in possession
of the tone
fifth, b,
the
melody of the seventh measure would probably be, d, c, b. The further development and practice is left to the student, but he will perceive more and more distinctly, that with our present poverty of tones, a careful employment of rhythm and a clear distribution of it, will lead him to an animated and effective arrangement of the whole. Thus No. 68 led to the last phrase, which, again, might lead to the following
:
Andante.
71.
^^Sfy^i^^gfef
We
perceive here, that the thesis
which the
first
falls into
two
sections,
(a) belongs entirely to the first mass,
of
merely
touches the second mass, and thus melodically and rhythmically forms an imperfect cadence, because the end note does not fall
upon a rhythmical chief-part. The same cadence appears end of the phrase ; but this time it is perfect.
at the
84
CHAPTEE COMPOSITIONS OF
When we now
consider
IV.
TWO AM) THREE
how
distinctly, in
PAETS.*
our previous forma-
by means of mass on a rhythmical chief-part, and how much more satisfactory a whole it forms, it leads us to form from tions, the
separated from the antithesis,
thesis
entering the second
Thesis and Antithesis,
a
Jf'irst
and Second part,
which parts for the present, are distinguished from, a single Period, merely by the even more distant separation, and by the fact that each strives to be considered as a different whole.
This leads us, then, to the simplest
TWO-PART FORM. of composition, as
we
find
it
in
many Marches,
We have formerly already found of measures (No. 30).
Songs, Dances, &c.
phrases of a greater
Let us employ them
number
for the two-part
form.
Each part
strives to
be an independent whole
have, therefore, at least the length of a Period
;
each ought to
— eight
measures.
These are the regular dimensions, but we know already that they can be larger or smaller. If the first part
is
intended to be an independent whole,
ought to have the most perfect form with thesis and antithesis.
But
it
—the form of the Period,
nevertheless, the part
is
merely
part of a larger whole, and, therefore, cannot have a perfect cadence, but
must
let
us expect the second part.
It
ends, therefore,
We draw the attention of the student to a diatinction which we have here, and the lack of which, in other theoretical works, has been the source of ranch confusion. We refer to the use of the word " part." If using it in relation to number of voices, we speak of compositions /or one, two, or more parts. If using it in relation to Rhythm, or form in general, we speak of compositions of one, two, or more parts. As we advance further we shall employ the words monophonio, duophonic, triphonic, tetraphonie, pentaphonie, &o., &a., to designate compositions for one, two, three, four, five, &c., (fee, parts, and endeavor to ccnfine the word "part" exclusively to Ehythm and form. *
made
_
85
Were we now
as formerly the thesis, with a half-oadence.
to
end the thesis of the first part in the same manner, the same ending would appear twice in succession consequently, the half;
cadence of the Part would lose
the whole part would be monotonous.
only be marked This
is
a
full
by
and the formation of
its strength,
The
thesis can therefore
a step from the second into the
cadence, but in order to
make
it less
advisable to represent this cadence imperfectly^ position to a former chief-tone (a) or
the lower voice (b) or
mass
72.
(c)
by an
—
mass.
first
important, either
by
by placing the Tonic
insignificant touching of the
into
second
which leads to the actual cadence.
^^m^^^
If the first part has
now become
a perfectly-closed phrase, the
second part has the same right, only that the latter makes a
and perfect cadence from the second mass into the
first.
tend to give to this second part also a perfect thesis, so
it is
trans-
by means of a
half-oadence,
If
we
full
we
in-
can do
which can now be succeeded by
the full cadence, without deducting from the strength of either.
But
this perfect thesis is
first
part has already had so distinct an organization.
not absolutely necessary, because the
of a two-part piece wonld therefore be like this 73.
-9-^
:
The plan
become? then our objeot to multiply our tonical meaus, aS it by means of rhythmical tone-repetitions, tone-figuration, &c., &c. The following It
were,
mj3
fl:
m
^_p=^fl
iW
?^ phrase
may
serve as example of a
measures, which has chiefly
It is easily
part of three times four
use of tone-repetition.
Ehythm makes
the variety of the bearable.
first
made
seen that the
Only
such extension possible and first
eight measures contain
melody, from g up to c, e, only a decided and distinct grouping which can make
in reality nothing but the steps of the
and g. It is so numerous a tone-repetition comprehensible. whole phrase
and
B,
c and d, and e,
Judging
this
We
see that the
sections of three times four measures,
falls into
f,
and
g.
a
i
phrase according to the acknowledged fundamental
form of a periodically-constructed
first part,
we would have
consider the ending of d as the end of the thesis, and e,
f,
to
and a
would have double the But its two halves with their subdivisions are so well separated, and so regular, that exactly in consequence of this, no misproportion is experienced in the unequal as antithesis.
In that case the thesis
length of the antithesis.
manner we might prolong the of equal sections, or, by giving it an Appendix (Coda), «. e., repeating the last section. The following little phrase in which, by the bye, we have not observed length of the two parts. antithesis,
by
either
In like
composing
it
— —may sowp
the original melodical direction of the thesis, and have
of a gentle relaxation
as example.
made
use
87
m m pii^S^S^
75.
^m^^^^mw-. The
thesis closes at
a
The whole
in the fourth measure.
to close in the eighth measure at b.
Instead of
this,
proceed immediately, without giving the end-note
ought/
the voices
proper
its
rest,
and with the ninth measure begins a repetition of the whole an-
The
tithesis.
final link,
merely, might have been repeated
S
76.
a figured re-formation of the repetitions would also have been admissible,
—
finally,
the junctiou of the two or
more
repetitions
might also be possible.
To
favor such
Codas,
cadence imperfect,
—
it
either
advisable to
is
by means of
ation or abridgment of rhythmical quantity
made
use of in the above.
make
the preceding
tone-position, or
by
vari-
the latter has been
;
The oomprehensibility and
simplicity
of the whole has permitted us to deviate from the strict propor-
We have also introduced a kind of " leader" to the Coda. Such Coda, however, premising the good proportions of all
tions.
parts, is not alone admissible at the
ond
part,
but
it
end of the
antithesis, or sec-
can also be employed at the end of a
thesis.
This requires neither example nor instruction.
Retrospection.
At
the very beginning of monophonic composition
resented the fundamental form of
all
we have rep-
tone-formations
Beginning,
Progress,
End,
Eepose,
Motion,
Eepose,
Tonic,
Scale,
Tonic.
by
:
88
Our monophonic phrases corresponded perfectly The form of the Period oheyed the same laws.
'vrith
we now examine our former (monophonic) but a feeble
was
tie
we
see that
For generally, each
connected thesis and antithesis.
because thesis and antithesis led from the
sufficient in itself,
Tonic through the
scale,
back to the Tonic
;
and only the ascend-
marked the one or the
ing or descending direction
With
Periods,
these
But when
ideas.
other.
the aid of the two harmonic masses and the two different
cadences
we have
The fiindamental
perfected the periodic form.
forms Eepose,
Motion,
Repose,
Tonic,
Scale,
Tonic,
might thus be represented
in the
harmonic Period
:
Motion,
Repose,
Reposei
t.
r
\
Motion,
Repose, Tonic,
Topic 8va.
Motion,
Half-cadence,
Tonic Mass,
Motion,
Repose,
Tonic Scale,
Repose, Tonic.
Scale,
Motion, Full Cadence.
Motion,
Repose,
Repose.
This more perfect periodical construction led us to the twopart form, which again corresponds with the
same conceptions and
fundamental features
Tonic Mass, Motion, Half Cadence, Motion, Full Cadence. If
we
represent
its
external construction of
two parts of twice
eight measures, with periodical formation of each part into thesis
and antithesis
:
Second Part.
First Part.
8 measures.
8 measures. Antithesis.
Thesis,
4 measures.
4 measures.
we
find, that the first thesis
Thegis,
Antithesis.
4 measures.
4 measures.
belongs chiefly to the tonic mass,
and ends regularly in the same mass. It is the beginning of the whole tone-development therefore the place where the design ;
of the Period, or
its designs,
have called Repose. of the
first
The
part, together
form the Motion.
are settled
;
first antithesis,
the
moment which we
with the half-cadence
with the thesis of the second part,
In the antithesis of the second
pai-t,
the
first
89
mass ought now again to be predominant dence of this part
is
We have permitted
this rule strictly.
as it "Were, the thesis this
the end should
codas,
;
but since the
of itself decisive enough,
ca
follow
ourselves even to solder,
and antithesis of the second
still
foil
w& need not part.
If after
be unsatisfactory, we can prolong
it
by
and thus strengthen the tonic mass. Compositions of Three Parts,
The shows
last
view we have taken of the two parts in one mass,
us, that in spite
of the separation of the
first
part
by means
of a cadence, there are in reality three principal moments in existence.
We
might therefore easily divide the two parts into
three
Motion,
Repose, First Part.
Eepose.
90
CHAPTEK
V.
THE DOUBLE DTJOPHONIC COMPOSmOir.
We
due
cannot, with our natural notes as means, extend the
phonic composition any further, without falling into undue repe tition
we have
different cadences,
only two masses, and only two essentially
which latter had to he repeated once already in
a composition of merely two parts
We experienced this stni
We can conclude this from
and losing sight of perspicuity.
the fact that
;
when with
codas,
still
oflener.
imperfection in the three part form, and in
more extended forms there woidd
certainly
be too much
repetition.
But the question increase of onr
is
means
;
whether we could not obtain an intrinsic
As soon
?
as
we add new
notes, our pres-'
Such acquisition
ent system will no longer be suflBcient.
re-
For the present we have
mains, therefore, for a later chapter.
nothing but the increase
of the mimber cf voices.
Since the two voices which
we have
used until
now
agree so
well with each other, the double duophonic composition seems to
be much more convenient than the trlphonic.
double our voices without confusioii,
we will
But
in order to
give to each of them
Here, then, are our present means
a different tone-region.
•
^^^
i 77.
e What
r
^m
do we gain by
volume of
.d.
J.
it 1
all,
a larger and broader
move
in paraUel directions.
First of
tone, if our voice-couples
f^
This certainly makes our whole tone-mass less susceptible of light
motion, and besides
this,
we h^ve
gained nothing absolntely
new
91 for the
two couples move
this leads us to 1,
in equal intervals
and direction
;
but
attempt
opposite directions,
2, different intervals
of the volce-oouples.
"Wherever the masses change regularly, our voice-couples can unhesitatingly
78.
move in
opposite directions.
^8
m
u tmm frf ^?
We will call this kind of motion.
Contrary/ Motion.^'
This and the former application of the double duophonio manner are the most natural, because they are based upon the gen-
most natural form of accompaniment (No. 61) of the duoIn sincfle instances, however, the two voicecouples might combine together in arbitrary intervals.
erally
phonio composition.
-
79.
P
i
s
-
1=r
i
———
m *
^
ei=F Since
we have
further discovered that the fundamental note of
first, two voices might sustain this mutual tone in various manners, while the others might move in
the second mass belongs to the
the two masses at pleasure.
We will call ment of the
such tones, which continue throughout the moveother voices, " Sustaining tones" for they give to the
whole tone-movement a material and bodily connection. But since all our tones and masses originate in the Tonic, we can bodily realize
this intellectual unity
by leading our upper
92 voices through the
two masses and
their different intervals, while
the lower voices sustain the mutual
fundamental tone, " the
Tonic."
81.
These sustaining-tones can be animated by rhy thmization of various kinds, which either strengthens the
or enters into a juxtaposition to
other moves, or
it
rhythm of other
voices,
remaining stationary where the
;
moving where the other remains
stationary.
m mu
Ld
L=rrLd
I
8v'a
.
.
When we 1.
2. 3.
4.
ri
&|-^-^
'Hi> ^^
>
\J
.
add to these new formations
The doubled voices (No. 77). The contrary motion (No. 78). The arbitrarily-composed masses (No. 79), and, The sustaining^iotes (Nos. 80 and 81) the double duo-
—
phonic and the single duophonic compost,
whole material before It
with
gives us a it
we have our
us.
new juxtaposition
of greater and
a third class of gradation, which until
lesser
now
mass, and
could only ob-
by the direction of tone-succession, and by the rhythm. In new juxtaposition we find, also, the means of more characteristically representing the more animated or light, and the more But firm or heavier character, than by mere rhythmical accent. even our former means of gradation find a new sphere in the astain this
cending of our voice-couples.
83.
93 Tliese are the nearest formations of the double duophonio composition
;
they give
material for the exercise of the fun-
sufficient
damental forms of all musical construction.
They only
require a
few directions in regard to Application.
Formerly we had only two voices
at our
command, which we
never separated, in order to have always Harmony.
now
out of which is
We
have
twice two voices, but can get along with a single voice-couple,
we
advisable that
gained the just-mentioned juxtaposition.
we employ
But
it
our means in a clear order, and ac-
cording to a consistent plan.
The former
requires that
we do
not arbitrarily cause the be-
ginning and ceasing of a voice-couple, but rather follow the idea
of the whole, as struction.
we have
The change,
seen
it
indicated in our rhythmical con-
therefore, ought invariably to take place
at a rhythmical section, as in No. 83, or at least with a rhythmical link, as in
No. 82,
The consistency permits no general
rule
;
it
can only arise from
the contents of every phrase.
With
the following
Part begins a
series of analyzations
and
exercises which will exclude, for a time at least, all free formation.
But we advise the student to keep up the practice of the
duophonic, or double duophonic composition, in order to preserve the susceptibility of his
mind
have their turn in future.
to
melody and rhythm, which
will
94
Third Part. The Harmony of ike Major
Scale.
However diversified our tone-world has been thus far devei we can clearly see the insuificiency of everything discov ered. At first we had the complete diatonic scale, with the license, even, of admitting foreign tones, but we could only move in it monophonically. Afterwards we gained the harmonic massoped,
es,
and the possibility of combining simultaneously two or four but they were insuificient for the complete scale.
voice-parts
;
The next step is obvious We must learn to use the complete :
scale in the
polyphonous
combination of the harmonic masses.
We
resume
at once, therefore, the
polyphonous composition,
and begin with the Tetraphonic composition.
CHAPTER
I.
DISCOVERY OF THE NECESSAET HARMONIES.
OnR
first
object
is
now
to find harmonies for the complete
scale.
Here we
are directed at once to the
importance and regularity of which
first
we have
hannonic mass, the already seen.
regularity consists in the position of its three tones
(c, e,
g),
This
which
are placed in thirds, one above the other.
The combination of three
or
more tones
to a
Harmony
is
called
a " Chord."
The lowest tone in such chord (c) is called " Fundamental tone." It is the most important tone of the chord, because it serves as basis for the
whole construction.
Therefore the proportions of
95 tlie
other tones of the chord are regulated and designated by (e) is called the " Third" and the next one
The next note
called the " Fifth"
i.
it.
is
of the fundamental tone.
«.,
No. 79 we have perceived that the tones of a, chord do not always appear in their original position. Tlie very fu-st Already
in
first the itself in No. 54 in the following manner fundamental note, then the Octave, then the Fifth, then again the
mass showed
:
Octave, and after that only came the Third, and again the Fifth.
Doubling of the Chord-tones.
same time we see that every note of the chord can be applied more than once either in different octaves (as in No. 54), or (as can easily be imagined) by different voices on the same place. Both proceedings are called ''Doubling" of the chord-
At
the
;
notes.
We we
doubling of chord notes immediately
shall require this
•
for
intend to write tetraphonic, and have but three tones in the
Which
chord.
But, if no other reason prevent us,
tone first, because
Nature
itself has
the
it is
used
it
double the Fifth, because
we
formation.
shall
double the fundamental
most important tone of the
oftenest (No. 54). it
is
ular concord,
we
shall
The Third,
the least appropriate to be
We have based this rule upon imitation Our
chord, and
After this
appeared originally twice.
which originally appears but once, doubled.
now be doubled 1 We make use of this license.
of these three- tones shall
are at liberty to double either, and shall
ear confirms this as the
most
of our natural
beautiful and reg-
and the Third as the most piercing and perspicuous
interval of the chord, which in doubling, for instance,
84.
easily
drowns the other
ir
r
intervals.
Transposition of the Chord Tones.
We have already means always
seen that the tones of a chord appear
in their regular position.,
voluntarily resigned
it.
In No.
by no
79 we have even
But these transpositions
require, for the
96
We
present, no particular consideration.
will
now
place our
tones as near as possible to the upper voice, unless particular reasons lead us to a different formation shall
always retain
cause
it is
its original
;
but the fundamental tone
position as the lowest tone, be-
always the basis of the chord, and by
But
recognize and designate the chord.
since
we can easiest we can place all
it
our other tones at pleasure, the Octave, Third, or Fifth are placed occasionally in the upper voice.
85.
r
r r
'-
-F
—
97
-f
.
98 and
The
its fifth.
each
is
a perfect
third in each
one on
fectly like the
a major third, and the
is
Tlte chords
fifth,
on /and
ff
fifth
in
are therefore per-
«.
But we know already, from the Introduction, that we can buUd a major scale upon every tone of our whole system, and that
major scales have like proportions.
all
Consequently the chords
upon the Tonic of every major scale must be exactly
alike.
We
can therefore find our chords /a-c, and g-b-d on the Tonic of i''and
G major, and
though they are also domesticated, as
We
jor.
G
major, or as
C ma-
were, in
borrowed from those keys.
we
stand to the one in which
These keys
(C major)
actually are
in the first
and thus we come to the conviction
degree of relationship*; that the
it
can consider these two- chords as reminiscences of i^
harmony of the major
scale consists of the tonic chord
of the same, and of the tonic chords of the two nearest related-
major
scales.
Therefore scales
:
as every major scale has its nearest related major
on the nearest
each major scale
,
above and below the Tonic
fifth
also, besides its
own
chords of the nearest related major scales within
This double point of view which
;
thus has
tonic chords, the tonic
we have
it.
taken of our second
and third chords 1,
as harmonies constructed
longing to the scale) 2, as
from domestic tones (tones be-
;
Tonic chords of the two nearest related major
scales,,
which we have borrowed from these, and which remind us of them will, in future,
hend
it
;
be of the greatest importance.
clearly, therefore,
* Nearest
and retain
We must compre-
it.
related or related in the first degree, are stioh major keys as other. major and Cf major for in-
d-mate in but one tone from each
;
stance: 1^ Cf,
differ
a, b,
f, g, a,
0,
d,
c,
d, e, /j), g.
e,
b, c.
major and jP major
from each other merely in the / and/{(. c,
d,
e,
b, c. f, g, a,
f,g,a,
bh, c, d,
e,
f,
are distinguished merely by one b, consequently they are nearest related. Bb, P, O,
M,
99
CHAPTER
II.
EXAMINATION AND JUSTTFICATION OF THE HARMONY.
A.
We
return
now
The Four
Voices.
to our last harmonic formation, No. 89.
Foi-
merly we had directed our attention merely upon the chords which existed in it. We will now look at it from another point of view.
We began with the we
scale
which as
Each tone of
placed highest.
this scale has first one, then a
second, and then a third tone under all
the
chains,
&c.),
we
and
it.
When we now
&c.), all the second {g,
first (c, d, e,
(e, ^r, g,
tone-chain or " voice,"
first
all
the fourth
(c, g, c,
b, c,
consider
&c.), all the third
&c.), as separate tone-
find a phrase of
Four simultaneously-sounding
voices.
These four voices are called Treble
(
Soprano)
Alto
or
first
voice.
or second voice.
Tenor
or third voice.
Bass
or fourth voice.
In order to recognize distinctly the different voices and their
progression,
we
will repeat
No. 89 in
score.
100
The highest and lowest voice (Treble and Bass) ' outer voices" the other intermediate voices (Alto
are called " inner
voices.''''
The Connection of Chords,
B.
But formed
it is ;
not
sufficient that
together they
each chord
by
should be well
itself
ought to form a harmonic whole, as the
became a melodic whole.
scale
are called
and Tenor)
They m.ust have
connection and
unitij.
Is this
A
the case in No. 89
1
superficial unity exists already in the fact, that all the notes
of these harmonies exist in one and the same scale.
not
we know
sufficient, for
merely borrowed from other
A more
g,
this is
scales.
distinct tie exists in the connecting notes wliich each
our chords has in that
But
that our second and third chords are
common with its neighbors.
Tlaus
we have
of
seen
om" two harmonic masses were connected by a mutual tone, first, second, and third chords connected
and thus are here our
by the mutual mutual
c,
—the
g,
—the
third, fourth, fifth,
and sixth chords by the
seventh and eighth again by the mutual g.
tween the sixth and seventh chords only this connection
The connection of the second, perceptible In the following
third,
is
Be-
wanting.
and fourth chords
is
best
:
-9
r
90.
Again, the
of page' '55
thi-ee
important notes,
meet our
eyes,
9—'=—f, and again we
find our
Tonic
c
as the
centre which connects these chords, and around which they move.
But they are no longer the single notes of
a'
scale
;
they are the
harmonies from which our whole harmonic development
is
de-
rived. C.
Before
we
Harmonic Designs.
return to our subject (connection of chords)
we must
101
we have
take into consideration the harmonic designs which
covered thus
There are two
far.
A, the progression B, tire
dis-
:
from one position of a chord to another
combination of two chords which stand to
eacli
other in
the relation of tonic and dominant harmonies.
nm
91.
The
cliords of the
rTfT^ r
Dominant and the Subdominant (/) have
no connection with each
other.
This cannot well be otherwise, for
we know
that these
two
chords have been borrowed from keys which, though each related to the principal key, C, have
D. Examining the enth degree,
we
Faulty Progressions.
deficient progression
find still
Firstly ;
:
each of our four voices takes throughout an independ in the -beginning, the first goes
second from g to repeated
;
from the sixth to the sev-
more undesirable proportions. OCTAVE-SUCCESSION".
1.
ent path
no connection with each other,
b
and
c
;
the third from
from e
c
to
<^
and
e ;
the
to g, which latter
the sixth to the seventh degree, bass and alto
is
Only from proceed from / to g.
the fourth goes from c to g, and back to
c.
m 92.
Ht The alto says nothing different from the bass. Neither is mere doubling or strengthening, as we have seen it in our
it
a
first
attempts at duophonic composition (No. 49) ; for it is right in the midst of the other parts, and, like them, claims to be a separate voice.
In this very ambiguity lies the
fiiult
;
the alto
is
neither
102 a separate voice nor a
lowing
mere doubling,
as, for instance, in
the
fol-
:
W: 93.
BE
r
r
r
Progressions like those of alto and bass in No. 92, are called false oT consecutive octaves
;
they give to the phrase an ambigu-
ous appearance, sound hollow from the tone-web, and rob full
variety of voices.
For
them, though the time will
we will come when we learn the present
of its
it
absolutely avoid to
make the right
use of them.
But how can we obviate the consecutive octaves in No. 92 ? The bass was indispensable we had for a and b no other har:
inonies than the chords
of/ and ff.
The
fault, then, lies in
because the alto, Hke the bass, proceeds from not be.
We
now remember
that the chord
nothing else than our former second mass,
/to g ; ff-b-d, is
g-d-f.
the alto,
this
must
in reality
We
might
therefore retain the /of the first chord in the second chord;
(7f=
^^
94.
no longer in octaves with the bass, and these two chords have now a mutual connecting-note, /
Tlae alto progresses
103 proportion voices
is particularly
obnoxions
as, for instance, in
;
wlieii it is
No. 94, with
unhidden by other
alto or treble left out.
we shall find these successions sometimes admissible we will avoid them. In the above case the fault
In future
;
for the present
consists in the progression of bass
and tenor.
y to g, while the tenor goes from c to tliis
fault
by
letting the first note of the tenor
clear that the c cannot remain, for
ing harmony. solutely go
But
down
But the note d
it
remain
now wantmg
!
w
avoided
here, it is
forms no part of the succeed-
into the nearest note of the next
is
we ;
it must abharmony (J).
ascend nor remain,
if it can neither
let
us distribute, therefore, the
time-space of the chord between h and
d.
-JSZ
95.
-^A
ei
We have
The bass goes from
In the octaves
d.
now avoided
the
and gained, besides, the com-
fifths,
The former we have gained by contrary motion, the latter has given us opportunity to give to one voice two notes of the same chord, and thus to obtain greater animation. We plete
harmony.
will call such notes,
" harmonic
which enter
after the other notes of a chord,
bye-notes.''''
There are
many
as, for instance, at
m
other ways of obviating the above a and b ;
s
:^-.
difficulty,
^
96.
f^^^g but for the present because
it is
we
will adopt the
one illustrated in No. 95,
within bounds of our present knowledge.
E.
The Dominant Chord.
This has involuntarily led us to a
new
chord, consisting o?fov.r
104 notes
;
ff,
The fdurth note
b, d, f.
is
the seventh of the funda-
mental tone.
We
-will
our former chords, consisting of three Botes,
call
" Triads," of
which we have at present three Triad of the Tonic,
;
c-e-ff
"
"
Dominant,
g-i-d
"
"
Subdominant,
f-a-c.
viz.,
;
The chords of four notes will he called chords of the Seventh, "Septime chords," because the added seventh distinguishes them from the triads. The one we have just now discovered upon the Dommant, will be of special importance, and to distinor
guish
from
it
we will
others, less important,
call it
the '^Dominant
Chord:' This Dominant Chord requires a more particular explanation. 1.
It exists
on the Dominant of each key, and
at
no other
place. 2.
The dominant chord of each key
Consequently, this chord
Thus the chord
a key. In the
is
key of
i''it
no other key
exists in
marks key of C. it would be
the one which most distinctly indicates at once the
g-h-d-f,
would be
c-e-g-b\t,
in the
key of
G
d-f'^-a-c.
3.
This chord reminds us of the second mass, and with
Tonic and the around-it-moving
scale.
It is
it,
the
the completion of that
which was merely indicated in former formations Q, O, G, Its destination is
;
a,
d,
e,
F.
I),-F.
— B, — B,— F.
to resolve into, the
notes follow this current. its third
C,
b,
leads to the Tonic
Its ;
first
mass, and
all its
fundamental note goes to the Tonic,
its
seventh leads towards the Tonic,
and enters upon the note of the tonic harmony in
its
way
;
97.
its fifth is
goes most naturally to the Tonic, though the tonic third
quite as near.
But we prefer
the^ former, because
we do
not
105 like
double the
to
No. 98
No.
third.
98 a
is
therefore better than
B.
9a
W:
^ This proceeding of the dominant chord is called its " resolution,'" and of any chord that absolutely draws after it another harmony
we say, " it resolves into" such chord or harmony. With this we have at last accomplished the faultless
harmoni-
zing of the scale.
— 99.
It is
a natural consequence of the regular resolution of the dom-
inant chord, that the last chord remains incomplete ; fifth.
is
We will
it
lacks the
submit, for the present, to this imperfection
not disagreeable, and will soon be justified or avoided.
seems, further, as
two
if
there were
last chords, g-b-d-f
tual tone.
But
this is
and
it,
it
It
connection between the
they have in No. 99 no mu-
only because the last chord was incom-
plete; the connective-tone to introduce
now no
c-e,
;
i^g) exists,
but
we have
not been able
because each of our voices had to follow a certain
prescribed direction.
^
106
100.
ii
^-
1=5
":22r"
T 1
We
involuntarily consider the dominant triad as dominant
chord, and, feel in a. degree the effects of the seventh, though
We
not heard.
with (c).
its
third as the highest note goes into the
An
exception will illustrate this rule
stance, in a chorus
from
^ ^S
-"
Israel in
Subdominant
triad
Handel
still better.
often leads the third of the dominant triad
101.
it is
have the same sensation when the tonic triad
downwards
;
for in-
Egypt :"
-4-W^
-U4-
^aiiii ^^^ rr" f-
f-
and thus obtains a strange, piercing expression, which makes perceptible that he departs from the natural way.
This
is
it
by no
means the only instance of great masters deviating from any given rules. Music as an art would be fettered indeed if her devotees were confined to the rules laid
sible or inadmissible
judges
whom
down
for the
guidance of
The master knows well when a deviation
the student.
;
and
his taste
he has to consult.
is
admis-
and intelligence are the only
Thus can we see numerous
illus-
above in the works of Haydn, Mozart, Beethoven, Mendelssohn Bartholdy, and a hundred others. But they are the trations of the
masters
;
we, the students, tnie to our principle, without calling
this deviation
wrong, wiU at present abstain from using
it.
107
CHAPTEE
III.
THE ACCOMPANIMENT OF GIVEN MELODIES.
A.
Limitation
to those
means which were found in
the
Ascending
Scale.
Our
melodies, for the present, will have to be very simple and
To each note of the we have found for it in No. 89, tones of the scale we shall always
contain the notes of but one major scale.
melody we give viz.,
to the
give
and
third,
the tonic triad
dominant
;
fifth
and seventh that of the
to the second
and to the fourth and
;
But when the
dominant.
we
first,
that chord which
sixth the triad
sixth note is succeeded
shall avoid the threatening faults
by
of the sub-
by
the seventh,
the introduction of the
dominant chord. In order to facilitate the finding of the chords,
by
how
we
shall indicate
below the fundamental note of the chord is to be found. We have seen in Nos. 89 and 99, that the Tonic has for a fundamental note the lower octave, and mark it therefore by 8,
figures
far
The second note of
above the melody.
fundamental notes
five
degrees below
cording to this proceeding the scale of
;
the scale {d ) has its
we mark
G major
it
by
5.
Ac-
would be marked
thus
IS2Z
102.^ tj
We
-a-
^
-
see that the figures 8, 5, 3 are regularly repeated, with the
exception of the sixth and seventh degrees, which are both marked
by
3.
It is
the
same point where we have discovered the
ent misproportions for the present,
iji
mark
the progressions of our chords. it
by
of consecutive octaves and nection.
f,
in order to
fifths,
remember
differ
We will,
the avoiding
and the strengthening of the con-
108 After this
we
and place the fundamental notes, and then
find
the middle voices.
As example we
give the following
:
This melody 5
3+3
83
5
83 55
^ has
fii-st
them.
zai -&—e>-
been provided with
the dangers
by
placing a
f
figures.
We have
where we are
Then we write the fundamental tones
104. -e-
3
+
3
8
33
also
remembered
likely to encounter ;
109 appears to us as a Period, with thesis and antithesis.
We
hare
always ended our thesis with a half-cadence, or a step from the into the second mass; i. e., from the tonic triad into the dominant triad. But here, the tone /of the melody does not permit the tonic triad, c-e-g. We have therefore seized the next important chord, " the triad of the subdominant," and have gained first
two forms of the Half-cadence.
The one
from the tonic
consists of the step
inant triad
triad into the
dom-
the other of the step of the subdominant triad into
;
the dominant triad.
The Descending
B.
We
now attempt
will
to find an
Scale.
'
accompaniment
for the de-
scending scale, in the same manner as the ascending one.
We
place our figures above the upper voice, and in accordance with
we fmd
bass and middle voices.
83 + 35 83
fcgzr
m^
106.
58 "25"
-&-
-s-
-&
it
?-!!-
31 Everything
is
right with the exception of that dangerous step
from
—
con-
the seventh to the sixth degree (h
nection
is
wanting, and where
utive octaves and It is clear
a),
we meet
where, again,
all
as heretofore with consec-
fifths.
dommant chord can
that the
not even applicable without falling into
aid us
new
no longer.
It is
For if we would have to We must find
faults.
were to change g-h-d into a dominant chord, c-e-g and h would have to go to c instead of a.
follow,
other means. In order to avoid consecutive fifths and octaves,
contrary motion in the middle voices. 8
iE 107.
BE
3
+
3
zz^
5
we will attempt
no The alto would have to ascend to a and meet -with the treble, and the tenor would have to take/ But this would render the chord incomplete, and tenor and bass would make consecutive octaves from the third to the fourth chord (page 101),
The Major and Minor Triad. ,
A second It is
self.
attempt can therefore only be made with the bass
the middle voice, that the faults
must this
it-
because the bass follows the downward direction of
therefore ascend to a.
new fundamental tone 8
108.
come
into existence.
Trusting to chance a triad.
we
The bass upon
construct
Ill
no.
OF -di we have
Ileie, too,
3±:
~:t±l
wrong
altered our figures, avoided the
gressions, but lost the close connection of the chords.
pro-
This loss,
however, considering the otherwise excellent connection of the
may be
chords and the good progressions of the voices,
easily
borne.
Comparing our new chords With the old though they are also
triads, their
they consist) are by no means
The former
alike.
of fundamental tone, major third, and perfect {JE
we
ones,
find
that
:
contents (the intervals of which
fifth
triads consisted
new
the
;
ones
and A) consist of fundamental tone, minor third and perfect
We will call the former major triads, the latter minor triads. We have now three species of chords, viz.,
fifth.
Major
1.
triads
nant—in C
upon the Tonic, Dominant, and Subdomi-
major, upon C, O, and F.
2.
Minor
3.
The Dominant upon G.
— We
in
triads,
chord,
The
fifth.
triad
;
the
.
and sixth degrees of the scale
fifth,
upon the Dominant
—
C
in
majof
already see one of the reasons which permitted us
to leave the triad after the
out
third
C major, on ^and A.
now
can
upon the
dominant chord incomplete,
i.
e.,
third suffices to indicate that the chord is a
which
is
no
distinctive
with-
major
mark, can be most easily
dispensed with.
With
this
our actual mission
We
is fulfilled.
can harmonize
the scale in every direction, and, consequently, every
which contains no foreign notes.
Here
is
E
8
111. 8 3+3
5
3^.3
8
5
3
5
8
3
5
8
3+3
5
3+3
I
m
melody
another example
-»-«.
8
1 -f
112
The treatment of the second and seventh measures which
we have
the
is
same
learned in No. 95, and applied in No. 105.
In
the sixth measure we have made use of the proceeding in No. 110.
The chords from the nectino- tone,
fourth to the fifth measure have
but since the connection of the chords
well-established,
we
can
In the second measure to ascend.
Why 1
have been forced to
by
degrees,
make will
d of the dominant chord melody ascends, we should
the
Because, since the
we
no con-
otherwise
let it pass.
we permit
consecutive octaves (a) or to use a
dif-
Whenever
as-
ferent progression of the voices (b).
cends
is
the
melody
always use the same proceeding.
&^^te-f^^=^ i 112.
i^i In the course of our last remarks
we have
frequently used the
vTord "note" for ''tone." Since there can be no possibility of confiision,
we wish them
to be considered as
we
until in
a future chapter
tinction
between " tone" and
shall its
synonymes
be forced to
;
at least
preser'fe the dis-
representative " note."
us
Fourth Part. The freer use of the chords
at present in our possession.
Until now we have used our chords merely
ment of given melodies.
Let us
for the
now see how we
accompani-
can apply them
independently.
Animated
phrases, like those of the
monophonio and duophonic
compositions (Nos. 5 to 74), would here be out of place. present,
we know
For, at
nothing. better than to write exclusively in tet-
raphonic chords, (in masses) and this does not agree with an intellectually-animated inovement.
A phrase
like the following
Allegro
^to^ii f=? do very well for one. ox two voices (a or b) but it would be drowned under the tone-mass of four voices, witld their bass walkwill
ing along in wide steps (a). Allegro.
The addition of a dominant chord would even make
We have to be limited, nies
therefore, to quiet
which develope themselves but slowly.
it
worse
(b).
and simple harmo-
114
CHAPTEE HAEMOmO
I.
DESIGlfS.
Development of a single chord.
A.
We have already seen chords- in diiferent positions among fifth
others the major triad of
in the
upper voice.
«;
mth
(No. 105)
;
either octave, thirdi, or
This leads us to the
first design.
•,
the
leading of a chord through all its positions.
115.
Tlie
m
-e&-
same proceeding can be applied
dominant chord
to every triad, to the
also.
^_-^&-
m
116.
"S"
"cr
-z3-
At a first glance the design of the last chord seems to be faulty, for we have admitted that the dominant chord must resolve into the tonic triad. But we can soon perceive that the moment of proper progression has merely not yet arrived. third,
The second, first, and
and fourth chords are merely repetitions of the
only the last repetition ought to resolve according to rule. -©<=117.
We
see,
also,
i
-e-
that the last repetition
is
imperfect
;
we have
employed two voices for the fundamental tone and its octave, and consequently have but two left for the most important The fifth is omitintervals of the chord: the third and seventh. ted, unless we give to one voice two notes in succession, as we have already done at No. 95.
115
A 118.
m B.
We inant,
-<^-
-^
— The
Combination of Major Triads.
are in possession of three major Triads, on the Tonic,
same key, hut the tonic
Dom-
All these are contained in one and the
and Subdominant.
triad alone indicates to us this key.
We
have borrowed the dominant triad of the key of the Dominant,
and we have borrowed the subdominant triad from the key of the Thus, though these three triads belong to one
Subdominant.
key, they indicate three different keys.
These chords stand in the same relation to each other as the C major and G major, and major and i'' major are near-
keys.
C
est related', consequently the triads of
J''
of
major do not stand in nearest
G and
this
C and
F,
major and
relation, consequently the triads
we
find, therefore,
Designs of Nearest Connection
1.
we
G
F lack also this nearest connection.
Premising
which
and G, and
The keys of
stand in the same degree of relation.
can represent in
all
the different positions of the chords,
triads of the Tonic
between the
U
\A
3E C-!
-e-
119.
^
-&-&-
-22"23"
«
and the Dominant
^
U
_G
!2_
::s&:
"Cr
betweeen the triads of the Tonic and the Subdominant
120.
^
"Og""
EiE -&-
&c., &c. 2.
between the versa
Designs of More Distant Connection.
triads of the
Dominant and the Subdominant, or
:
-(9-
121.
""221
-&&- jSI
-%--
vice
116
C.
— The combination
of Minor Triads, and of Minor and Major Triads.
We have found two minor triads,' one upon we
scale,
find that
degree also
now
have grees
we
three major triads
and three minor
;
neither major nor It is
now
minor
;
triads
Upon
degrees of the scale.
an-
C
major upon d : df-a. Thus we upon the first, fourth, and fifth deupon the second, tliird,' and sixth :
we can
the seventh degree
triad, for the perfect fifth is
we
the question what independent use
these chords, of which,
and
examine the
can construct a minor triad upon the second
for instance, in
;
the sixth,
When we
other upon the third degree of the scale.
till
construct
wanting.
can
make
of
now, we have used but two, and these
only from necessity. In order to arrive at the solution of this question,
we must first
examine their relation to each other.
and the same key,
clear that all the notes belong to one
It is
and that some have mutual notes among them, others not. triad of
G
thus related with those
is
remaining chords
is
oif
e,
g,
The
and a ; each of the
only related with three others
by means
of
mutual notes.
As
the three major .triads, represented the three major keys,
thus the three minor triads represent three minor keys, which on
examination will be found to be
the, parallel
keys* of the above
three major keys.
Each minor key, however, stands in the first degree of relation key (they differ only in one note) consequently, G
to its parallel
major and
;
A minor, Q major and
.fi"
minor,
i**
major and
D minor,
are nearest related, "and thus the triads of
the
first
and
sixth,
the
fifth
and
third,
and
the fourth and second degrees
belong together.
We have, 1.
therefore, again,
Designs of nearest connection, or such as are connected by the relation of the keys they represent.
* Parallel keys are those major and minor keys having the same signatures C major and A minor, G major and minor,' i*" major and I)
for instance,
minor.
E
117
s-
m
122.
-s-
Designs of more distant connection, or such which, though having mutual notes, do not represent nearest-related
2.
.
keys.
—&— 123.
-d3.
124.
Designs without mutual notes.
—
m 'Sp-
D.
isgr-&-
Harmonic Designs from
Till
now we have As
The dominant triad.
adding of the dominant chord.
such
it
We will meets us
attempt, now, to use
in a
chord, as
we know
and according to
its
already,
the end.
is
the best decisive
nature resolves into the tonic
In connection, therefore, with the latter,
most decisive cadence.
it in-
very important relation
The Dominant chord preparing
1.
sign of a key,
the
used the dominant chord only in order to
avoid faulty progressions. dependently.
33^
iS.^
Let us observe
it
now how
serves as the
in its four po-
sitions it resolves into the tonic triad.
125
^S»iszz:
m iy
In
A the
last
rO-
:22z
3F^
chord appears with
In B the third is above.
only perfect when the
its fifth in the upper voict'. Such cadences are imperfect; they are
final
chord has the Tonic in the upper
118 In the above cases we could not well do differently, therewhenever in the dominant chord the octave or third are in the upper voice, we shall have an imperfect cadence. If it is in the upper voice, it can either ascend into the third of voice.
fore
the tonic triad as in (c), or
can descend, as in (d), into the
it
we have again an imperfect, when the third of the dominant chord (as in e) is in the upper voice, we obtain, again, a perfect cadence, aud a stronger and a more satisfactory one octave of the same. in the second,
than in d
In the
case
perfect cadence.
a,
for the third
;
first
Finally,
must ascend into the octave, while the
can either ascend or descend.
fifth
Other Chords in connection with the Dominant chord.
2.
The nearest
relation of the
dominant chord
is
the dominant
triad
127.
Srlz (a)
=i=
-0-
which by adding the seventh becomes a dominant chord.
Tlie next is the tonic triad (b),
on account of
its intrinsic
connec-
tion with the dominant chord.
After
this, all
the remaining triads (with the exception of the
one on the sixth degree) stand in close connection to the dominant chord, thus
making
this
chord the animating agent of
all
our har-
monies.
-&-
m
128.
s-
-Sr =i:
-<3£2-
Extension of the Harmonic Designs by means of Rhythm.
E.
Every
chord, or every pair of connected chords, can serve us
according to
tlie
above, as harmonic design
;
and consequently
every harmonic design can, by means of rhythm, be carried out.
Thus a or
by
single triad could,
by means of rhythmical repetition made a design.
the use of its difierent positions, be
(a),
119
The same could be done with two
or
more connected chords
;
for instance,
130.
imm
t f=F
fl
-&--»-»- -&- G-
n
Y'n
or alternating chords might be led through their different positions, as in
one phrase
;
No. 119, if we wanted to employ all the chords in or they might be employed as here
131.
in various rhythmical forms.
Such formations are to be no further
Far more important F.
effected so easily that
they require
instructions. is
The Formation of Harmonic Passages or Sequences,
as they might better be called here.
Every succession of chords which does not end of a period or a phrase,
is called
manner Thus the
in the
a harmonic Sequence.
following part of a harmonized scale.
132. -•- -»
«-
j
-#-
might already be called one. „ 133.
mg
A,
-#
-#I
.
-m-
I
No. 126 gives us another,
consist
-Bz
m
t±^MrS:
^
of the dominant chord and the tonic triad with their positions.
The design of No. 119 gives us a
third
and
fourth.
We
connect
120 the tonic and dominant harmonies, and write the bass, perhaps, in this
manner
134,
P
a
fea^
^m
Y
or in this
135.
as far as
it is
convenient (the * marks the point where we' are
forced to leave the design), and effect the end
by means of
near-
related chords.
The formation of such sequences is absolutely necessary to the who should practice them in all positions and in all keys, perhaps in the following manner also student,
136.
iiii
s
^^m
rr
f
i
m
f-T
Such designs and sequences receive a
j-
r
special' destination,
when
Prelude,
they serve as introduction to a key, or the performance of a composition.
These introductions, perhaps intended asprepara
tion for a singer to begin
on the right note, &c., can be limited to
the simple tonic harmony, or a connection of tonic and dominant
harmonies in their .
different positions.
More complete would be
the combination of tonic, dominant, and subdominant harmonies,
121 '
o
g~
-3-
137.-^
-&~ "ST
or the addition of minor, triads T+t
138.
<^
-s;
for instance.
122
CHAPTER
II.
THE FREER HARMONIZATION OF GIVEN MELODIES.
We have formerly
said that the third,
it,
octave, or seventh
fifth,
of any chord can be laid in the upper voice.
Let us
now
reverse
and say that
Each tone of a melody can be
either thirdj'
fifth,
octave, or sev-
enth of a chord. Until
now we have had
a choice of harmony for but two de-
take for b the triad of either g ot
e ;
/or a (108 and
our object
But
110).
A.
We
ascertain
now
to choose oui
first
1.
2.
first
Freer use of the Triads.
of every tone of the scale whether
tone, C, can
be
in that case the
;
the chord would be Fifth
;
Thus we can take to c-e-g,
This would
The second
m
it
isf,
^
^
be would make the chord and the chord would be g-b-d.
Octave ; which
2.
Fifth
;
and
and the chord /a-c.
tone, d, can
1.
a,
which was formerly always accompa
three different chords.
140.
it
to seek the fundamental tone five
consequently C,
make
a-c-e.
we have now
;
degrees below
by
can be
fundamental tone would be c, and the chord would be c-e-g. Third; in that case we have to seek the fundamental Octave
tone three degrees below.
3.
it
octave of any of our triads.
third, fiilh, or
The
it is
could
or for a the triads of eithei
In order to secure safety -we will divide our material.
chords.
uied
C major, we
In descending the scale, for instance,
grees.
d-f-a.
123
We
camiot consider
the fundamental tone
b,
it
as Third, because
and the chord
have had no such chord,
i-d-f.
for all our chords
tMs would give us But until now we
have major
fifths,
while
A continued examination gives us the entire tones of the
scale,
this has
a minor
fifth.
with their respective harmonies at present known to us. 141.
^S
W-.
BE:
Each tone has received
three chords as accompaniment.
could not be used as third, nor note, because this
/as
fifth,
D only
nor b as fundamental
would have given us the chord
b-d-f,
which, for
the present, we.do not know. Accidentally, this phrase, gives us a four, at
like the following CI
new design.
We see
at
a
B and c six triads whose fimdamental tones form a design
'^V
1
1?4
By
this the
movement of our
voices will be surer and
more
quiet.
The advantage of this new mode of treatment tible in those melodies in
which
many
is
most percep-
tone-repetitions occur.
These (as in a) cause repetitions of chords, and make the accompaniment monotonous, whUe the new mode (b) gives variety to
Below we give some melodies on which practiced.
144.
n
this
it.
new mode can be
125
most consideration;
sign consistently through, deserve the
for
instance,
^N^
m
-f-
g
147.
-j—j-
e; Finally, he
must take
particular care that these novelties
do
not destroy the forms of phrases or periods. '-
In this respect
we know
has to end with a perfect
"
that every phrase
full
cadence
;
and every period
for instance, in
C
major,
with
148.^ ^^
^S=
^^^^-^
r further
:
,
that every thesis has to
r end with a half-cadence, or perhaps
149.
like
|
-&-
M: or with
150.
W-
g
--^z.
C3
-&&-^
-J These rules must
still
be respected, and in No. 143 we find them
attended to in a as well as in
After the harmonization
is
b.
thus completed,
ascertain whether, with the introduction of the
progressions have not found their
way
into
it,
it
will
new and
be well to
chords, faulty after this, the
whole should be played through.
B.
But
little
The free introduction of the Dominant Chord. remains to be
said.
Like every
triad, the
dominant
126 chord can be used for every note contained in it but care naust be taken not to cause faulty progressions by it. We know that the dominant chord must resolve into the tonic ;
triad
;
that the third ascends one step,
scends one step.
We
and that the seventh
can therefore introduce
these conditions can be
fulfilled.
Thus
following phrase, to consider the h
it
only -where
deall
would be wrong, in the of the first measure as third, it
or the /of the second measure as seventh, or the
g of the
third
measure as octave of the dominant chord.
^
r
151.
.^
BE Let us
now attempt
another haiTQonization of No. 111.
152.
The three chords
at
a have
little
or no connection
;
they have
only been selected in order to have the dominant chord succeed the triad of it
d.
The two
are related through
d and/;
succeed the triad of the subdominant, with which
at e
it is
we see related
At c it is introduced to d. The melody ascends from d to e, and the seventh of the dominant chord descends to e. Thus the succeeding triad has two thirds which are very perspicuous, and lacks the fifth. The latter is not of much importance, through/.
and against the double third we have at present no help. We could have avoided this if it had not been our object to introduce the dominant chord as often as possible. At d we see the advantage of our
new
principle.
We have not
placed the middle voi-
ces in closest proximity to the upper voice, but have preferred to
give
them the nearest
interval of the next chord, because the for-
127
mer proceeding would have caused an inconvenient progression of the voices (a).
B^ Mski
153.;
r r
r
r
'I
"
more convenient would have been the progression of b, though by it we should have lost the fifth of the dominant chord. Thus much of the dominant chord. We will make it a rule to effect our full cadence by it. Still
M-eer treatment of the Dominant Chord. Until
now we have always
treated the dominant chord strictly
The consequence was, that the tonic triad after Now, when we have to use it more it, invariably lost the fifth. frequently, and particularly for our cadences, we can permit some according to rule.
slight,
imperceptible deviations from our rules.
Formerly we have
now
step;
we
when
the seventh
will
insisted
upon the seventh descending one
occasionally permit ourselves
is in
(particularly
one of the middle voices, and another voice
takes the tone into which the seventh ought to resolve), to let the seventh ascend.
154.
m
m
r
Here the seventh,/, goes
to g, but the tenor has the
ought to have succeeded the seventh in the alto however,
is
hidden, and
we have gained by
it
;
e
which
this deviation,
a complete
final
cho;-d.
The
,
third ascends one degree.
Here we
see
it
descend
two
degrees 155.
but the tone
c,
m
into which the third
would have
led, is alreadv
128 taken by the treble, and we gain, by this slight deviation, the completeness of the second chord.
156.
^^
E
r
I
1
This deviation, however,
not so admissible
is
when
the tone
dominant chord properly resolves
into which an interval of the lies
4=
T r r r T
not alone in another voice, but in another octave also.
i 157.
4
r Here the seventh viation e
is
which
in a
middle voice ascends
also.
But the
de-
not hidden, because the voices are too far apart, and the
we
expect in the alto
is
given to another octave.
DOUBLING OF INTERVALS IN THE DOMINANT CHORD.
The
intervals of the
dominant chord most proper for doubling
are, 1,
the fundamental tone, and
2,
the
fifth
;
but,
the third and seventh cannot be doubled without falling into
For we know that both
faulty progressions.
regular progression
cends a degree. If,
;
intervals have a
the third ascends a degree, the seventh des-
,
now, two voices take the third or seventh, both will have to
resolve in octaves (or unison).
158.
unless
thus
we
proceed against the nature of the chord and have
it
129
n
130
Here was material enough tion if
bidden
:
to puzzle the student with the
for
some of these
successions occur in the
and indispensable progressions of harmony ; for natural harmonies and the necessary cadences.
E making
ques'-'
or any, and which of these cases were allowed or for-
all,
most simple
instance, ia the
~s>
t-
-f-
it
sy
r^
nr-
absolutely impossible to write a harmonic phrase with-
out such progressions.
But with the same right they might, under similar cireimistanhave forbidden the use of thirds, sixths,^ and sevenths, which can also become very conspicuous ; for iastance.
ces,
P
-&-
^
^-
^
-00--^
fact, leads us to the solution of the whole question. Such progressions are only conspicuous and disagreeable when
This very
they occur between unconnected chords, or when they are caused
by unmelodious, unnatural progressing of one or more when a voice instead of the nearest interval takes a more one of the next chord.
becomes conspicuous.
Under such circumstances every
voices distant interval
131
Fifth Part. The Inversion of Chords. Until now we have principally thought of the discovery and connection of chords, while
we have
paid hut
We
middle voices as near as possible to the upper voice in
No. 143 we have deviated from
this rule
attention to
little
the melodious progression of every single voice.
by
;
placed the
but already
giving to a voice
was nearest to it. Our bass always seemed the least flowing and most unmanageable, because we had nothing but the fundamental notes of our
that interval of the next chord which
harmonies to give to
it.
we will now extend the we have given to the upper
In order to obviate this awkwardness
same
privilege to the bass which
voices
we will take third, fifth, or seventh of a chord in the bass, we give the fundamental note, or rather its octave, to an-
while
;
other voice.
This proceeding does, not of course, influence the character of It is a mere exchange of one or more intervals of one and the same chord, and has assisted us already in developing our melodic element of the upper voices. Such chord, the fundamental tone of which has been transposed
the chord.
to another voice, is called an inverted chord, is
called inversion.
and the proceeding
In juxtaposition to the inverted chords
will call the uninverted ones ''fundamental chords."
we
132
CHAPTER
I.
ENUMEEATION AHD APPELLATION OF THE INVERSIONS.
When
a fundamental tone leaves
its place,
another tone of the
chord has to hecome the lowest.
But it becomes only hwest tone, not fundamental tone for jundamental tone we only called that one which in the original construction (by thirds), was the lowest. ;
This one remains the fundamental tone, whether
it
be above, be-
low, or in the middle.
There are as
many inversions
there are tones in the chord
;
as (besides the fundamental tone)
consequently every triad has two,
and every septime chord three inversions. 2.
1.
1.
3.
2.
E^
P^TlT
^^W=W -^
F
These inverted chords are so important, that they have ceived particular names.
Thus the
first
re-
inversion of a triad
called the chord of the sixth, or Sext chord as
we
is
shall call it for
brevity's sake.
It
has received this name, because the most im-
portant notes of
it,
the third and fundamental note, form
interval of a sixth.
The second inversion of a
chord of the fourth and sixth, or Quart-sext chord, as call
now
the
triad is called the
we
shall
it.
In the dominant chord the fundamental tone is again the
important tone, but next to
it
Con-
name
to the
sequently the position of these two tones gives the inversions of the chord.
Thus the
nal third in the bass,
called chord of the fifth
Quint-sext chord, as
is
we
first
inversion, with the origi-
and
sixth, or
The second inversion is and fourth, Terz-quart chord. The
shall call
called the chord of the third
most
in importance is the seventh.
it.
third inversion, in which the seventh itself is in the bass,
the intervals from the latter, and call
it
we count
the chord of the second,
or Secunda chord. * See Appendix A. f See Appendix B.
133
The names thus obtained
are not influenced
position in the upper voices.
The two
first
by any change of
chords of the follow-
ing are both called sext-chords, and the others are all called terz-
quart chords.
""W
f-^-T—f=7
This addition to our chords, though of great advantage, gives us
no new
For
difficulty.
all
inverted chords follow the same rules
which govern the original and fundamental chords.
we
said of the
and that still
dominant chord, that
its
descends or ascends one step
its fifth
^
3
»=*
rr
There
Why,
r
J-
¥ r
;
the same rules
M
hold good in the different inversions.
162.
Thus when
third ascends one step,
n=f'
r
but one thing which might appear strange to us.
is
in the above, for instance, does the fundamental tone
main instead of going to the Tonic, according Because
we
progression the Tonic
consider is
is
it
as octave of the fundamental tone,
and
?
its
prevented by the surro\mding voices.
Besides this
If the position
of the other
otherwise represented."
voices permits
g re
to the original rule
it,
we can
still
go from the fundamental tone of
the dominant chord to the Tonic.
J163.
though
m
this proceeding is
^
r
always most proper when done in the
lowest voice.
When we by them their
analyze the effects of these inversions,
we
find that
the chords are taken from their original position, from
proper and firm foundation, and that they lose their natural
clearness
and security in the same degree as we increase the
dis-
134 tance of the lowest note from the fundamental same degree they partake of a mobility which
But
tone. is
ia the
foreign to the
original chords.
Therefore the sext and quart-sext chords are not
fit
to be final
The latter particularly brings the tonic triad in so strange a position, that we wiU only employ it when we are led to it by the drift of the bass, or when we have particular reasons for it, of which we shall learn some in future. For the same reason neither quint-sext chord, nor terz-quart chord, nor secunda chord, are fit to prepare the end. Though they all must resolve into the Tonic, the strength of the step from chords.
fundamental tone to fundamental tone in the bass
some even
wanting
is
forbid the Tonic in the upper and lower voices.
NECESSITY OF A DIFFERENT FIGURING.
we
Before
we must
return to our practice,
take a precautionary
measure which becomes particularly necessary on account of the inverted chords.
As long
as
we placed
harmony made
at
every chord there where our
necessary,
we
every tone of the melody, but
we can
the
It is clear
that the figures which
melody are no longer
attempts
sufficient.
diiferent triads
also introduce the
inant chord arbitrarily, and in addition to this sions.
first
could hardly speak of a choice
But we have not merely the choice of
of chords. for
it
we have
dom-
the inver-
we formerly placed above
We require now a
kind of signs which remind us what chords
diflferent
we have chosen, and This new proceeding
what chords we have to carry out in notes. called figuring. The composer in his sketches often makes
is
use of this figuring in order to contrast the most essential points
would suffice to a degree, but it is imwhat we express in notes, and instead of that importance which many theorists attach to it, we
of his work.
For
this it
possible to express in
giving
it
it
will only introduce it as
We are
we want
already accustomed
then to add the middle voices in the
remarks will be
;
to
remember the bass and
the bass aids us to find our
way
Over or under the bass we place, therefiguring. For the present the few following
harmonic mass.
fore, this so-called
it.
first
sufficient.
135 1.
simpler chords in existence.
If,
passage to be unaccompanied, alone,
we
will niark it with
t.
all' ottavij, ;
if
intend a
bass shall go on
if the s.
we
however,
When
{(asto solo).
voices proceed in unison, or in octaves,
unisom, or
no
figuring, because there are
Triads generally have no
all
marked alV
it is
a single tone in the bass
is in-
we will mark it by a°. is indicated by figures which correspond
tended to be unaccompanied 2.
Every other chord with
tJie
3.
as
Septime chord
is
marked by
7.
the Sext chord
"
the Quart-sext chord
"
by by
the Quint-sext chord
"
by
the Terz-quart chord
"
by
the Second-chord
"
by ^
The dominant
it is
Therefore
its principal intervals.
e-
\
or
*.
^
or
|.
^
or
|.
chord, if before the end, requires
no figuring,
too important to be forgotten, even without them.
We will make use memoranda, as
it
of these
were, of what
figurings,
we
and consider them as
are going to do, as
we
are not
yet able to represent to ourselves a whole series of chords with all their
different
voices.
For the
merely write down the bass and voices afterwards.
present, therefore,
figurings,
we
will
and add the other
136
CHAPTER
II.
THE FREE USE OF THE UTTEESIONB.
New
A. 1.
As we
Designs and Passages.
formerly passed through the positions of a chord,
caonow combine a chord with
its
inversions
;
we
for instance a triad, <^
164.
6
4
6
6
The quart-sext chord is here introduced, but we have been led to it by the bass which passes through all the intervals of a chord. The same proceeding can take place with the dominant chord, 165.
^
Y^ 5
^T „ 3
"*
3
4
Y J 6
and with every other triad and septime chord.
Formerly we dared not attempt a succession of triads in on account of the consecutive fifths and octaves which would make their appearance, 2.
parallel direction,
I22I
166.
s:
:sr:
but the more mobile sext chord permits us to
make
such succes-
and to employ them for new designs and passages and at the same time gives us means for the accompaniment of the sions
;
scale.
167.
^
!^
137
None of tones with
these sext chords,
its
neighbor
;
all the voices serves as
The strong
link.
drift
it
is
true,
have any connecting-
but the flowing diatonic movement of
new and
a
quite satisfactory connecting
of the voices gives us no time to perceive
the lack of internal connection. 3.
Such successions can be made
tetraphonic, either
by adding
the octave of the lower voice,
168,
or
by a middle
-I s
$
^'
f
voice alternately doubling the third and fimdar
mental tone of the chords.
169.
It is
iM^E^y
$
J J T r T f f
apparent that the manner of No. 167
No. 168
is
also flowing, but the zigzag
voice in No. 169
makes
it
is
the lightest; that of
movement
of the middle
heavier and only appropriate for slow
movements. 4.
The
quart-sext chord can also be
employed
in
a small
suc-
cession, like,
W
170.
j=^ rrT f
but a longer continuation of
The
figuring
it
of the above
gives a very unsatisfactory result.
is
easily found.
constant repetition of the same figures,
dashes placed under or over the bass.
J 171.
m
i i
we
If
can
we
dislike the
mark them by
Thus the following
:^
-f-^-^^-^-r-^^ See Appendix A.
figuring
138 us that to each tone of the lower voice
tells
we
are to take a
sext chord.
Combination ef Inversions with fundamental chords.
B.
we have used
the inversions independently.
The
combination of inversions and fundamental chords gives us a
much
In the above
more extensive source of designs.
We need not mention that evert/
inverston can be combined with every fundamental chord, as long
But the nearest-related
as they do not cause faulty progressions.
chords enter most conveniently into combinatsions, be they
fundamental chords or inversions.
most easUy
Tonic, Dominant, and Subdominant or Parallels are
combined in
172.
their inversions
for instance,
;
^ i
m
more convenient
In fact, the
combinations
much
now
Therefore the chords of the
3
zz
position of the tones
O
gj
makes some
easier than in the fimdamental position
;
thus
the following chord-successions
-3 173.
are
i
-f-r-r
much more
flowing than the
same
in their
where the bass has to take such wide
tion,
174.
steps.
J-
d= =s
m
Y
fundamental posi-
r ^ r T r ^
Still
ges,
more important
is
the formation of
new harmonic
passa-
what we have said of them will be comparatively Only as examples we give a few passages, produced from
which
easy.
after
our present means. In No. 167
we
of sext chords.
chord
;
this
first
saw an ascending and iescendiag passage
Each
sext chord reminds us of its flindamental
prompts us to mix the two
:
139
r
wu 175.
sss I
r
The
176.
I
d:^
^^ff
r W=F^
p zz
&^
22:
anticipating of the sext chord
^^^ S
?z:
would give us a second passage,
r
=P2:
:=\-
?^
We can 177.
178.
?=
descend in similar manner,
W^t^^
i i
g
-(9-
r;
~
=s
~z5'
The addition of a third chord gives us
still
more
variety, which,
together with the thorough practice of every design through positions,
instance,
we
leave to the industry of the pupil. '
all
for
might be carried out thus
^*iP ^
179.
No. 173,
I
J
I
gE
or thus
&o.
^=i:
3:
**
&e. JffiC. I
m
F=^-
180.
I
&ism^^
See Appendix
C.
140
These inversions give us additional means C.
for the foimation of
Preludes and Final Cadences.
We have already
seen one of the simplest preludes, consisting
of tonic triad, dominant chord, and tonic triad.
181,
Now
we
that
i
Efe^ T
have a better control of the bass, though the
progression of the same
is
awkward.
first
182.
Leading the
m-
vigorous and decided,
chord through
^=^
it is
nevertheless
its inversions,
it-
s 6
6
7
i
we
arrive at the quart-sext chord, the lowest tone of which is at
the
same time the fundamental tone of the dominant chord, thus much more flowing connection. We will prepare
offering us a
our is
full
cadences, therefore, with the quart-sext chord, though
it
not absolutely necessary, as long as the fundamental triad gives
us an awkward, but
more vigorous
preparation.
183.^
We have also
employed the subdominant chord for the more For it, too, the quart-sext
perfect decision of key and cadence.
chord serves as a more flowing progression in the bass.
W. 184.
"7
9l
1
141
D.
The
Avoiding Faulty Progressions.
inversions furnish us also with
progressions
new
fording us to substitute a
IZC
of avoiding fault,
^
T
SgE -&-&-
J. -& -.ztssz
Hf=Fp
^
2
faulty-
without
chord.
E3=
-&-
185.
new means
permit that the bass avoid a
for they
;
221
*=
3
3
6
4
4
Here we have avoided the faults attendant upon the sixth and not by alteration of the middle voices, nor by the addition of a new harmony, but simply by means of inversion. seventh degrees
:
A new
E.
Here something new
chord, the
Diminished Triad.
offers itself to
our consideration.
xeaping progression of the tenor in No. 185, displease us.
tenor to the
186.
Trusting to chance,
d of the next
we
b,
The
might in some cases
lead, therefore, the c of the
chord.
i^^
w.
r
-r
^ This brings us to a chord^the dominant chord without
its fun-
damental tone, reduced to three tones, and having the appearance of a triad. This triad (we have often met it without knowing what use to make of it) distinguishes itself from the former ; it consists of
Fundamental It
tone,
minor
third,
contains less than the minor triad, and the
Like every other
and minor
fifth.
is called, therefore,
Diminished Triad.
triad, it has its sext
chord and quart-sext chord.
142
187
m new chord
But, in reality, this
Consequently,
dominant chord. Its
fundamental tone
ascends one degree to
one degree to scend.
viations
b (the
nothing else than an imperfect
its
tones follow the same laws.
former third of the dominant chord)
c ; its fifth,
e ; its third
is
/ (the former septime),
only (the former
fifth)
descends
can ascend or de-
But in Nos. 153 and 153, already, we have permitted defrom these rules, and we may therefore admit them in
the diminished triad.* jSl 188.
-OZ
i
-s=
Here, at a, sionally
-&isz:
b,
may be
of the voices.
and
c,
we
see the seventh doubled, which occa-
necessary in order to obtain a flowing progression
In order to avoid consecutive octaves
we must
de-
viate from the original law, and permit one of the original sev-
enths to ascend.
This
occurs in a middle voice is
is ;
done best at b it is
at a,
more
this deviation
and
at c it
disagreeable on account of its being in the upper voice. It is
not to be denied that this diminished chord lacks the
ness and firmness of the dominant chord to
where
perceptible,
employ
it
;
but
we
full-
are often fbrced
where the dominant chord would only disturb the
movement of our
voices
;
for instance.
189.
rr-frf^ * See Appendix D.
143
CHAPTER
III.
EMPLOYMENT OF THE INVEESIONS IN THE HARMONIZATION OF GIVEN MELODIES.
As
we cannot introduce any chord in a And we must consider as faulty the entrance of which we have no reasons, or which does not aj/'
a matter of course,
faulty manner.
every chord for
pear in proper connection.
manner of harmonization therefore, too, we must what 'lies nearest to us, and thence arrive at the more dis-
In this third seize
tant
;
but
we
will not pass over the former without sufficient
reason,
We
will therefore generally
chords.
think
first
of the fundamental
Nearest to these fundamental chords are
These we
its inversions.
when we remain longer in the harmony of the fundamental chord. Moving from one harmony into the other
We
will use
will again seize the fundamental chord of this latter, unless its
inversions serve to avoid faults (No. 185), or unless the current
of the bass, or of the middle voices (No. 189), or the object of writing flowingly (No. 186), or fear of crowding severe succesinduce us to employ the inversions. The method of practice for this third species of harmonization the same as that for the second. Another treatment of No.
sions, &c.,
is
147
may
sei-ve as
example
:
144
CHAPTER
IV.
CLOSE AKD DISPERSED HARMONY. ,
inversions have given us the possibility of giving to the
Ths
bass a
more
flowing
melody
;
the other voices, also, have gener-
ally received a better connection,
It
and
for this
purpose have often
place next to the upper voice.
left their
now remains with
us voluntarily to resign this close connec-
tion of the voices throughout whole phrases.
We know
already
that the inversion of the different intervals of a chord are permitted,
and that they neither disturb nor change the inner character-
istics
Thus the chords
of such intervals.
at
a are as admissible
as those at b.
193.
_£2_ £?~
m BE
We have What
m
in
occasionally is it
-
employed them. at a ?
now we have done
of the chords apart.
our sensation.
This
is
We have drawn the tones
externally true, and corresponds with
They seem no longer pressed closely upon each and have thus become softer and more
other, they are extended
It is evident, also, that in this form the voices have and can move more independently.
transparent.
more
play,
This form of representation
is
called the
dispersed position, or dispersed
harmony.
We know already where the chse and where the dispersed harmony has the advantage. We shall, at least, never employ it where it
leads us into unnecessary difficulties.
with the
whether
latter,
we can
we must do continue
it,
troduce the chse harmony.
If
we
begin, therefore,
so only after having ascertained
or whether there is a
fit
place to in-
145
The moment we
desert the close position, an almost inexhaust-
ible field of different positions of our intervals lies
But not
all
of these positions are suitable.
tervals too far, If
we
place
harmony
we
some or
all
194.
open
for us.
spread the
in-
the intervals in the higher regions, the If
we
place
regions, they will lose their distinctness.
-9-
we
disturb the material connection of the chord.
will lack fnllness.
own harmony,
If
has given us a model which
--^
r—
them
all
in the lower
Nature, however, in
we may
its
safely follow.
146
ijj-ij
Wwm 6
But ing
first
we must
t 26
a
6
iij.jjijj.j;i. 6-
3
7
p
observe, that horizontal dashes in the, figur-
signify continuation of the
same harmony
;
as in the second
chord of the penultimate measure, where thty stand instead of the repetition of
|.
The above, for comparison's sake, is treated at a in the first manner. At b we have treated it in the third manner, with employment of the inversions, but
Above
all,
we
Only
the evenness of distances.
of the antithesis the bass
But
voices.
in dispersed
harmony.
perceive at b the transparency of the voices and
this
is
at the close of the thesis
rather
more
distant
and
from the othei
happens only on unconnected parts, and
the'
immediate preceding of the higher octave. This d(^t on
new manner all
of treatment should be practiced
the former phrases, and on melodies of his
by the stuown inven-
tion; 1.
According to the Jirsf manner of harmonization.
2.
According to the second manner of harmonization, and
with arbitrarily-chosen chords. 3.
According to the third manner, in
4. In dispersed
close
harmony, and
harmony.
Finally, he should pi'actice the dispersed
passages, of which
we have had
harmony in harmonic Each passage
several already.
can be represented in more than one position
one of No. 179 thus:
"197.
w
zzL
or thus See Appendix C.
;
for instance, the
147
:si
&-
^EB 198.
s-
4 -J
J-
A: zU
BE
~A
:iii
Pff ^±f. r
:^
^.^E^EidE=
I F¥=FfF=PFf
l9-
RETROSPBCTION.
With scale. 1.
we
this
It
Triads
:
versions 2.
harmonic development of our major
close the
has given us the major, minor, and diminished, with their in:
Sext chord and Quart-sext chord.
The dominant chord with quart,
and Secunda
its
inversions;
Quint-sext, Tere-
chords.
We have learned to combine these chords in various manners, and to form with them phrases, passages, and periods. The de-
velopment of the harmony in accompaniments, phrases, passages, or periods,
we
will
now
call
MODULATION.
We had to
resign the invention of periodical compositions, bo-
cause our tetraphonous formations were not sufficiently free to
permit us the equal consideration of period, such as Melody,
all
the requirements of
a
Rhythm, Construction, Harmony, and
Voice-progression.
But instead of this we have learned how to find for one given melody three accompanying voices. We must attach one more observation to all our former results.
We
have obtained the justification of the major
accepted
it
justification
as ;
custom has given
We
to us.
scale.
At
first ^Y0
This serves already as
but since we have arrived at harmony, the question
whether our major scale ance.
it
is
well formed gains additional import-
have to consider whether
monic treatment, whether modulation, whether
it
it
it
is
well formed for har-
contains the material for satisfactory
can close harmonically as well as melo-
dically.
We can now answer these
questions in the affirmative.
Thi'ee
148 major, three minor, one diminished triad and the dominant chord, together with
means
the inversions arising therefrom, are sufficient
all
to harmonize the scale,
and
all
the melodies therein con-
perfect cadence, the maremind us of the nearest-related keys, and means for half cadences and imperfect cadences.
The dominant chord gives us a
tained.
jor and minor chords
we have
We
sufficient
can
must be
fit
now
confirm the conception of a hey, that such a one
melodically and harmonically as well, for the forma-
tion of phrases
and periods.
But we must not
close this chapter without drawing the atten-
tion of the student to the fact that it is absolutely necessary for
him
to play over all his compositions and exercises. In dispersed harmony, particularly, it will require some practice to do full justice to the different voices. These voices are all alike important, and should be played with precision and equality of strength.
When thus practising, the student should watch the effect of every chord, and the results of this attention will be a better command
of means than can be acquired in any other way.
149
8ixth Part. The Harmony of the Minor
Scale.
1
CHAPTER THE
We
have
we found
justified
also
THE MINOR RH AT.-R.
FOEMATIOlir OF
chord was a major
the major scale harmonically.
Upon
triad.
major
I.
triads,
and
Its
tonic
the dominant and subdominant
in the tones of these three triads
C-e-g g -
C
e
b~d.
f-
a -
c
fg
a b
c
d was contained the complete major scale. major scale we found some minor triads.
We ought therefore to
But already
in the
admit that as the major scale had ma-
jor triads upon the Tonic, Dominant, and Subdominant, the minor scale ought to
chords, in
have minor
A minor,
upon the same
triads
points.
These
would be
A
-
c
-
e
e - g -h d-f-a.
This would give us the scale
A,
b,
c,
d,
e,
f, g,a.
But in that case the minor scale would lose that most important of all chords, the dominant chord ; for the latter is based upon a major triad. Consequently we must change the minor triad of the dominant into a major chord e-g-b,
For
this
proceeding only
;
into
we have
for instance in
A minor,
e-g}^-b.
sufficient
reason
;
for the rest
150
above analogous formation. Were we to subdominaat also into a major one {d-f-a into d-f^-a), the minor scale would differ in but one chord and tone from the major scale.
we mil
retain the
cliange the triad of the
A,b,c, d, 6;f,gla, must therefore be our minor scale. Its character, harmonic treatment requires In this manner,
from /to
g'jf,
it is
in regard to
it so.
true, it contains a conspicuous progression,
but at the same time
by
also clear that
it is
substi-
tuting/I for/ the distinction of tone-sexes is almost completelydestroyed. It has therefore been concluded to write the ascending
minor
scale,.
and the descending one,
A.g,f,e,d, There, however, are in reality
minor
scale in
two
c, b,
a,
minor scales; or a
different
which two degrees are contained doubly
A,
b,c, d, e,f,f^,g,g'^,a;
and which appears in every way unsystematic.
We shall
therefore, witKout further explanation, take the
systematical one as foundation.
ous second does not agree with our melodies,
but place another tone between (/
we
take the
g!^
above
If the harshness' of the superflu-
—
e
g!^,
a
we need
not use
—g^ —as—
it
/, &c.), or
an octave lower, as seventh from/
Later
we
means to introduce in major or minor foreign chords and tones. It wiUthen depend upon us to avoid this obnoxious progression, by raising the sixth, or by lowering the seventh degree. But for the present we shall win from it several important shqjl find
discoveries,
and even in future we cannot so easily be convinced,
that on account of its harshness too,
it is
inadmissible.
must have a corresponding representative
—The student here advised again to read over carefully the ApA and B, that he may have a clear understanding of the whole —G.
Note.
pendixes subject.
Harshness,
in sounds.
is
151
CHAPTEB
II.
HAEMONIZATION OF THE MINOR SCALE.
Wk have now to find harmonies for our new scale in the same We will as we. formerly found them for the major scale.
manner at
first
follow our figures above the melody, and avoid the
85
8
3
3+3
5
8
:si: 200.
m
-|S>.-
?=
^ faults
221
between the sixth and seventh degrees as formerly.
Here
is
again the beginning of our
_first
manner of harmoni-
zation.
But the succession of the
sixth
and seventh degrees becomes
more difficult in the descending scale for in addition to all mer difficulties we have now the harshness of progression in ;
We might cha,nge
for-
the
No. 108) the second chord, and thus avoid consecutive octaves and fifths, scale itself
(as before in.
-h 201.
m
but in that case the harmony has no connection, and
a point where the harsh progression of the were, the thread of the melody.
connection of these two degrees therefore, to retain as
many
We by
as it
ought rather to double the
their chords.
We
tones as possible of the
or perhaps the whole chord for the succeeding degree
202.
that, too, at
melody breaks,
attempt^
first
chordj
;
-k
m
but in order to make room
for the succeeding tone of the
melody,
153
we will place the two upper tones have a new harmony before us,
in a
Here we
lower octave.
e-9l-b—f, which even exhibits the normal construction, with the exception Our second harmonic mass has of the vacuum between h and/ already exhibited to us such a vacuum, by the filling of which we
Here too, therefore, we will fill the vacuum with the intermediate third d, and have thus a new chord gained the dominant chord. oifive tones
e-g^h-d./
before us, which
we
place at once into the succession of chords
.........
which accom.pany the descending minor
203.
P
#g=
scale.
s=
;?:
-&-
BE 221
Our main
object
is
now
achieved, only that
we have
into a tetraphonic phrase a chord of five tones. to
introduced
This leads us
a further consideration of the new chord.
The
fifth
tone, which distinguishes
it
from
all
former chords,
the ninth from the fundamental tone, and gives to
it
name
the
is •
Chord of the Ninth. Ninth-chord, or Nona chord. Apart from
this ninth
and progression of which
we have is
a dominant chord, the character
already
known
to us.
We
can ima-
gine the nona chord, therefore, as a dominant chord with added ninth.
This additional interval
highest interval of the
first
is
nothing but an addition to the
chord (the seventh) and consequently
follows the progression of that interval.
In the nona chord,
therefore.
The The The The The
Fundamental tone proceeds to the Tonic Third ascends one degree,
Seventh descends one degree.
Ninth also descends one degree, and Fifth
may
either ascend or descend.
In the following
153
^
204.
BE
-£2I
-©-
:22=
=lte
the progressions can be seen the
fifth
consecutive It
we
descend,
it
more
distinctly
only that in having
;
above the ninth, in order to avoid
(Compare a and
fifths.
now remains
place
b.)
nonachord to four voices,
for us to reduce the
because a pentaphonio (five-voiced) harmony
a tetraphonic phrase, and
it
might not at
205.
Which fifth.
m
times be
we have
tory to give two tones to one voice, as
inadmissible in
is
all
satisfac-
formerly done.
J^
^
r
tone here can
Fundamental
now
best be omitted
—
tone, third, seventh
all
?
Undoubtedly the are too significant,
is decidedly the most characteristic tone. The harmonization of the minor scale is thus completed, and
and the ninth
we
can practice
it
in the following,
and in the melodies given
below. 6 5 8 8
3 8
3+9
5 3 8 3 5
3+3
8
154
CHAPTEE
III.
THE NONACHORD. CONTINUED. Our new gladly win
chord
seen, of the
is so
conspicuous a formation that
our major scale also.
it for
It consists, as
dominant chord with an additional
nor, for instance, it
we would we have In
third.
Q
mi-
would be g-h-i-f-a\,.
If we
now add another
third to our
dominant chord in
C major, it
would be g-h-d-f-a ;
and thus we have obtained a nonachord in major, constructed from the tones of the major scale. It is only distinguished from the nonachord in minor
while in the former
by
the ninth, which in the latter
major.
it is
We will
is
minor,
therefore call the one
the major nonachord, and the other the minor nonachord.
But since the major nonachord, is constructed exactly as the minor jiona chord, it follows the same rules.
^ -£2-
207.
m
-0-
^-
-&-
ZS2Z
The Fundamental tone goes to the Tonic The Third ascends The Seventh descends The Ninth descends and The Fifth, if helow the ninth, must ascend (a), otherwise it would create consecutive fifths. If above the ninth, the reason of ;
this rule falls to the
groimd
(b)
and
if can consequently eithei
ascend or descend.
En passant, we chord
is
marked
must
9,
state that in thoroughbass
from
its
most important
figuring
interval.
this
155 Inversions of the Nonaohord.*
Examining the usefulness of the nonachord, we enquire once for
its inversions ; its
But the
the above.
way.
we
positions
we have
at
seen already in
tone-riches of the chord stand here in our
oversteps the boundary of the octave, and no sooner do
It
attempt an inversion, than the whole construction
falls
into
confusion.
-©£2208.
S
m
:si^gg—^^
-go-
In particular positions only are these inversions of the nona-
chord possible, and even then only under
many -g--
209.
m
troubles and carefully,
^" hesitation. We
^ much
"23-
and require no particular names
omission of the
fifth
them Even the
shall therefore only use for
gives us here no relief
them.
For the
collision
takes place between seventh, ninth, and fundamental tone, which latter in
an inversion steps right between the two former.
This leads us to another manner of relieving the chord of tone-burthen,
We
new chorfs of four
its
omit the fundamental tone, and thus gain two tones, therefore
new Septime
chords.
same manner we gained formerly the diminished triad from the dominant chord. Below are the two new septime In the
chords, as the issue from the nonachord.
210.
m
The latter only deserves a new name, because by and by it will become important and since the diminished triad is contained ;
therein,
we
will call it
Diminished Septime chord.
We need hardly mention that the intervals of this chord follow the same laws as those of the original nonachord, i. e., the * See Appendix E.
156 fundamental tone
h
(former third) ascends, the
(former sev-
fifth
enth) descends, the seventh (former ninth) descends, and the third (former fifth) can either ascend or descend.
These new septime chords can be inverted without and without requiring further rules.
diificulty,
311.
What
intervals,
ask now, can be omitted or doubled?
we
According to former rules the third
omitted or doubled
;
is
the one which can best be
the latter, because
the only one which
it is
can either ascend or descend.
4
-e-
212.
m3 r Former
A
&. -ei tfe
'
i& te
"^
Y
theorists
ent of inventing
-G>-
1
have prided themselves no
names
little
for every insignificant
on their
new
tal-
formation.
This served only to confuse the, mind of the student, without in the least facilitating his labors. the most important chords.
be
sufficiently designated in the
if
have only given names to
little
variation
figuring.
We
from these can
know
that the
most important intervals of these chords, we represent them in our figuring it will be all-sufficient.
ninth and seventh are the
and
We
Any
157
CHAPTEE
IV.
THE FREER USE OF THE NEW CHORDS.
We cies
are
now in
possession of three species of triads, three spe-
of septime chords, and two species of nonaohords.
We
are applicable in major as well as in minor. rules according to
;
us, therefore,
new harmonic
instructions can
ted here
know
also
the
which they are applied.
Each new chord gives tion with others,
mer
All the
two of the septime chords and one of the nonaohords
triads,
by
itself,
and
combina-
in
designs, which according to for-
One only
be easily found.
shall
be indica-
the combination of those chords which have arisen from
either omission or addition of intervals.
214.
:i=
m
'^
-&-
These chords give us the best harmonic connection possible, except the combinations of positions and inversions of one and the same chord.
We
also discover here a
new manner
of avoid-
ing the resolution of those intervals which are bound to a certain In No. 160 the third h went to d, the seventh, _^ went to g, because the same chord remained, and these tones were represented by other voices. Here progression.
215.
E
-©-
T /goes
to a instead of .
a nonachord.
r «,
because
it
chord remains and becomes
Then again atof, and ftob; not because the nona-
chord remains, but because
whence
tfie
it
goes back into the dominant chord
issued.
However
brief
we
can
make our
instructions
by
reference to
158 the preceding,
it is still
necessary for the student to continue his
practice of harmonic combinations, in all inversions and positions,
and to employ them in the formation of sequences and preludes, and particular attention should be given to the harmonization of given melodies.
To
this
we add
the following remarks
1.
Major Melodies.
"We have foUnd two new chords
for
them
;
the major nona-
chord and the septime chord arising therefrom, with
its inversions.
Both chords may be applied to all the tones contained therein, if it can be done without causing confusion and faulty progressions, for instance,
^feS—tfifS
N
J
'
rrrE^ ' J
1
h
i-^J-
U JJ
=^ 6
2 6 3
4 5
4
6
2.
5
6
6 7
„
-•-
4
Minor Melodies.
We have occupied ourselves so little with the minor scale, that we now
require a
more thorough
practicing of formations in its
compass.
As introduction it would be well for the student to construct, from the chords of the minor scale harmonic designs and sequences, as
many
as he possibly can.
Then he ought
to treat every
159 given melody in two manners.
First according to thej^rsi
ner of harmonization, and right below
and third manners
;
i.
by choosing
e.,
man-
according to the second
it,
his chords
and using them
in their inversions.
We give here
an example
of,
the last manner; for the
we
first
have no room.
^iite^i
217.
'M
'^i
isi -i»
EBtt.
1
5
-M-li
§t -l^ 6
H3 1
4.,
tl8
iEk^ ?•=
M^
i»^=S--
t
H
'&Uf.
:p— •-
3E£
ife^ 4 t!3
^-i: S*-
6
t|6
2 6
6
4 5
H4
m
4-a^
H
87
We find in
of the above some new signs which
the figuring
require an explanation.
Until
now we have taken
all
our chords
as the ordinary key-signature (the sharps or flats placed at the be-
ginning of a composition) indicated them.
very well.
Bnt
with the actual
The same has
in
minor
scale,
In major this answered
this key-signature does not correspond
and we have to make use of
to be done in the thoroughbass
figuring.
accidentals. In,
C mi-
d would indicate the sext chord d-f-bb. minor, and we, therefore, our scale of
nor, for instance, a 6 above
But there is no h\, m must place a before- the i\
If
6, in
order to change the
an accidental without figure
is
Thus the
bass, it always refers, to the third.
b},
i\
g-b],-d)
is
would indicate the
If the
triad d-f^-a.
G
g-bVf-d
(not
minor, a | above the d Frequently the figures are crossed
key were
instead of placing a # before
Jt|.
under the second
note of the bass in No. 317, indicates that the triad
wanted.
into
placed above or below the
them
:
%, $, 4, 0,
jS,
%.
160 Additional Licenses of the Dominant chord.
3.
We
now completed
have
immediately from the
first
the circle of harmonies developed
fundamental harmony and the tones
of the major and minor scales.
Among
all,
the dominant chord has proved itself the most pro-
and to the Already on a former
ductive, having given birth to the diminished triad
two nonachords with
their
septime chords.
we have permitted this chord a its third, if covered by the middle
occasion
less restricted progres-
sion;
voices,
was allowed to
descend, while the seventh was permitted to ascend, in order to
make
the succeeding chord complete.
It is
to favor the better connection of chords.
fundamental tone, therefore, to remain as chord (a) as tal
tone (b)
if it ;
or
now
our next object
We
will permit the
fifth
of the succeeding
were merely the octave of an omitted fundamenit
may
descend into the third of the succeeding
chord, instead of its fundamental tone (c), while the seventh (cov-
ered
by
taves,
the other voices) ascends, in order to avoid covered oc-
which might be obnoxious, particularly when in the outer
voices (d).
218.
P^
rr
T-
The fundamental tones of the nonachord may
also participate
in the first license
219.
but the second
^i i =F=^
is less
admissible, because the accompanying ninth
forces the seventh to follow its natural laws.*
* See Appendix F.
161
SeTcnth Part. Modulation into Foreign Keys.
All our formations thus
far
moved
'within the
compass of
any-
one particular major or minor key, and contained neither tones
But in order to extend the sphere
nor chords foreign to that key.
we we must
of our labors, and to add to our melodic and harmonic means,
must
call
other tones and other chords into action,
i.
e.,
combine the tones and harmonies of two or more keys in one The technical term for this proceeding is " fo modu-
composition.
late into foreign keys,"
or "
to
modulate."
This combination of several keys in one phrase can take place in
two
different
remain in
it
ways.
We can
an essential part of the same.
key
iri
it
In such case the step from the one
into the other is called a " transition."
Or we can merely touch or even a sequence. If,
modulate into another key and
to the end of the composition, or at least form
therefore, in a
new key, use one or a few chords, we have a mere " digression." composition in major we would introduce the
In that case
passages and phrases like the following.
220.
which are not indigenous to that key, but which would have been touched merely accidentally, without actually exchanging jor for another key, these foreign chords sions."
how
How to
arrive at such chords,
would be
how
raa-
called " digres-
to classify them, or
to construct them, requires no particular instruction, as the
results of the rules of transition will furnish all the requisites.
Transition, then, according to the above, is to leave one key, in the course of a composition,
and to se^e
one, in order to construct, or execute in
whole.
it
distinctly another
an essential part of the
162
CHAPTEE
I.
MODULATION FROM ONE KEY INTO ANOTHER.
We
modulate from one key into another by exchanging the
tones aes and harmonies harmonies of the one for those of another instead of
'^i
with
its
its
<^>
three major triads
a,h,
with
;
for instance,
C major, «i
fi
((7,
«!
ffi
ff,
h
F\
«i
&c.,
c\,d,e,f%g%
we take
A major
'
a,
This womld be the most troublesom,e manner of modu-
three major triads {A, E, D), dzc.
most complete, but
also the
lalting.
But we perceive immediately that much is here mixed' up wMch The two keys, however distant from each other, have several tones in common (a, 6, rf, e), which tones, therefore, they are not distinguished from each other, and in which we do not perceive that C major has beeir excMnged for A major. These mutual non-distinguishing tones need not,, therefore, be touched. The remaining three, /|, cjf, g^, indicate the transition. But even in our monophonic phrases we have already used foreign tones without exactly exchanging one key for another. We require a more distinct sign of transition than mere single tones. This we can only expect from that harmony in which we have discovered the first conception and the foundation of keys. But which are the harmonies which serve us as the surest sign of a transition ? Those which surest indicate their key. Therefore might be called superfluous.
iiii
the dominant chord with the nonachords derived from triads contained in it are the ones.
chords appears in the course of our modulation,
have entered
We
its
it,
and the
The moment one of these
we
say that
we
key^
attach all further observations at once to the first transitionchord, the " dominant chord," and then pass on to the others.
163
THE DOMINANT CHOED.
1.
We know already that every own key and
Its
in
no other.
foreign dominant chord
major, the chord
makes
e-g!^-b-d,
dominant chord can only therefore, in
If,
appearance, for instance, in
its
at once impossible that
it is
exist in
one modulation a
we
C
can
in major, or in any key but A. The dominant chord is the distinct sign of the introduocion of its key. But it is no sign for the tone-sex for in major and minor it is exactly alike. The above dominant chord tells us dis-
be
;
tinctly that
whether
we
we
are no longer in
A
are in
the following chord
we
are in
;
A
major or
(7
major, but
This
minor.
we have gone
if a-c|-e,
it
is
to
is
undecided
only decided by
A major,
if a-c-e,
A minor.
Since the dominant chord
is
the decisive sign of its key,
it
must
be the decisive means to modulate into its key. If we tend to modulate therefore into any other key we have but to also
troduce the dominant chord of the latter.
inin-
In order, for instance,
A
major or A minor, we have to modulate from any key into but to introduce the chord e-g^b-d, and since the dominant chords of major and minor are exactly
We
major or minor.
alike,
we
are at liberty to go to
need, therefore, only to
know
the domi-
nant chord of a key, and the proper manner of its introduction, to
modulate into the same. But this modulation must be effected in the course of a composition,
Not
according to the rules of harmony.
alone that faulty
must be avoided, but the chords shall also appear We must bring the transition-chord (the domiwell connected. progressions
nant chord of the
new key)
into connection with the last chord
of the preceding key; both chorfls must be connected
It is
by mutual
•
tones.
necessary,
first
of
all,
ding key was last touched.
to It
know which chord
nor a nonachord, nor a diminished triad to return to
tll%
tonic triad.
of the prece-
cannot have been a dominant chord,
Our
;
for all of these
have
transitions can therefore only
be attached to major or minor triads. major triads and three minor triads. major and two minor triads. Here
We In
have in major three minor we have two
164
:£S=^E1E:: '-^=W
a the six triads of G major, and at b the four triads of minor to which a transition-chord could be attached. It is clear that we can attach to each of these chords any tran-
we
A
^
EES
221. see at
more tones
sition-chord which has one or
With
the chord
for instance,
c-e-ff,
we can
in
common
with
it.
connect the following
dominant chords
222.
*
m
W
-&&&
Deducting the dominant chord at preceding key,
the
D,
F,
D\,,
tion that
B\,,
we have
G,
A, B, and
we have used
h,
still
because
it
brings us back to
eight actual transitions
We
'A\,.
:
to
need hardly men-
the inversions of the dominant chord, in
order to effect the transitions as fluently as possible.
we
If
intend
stance from
c-e-g,
now
to
make
a transition from a chord, for in-
into a key, the dominant chord of which is not
we make use of a mediator. In going we would require the chord which has noTnutual tone with c-e-g. We, therefore, go
connected with the former,
from
C major
5-c?|-/|-a, first
to E, for instance,
to another chord in
G major which has one or more tones in com-
mon is
with the dominant chord of S, and which at the same time connected with the chord c-e-g. Of such chords there are sev-
eral,
and every other chord
the mediator between 223.
A
c-e-g
in*
and
G major
can here accidentally be
J-rf|-/}f-a.
B
i=
z^z W-.
-fr =^^
feE ^3Z
m 1
165 It is
lies
easily perceptible, however, that one of these
nearer than the other
the one at e
;
the mediating chord has no tone in
and
common
only related to a degree, because
is
it
mediations
the loosest, because
is
with the
first
chord,
belongs to the same
key.
However, the connection by means of tones in common, (as already know) is merely external. A more intimate relation exists between such chords as indicate nearly-related keys. Since a major or minor triad always reminds of that key in which it is the tonic chord, we must consider those chords -which remind us of the to-be-expected key, or indicate the way to it, as
we
In No. 223, for instance, the chord e-g-b
nearer than the other.
reminds us by
at B
itself
E
for the transition into
;
of the key of E, and prepares us best
the chords at c and a, indicate at least
the direction, following which at
D and e
i. e.
;
keys with
ation, while at
Finally
we must
consider that a transition-chord, though con-
may
we
Therefore
shall
foreign chords to prepare the transition,
major
to minor,
major
:
in
chord
and minor to major
c-e\,-ff,
dominant chord
and
a\,-c-e])-g]},
by means of c, was
stance, at
we
i
--§-
by
less foreign
use also of
arbitrarily changing ;
for instance,
in
Thus, in No. 224,
c,
too distant from a\)-s\r-gh-
C major,
on
-@-
^ ^jp¥
321
ac-
In order to effect a bet-
interpose another chord as mediator
Z2©=
.»-
Sr
C
the
though connected with the previous still
;
as for in-
A
224.5fe^=§=
$
foreign tones
now make
triads
a-c-e in a-cj(-e.
count of the three foreign tones ter connection
many
contain so
by means of interposed chords with
desirable.
c-e-ff
direction,
At b, therefore, we see the nearest mediwe find the most distant ones.
flats.
that a mediation is
E
afterwards find the key of
d and e
taining one connective tone,
tones
we
however we are led into an opposite
-tr--^
=i-=
^fepE
-|S>-
-#-
-&-
W^-ft
166 the chord
c-e\,-g,
(we change the major chord into minor) and thus
gain not merely an additional mutual tone, {c-e\,) but obtain also a harmony -vphich reminds us of C minor, and brings us
C
than
Sh major
nearer to
major.
mediations of the same transition tor for the abrupt transition of
;
at
At b and
c
we
find other
d and e we find a media-
No. 222,
g.
any key, the most practical the chord ^om which we modu-
In order, then, to modulate into
proceeding
is,
to write
down
first
late
and at some distance from
key
into
ting
from
225.
S:
226.
which
C to
we wish B, the
this the
dominant chord of the
For instance, in modular sketch would be the one at a.
to modulate.
first
fe fe=
3t-&- -3-
iSj -& -&&-
=fe-
MP
'ZSl
^
Then we must examine whether these two chords have sufficient connection.
In the above case the tone e is the connective tone, but
the remaining tones are in absolute contradiction to the first chord
G major. If the connection of the two is not satisfactory, a glance at the chords will soon suggest a harmony which conand to
nects the two chords.
Thus in the above (b), we have first interthen the major chord, a-c|-e, and finally have taken the dominant chord of B. We must be careful, however, to place the foreign tones in that posed the minor triad
a-c-«,
voice which can take
it most conveniently, i. e. which has formerly had the same degree now to be raised or lowered. Thus in No. 225, a, we have given c| to the upper voice which had c and aj} to the lower voice which had o. A strict adherence
to this rule will be our best safeguard against harsh progressions.
According to the above developments, the dominant chord gives us the following modulations or transitions into all the dif ferent degrees of our tone system.
From Cto
167
f-
We have here only
employed the nearest and best mediating chords. Mediating for every particular case and its application to minor keys, and the exercise in diflferent positions of chords and other keys
is left
to the
pupiL
Each of these modulations, as we know already, can lead to minor as well as to major and, as a matter of course, the keys of B\), E\, F\^ &o., can he exchanged at any time for their enharmonic representatives C|, i)|, G'b, &c. We must now speak of a modulation which does not strictly ;
deserve that name, and
for
which our ordinary transition-chord
suffice. We have reference to the major and minor of the tonic, (for instance, C major and Cminor.) The dominant chord which the two keys have in common is cer-
(dominant chord) does not
tainly the nearest mediator
228.
it
could
seize.
TM
but exactly because of these keys,
we
its
being a chord belonging, to either of
can no longer be the sign of a transition.
sign is required, the
the nearest indication of our going to minor, (a)
229.;
If
such
minor triad of the subdominant would be
168
and the major major tonic
triad of the subdominant, perhaps preceded by the
would indicate the
triad, (b)
transition
from minor to
major.
THE BrONACHORDS.
2.
these chords
Since
complete
contain the
they must be capable of having the same into a key,
only that
modulating
And, indeed, they
demand and find
fur
same mediation, on account of their tone-bulk they are somewhat more
nish us the
difficult
and characterizing the same.
dominant chord,
facilities, for
same
transitions,
the
to manage.
But on account of their nature they have the additional advantage of being at the same time indicators of the tone species into which we modulate. The major nonachord leads us to expect major (a), the minor nonachord indicates ininor (b).
23o.a^^3^3i;
-bpg-
Owing, however, to the just-mentioned existence of the dominant
we
chord in either,
take occasionally the liberty
of considering
every nonachord as a mere dominant chord, and resolve them in either
major or minor.
-&-
«^
S-
-&-
S-
S-
-&-
That the resolution (a) No. 231, is less satisfactory than the one of (b) 231, is apparent, and that the one of 231 (c) is more satisfactory than the
3.
one 231
(b), is apparent.
THE SEPirME CHORD OF THE MAJOR NONACHORD.
We know that this chord originates from
the nonachord, and consequently indicates that chord and the dominant chord as well as the key. Nevertheless it has not the perfect characteristic decision of others
;
for,
according to
well in the parallel key well as in
major.
;
But
its
for instance
tone-contents,
it
can exist as
h-dfa can be
in
A minor as
this insignificant
doubt
is
soon silenced
169
by
the succeeding chord, -while our
own feeling anticipates
the signification and the progression of the chord. stance
the
resolution
of
C
into
h-d-f-a
and yet the one at b
fectly satisfactory,
already
Thus, for
major, as at a,
is
in-
per-
not exactly inadmis-
is
sible,
232.
ii but requires a certain confirmation as at c. Independent of these deviations, however, the septime chord furnishes
of modulations with or without mediation, for
its series
instance to
D
F
~^*"~
Si=
233.
E
Ab
M m:
m
i
-&^"
fei::
simply lacking the vigorous step from fundamental tone to fun-
damental tone, or from dominant to
THE DIMINISHED SEPTIME CHORD.
4.
We chord, it
know
that
and with the
must share the
this
latter
chord
is
derived from the minor nona-
from the dominant chord.
faculty of either, in effecting
With
modulations.
tonic.
the original minor nonachord,
the minor species, but like the former
:^=
234.
=a^
it is
:i^--
it
-•-
were not so
its original position, indicate
turn
belongs to
--^i-
-#-
-M-
If this deviation
it
used in major.
--ii
-m-
Consequently
and characterizing
-»-
trivial,
it
-0-
would, according to
the minor key at once.
But in
has none of the vagueness of our last septime chord.
cording to
one key
;
its
derivation and tone-contents
for instance the chord
h-drf-a\)
it
re-
Ac-
can only belong to
can only be found in
G
minor. 5.
We
have
first
THE DIMINISHED TRIAD.
considered this chord as a dominant chord with
170 omitted fundamental note h-d-f, for instance, appeare.d to iis as But since the diminished the incomplete dominant chord of G. ;
diminished septime chord, consists of thiuds, placed
triad, like the
we can also derive it from this chord by fundamental tone and retrace it to the key of the diminished septime chord. For instance, J-c^ referred to g-h-dr-f, one above the other, omitting
its
major or would indicate the key of it would refer to g\-h-d-f, therefore to
C minor.
In the other case
e-g^-b-d-f,
or in other words
key of A minor.
to the
We
see
by
that the diminished triad,
this
though sharing
the modulating faculties of the dominant chord, modulates with less decision.
indicated keys
The succeeding chord only tells us which of the two was meant. The following modulations, for in-
^^
stance,
235.
=2Z^fi
i; -&—S-
can be based on the dominant chords of and lead to F,
major or minor
;
J3\,,
A,
£
but they might also be based upon the dimin-
ished septime chords,
dingly to B, G, F^,
-cjlf/;j| ffjf,
ejif*,
minor
and we might lead them accor-
(or major.)
236.
4 Only the
/*
final chord's in
fU
4
each of these examples
tell
us what key
follows in reality.
Our
ear,
key which
however, always expects after a diminished triad that is
nearest related to the previous one.
major, for instance, the chord b-d-f occurs,
and expect
C
major, because this key
A minor.
is
we
trace
Thus it
if in
G
to g-b-d-f,
nearer related to
G major
same chord occurs in ^minor, we trace it to g^-b-d-f, and expect A minor, because this latter key is much nearer to minor than major. than
But
if the
F
6.
THE DOMINANT TKIAD.
This chord evidently lacks the decision of characterization which the dominant septime chord vrith
its
sub-species is in possession
171
The chord
of.
that the
can belong to either
g-h-d, for instance,
D major, C major, dominant
or
C minor.
triad, if
major,
Yet we have observed already,
succeeded by the tonic
triad, will
be
treated as an imperfect dominant chord, and be resolved accord-
Therefore a mere triad can also become a sign and means
ingly.
of modulation
if it is
distinguished sufficiently from the until-then-
prevailing key, and if
resolves like an imperfect dominant
it
chord into the tonic harmony of is
Thus
fundamental tone.
its
it
here at a
237.
The phrase according
A
to the first chord is in
the triad g-h-d disagrees with this key, and since
it
minor.
But
resolves im-
harmony, it indicates sufficiently the minor to C major. Certainly it might also as at B have been led to major or even D, and this is exactly the lack of decision which we have mentioned. But even here, our mediately into
its
modulation from
tonic
'
A
ear anticipates the decision
major, because
nearest relation, while tion to
;
it
expects the
A minor and C major Cf
or
D
first
modulation to
C
stand as parallel keys in
stand only in
more
distant rela-
it.
7.
THE MINOR TRIAD.
Finally this chord can also be the sign and means of a modulation, it
provided
it
contains one or
indicates at least that for the
no longer, and
we
238.
(b).
By
foreign tones.
this
the original key reigns
expect either a return into that key (a), or an
actual modulation into, a
nous
more
moment
key to which the new chord
is
indige-
172
We need not
add that our former mediating chords with
for-
eign tones belong to this category.
In regard to the succeeding chapter, the application of these
new means, we have now them that
in three
we have
1.
to remark, that
different views, each
to consider each one
We consider the modulation
by
we have
of which
is so
to consider
productive
itself
into foreign keys, merely as
means to combine the harmonies of
several keys in one compo-
sition. 2. 3.
tions.
We construct with them, independently, new formations. We use them in more extended and well constructed formar
173
CHAPTER
II.
THE NEW MEAJSTS INTO THE HABMONIZATION OF GIVEN MELODIES.
INTEODUCTIOlSr OF
We
have now, therefore, before us the
combining
ability of
A
one phrase, in a single melody, two or more keys.
in
tinction arises
must
dis-
We
now, which formerly we had not to make.
distinguish
melodies which absolutely require modula-
tion into foreign keys,
from such melodies as merely permit,
We might call
without absolutely requiring them.
them
indi-
genous and digressive melodies.
The
digressive melodies will always lead us for
Our harmony,
time into foreign keys.
be constructed so that the
new
How
key.
in the last chapter.
It
and effects this modulation into be done we have already learned
Once arrived
in the
new key we
modulation leads to
;
Whether the melody
3.
treat
it
for
no further instruo
a modulation, and where this
or
of one or
adnqjts
sions.
shall rather
more
digres-
'
In the latter case
and
it
remains only for us to ascertain
Whether a melody requires
1.
less
have to
it faciliates
this is to
the time as an original key and require for tion.
more or
therefore, will
we
shall
always prefer that which lies nearer,
modulate into nearest-related keys, (the keys of
the dominant, subdominant and the three parallel keys), than into
more
distant keys.
Having arrived
ceed again on the same principle, to unnecessarily seizing another
A.
The
i.
e.,
new
we
in the
new key we
pro-
prefer remaining in
it
key.
The Ascertainment of Digressive Melody.
characteristics of a digression can
be external or internal
the former actually exhibited, the latter merely indicated in the
melody. 1.
These consist
EXTBENAL CHARACTBEISTICS.
in the foreign tone of a
melody.
If in a
melody
174
Q major the tone f\ makes it's appearance, we consider it as no longer in C; for the tone/| is foreign to the key of C major. Having arrived now by means of this tone at another key, O in
major, for instance, and the tone/t] to consider the there
/
makes
its
we have
appearance,
again as a sign of digression, for in
major
no /
is
But to what key does
this foreign tone of the
melody lead us 1
we cannot answer with complete certainty. We suppose at first we have arrived in the key in which the foreign tctoe first appears. Proceeding from C major, for instance, we This question
would consider f\, but to
O major,
major,
we do
not as leading to
as the
key in which /jj
D
D
major, as the
first
A
appears.
A
not consider as belonging to
but as belonging to
E minor, &c.,
major,
first
major or
c| in (7
B. minor,
key to which the
c\ is
indigenous.
But these are
mere suppositions
all
239.
;
we
can
make
quite
diffei'-
This melody, for instance,
ent uses of such tones.
^
i
can be conducted from
C
can also be conducted to
major to
O major
(a), it is true,
but
it
^ minor (b).
-J240.
At some viz.
future time
we shall even
discover another possibility,
that a foreign tone belongs to no
:
harmony, and consequently
harmony, nor modulation, nor digression.
indicates neither
This insecurity of external characteristics leads us to
INTEBNAL CHARACTBRISTICS.
2.
These are based upon the regular progression of tion, and upon the principles therein developed.
To sion,
wit
we
—as soon
interpret
modulation, and
which
is
as
it
we
all
find a doubtfiil external sign
modula-
of
digres-
according to the principles which guide our
among
the probable keys
we
select that
one
the nearest to the principal tone, or which otherwise cor-
175 responds with the laws of construction,^ led,d
the phrase No. 239 from
and not to
est related,
melody the nearest key
Even
if
a
E
G
major to
minor.
/
again appears,
to
G
we
If
Accordingly
Q
we would
major as the near-
then in the course of the
G
should go to
major, as the
containing an_/5 in preference to any other.
melody contained no
foreign tone,
we would
aslc
whether internal signs would not make a digression advisable, nay, preferable to the retaining of the the
melody of a
241,
first
part in
C major
same key
;
if,
for instance,
should end thus
:
176
We ascertained still later, mental tone,
third,
fifth,
that every tone can be either a funda-
seventh, or ninth of a chord.
But at
we were limited to the indigenous chords. have now a much larger field for such investigation
that time
We
every tone of a melody can be not alone, third,
fifth,
;
for
seventh, &c.
of a triad, septime or nonahchord of the key in which the melody is
written, but in
Thus the tone 1.
any key which contains that particular tone.
C, for instance,
can be
Fundamental tone of a major, minor, or diminished
three septime chords, and
triad,
two nonachords.
244.
i 2.
^
Third of three
^.
^
^s '&-
triads, three
=p^
-&-
septime chords and two nona-
chords.
245.
&
1?"
'-»-'
W--
3.
^
^
Fifth of three
>fe«-
M ^
triads, three
^
septime chords, and two nona^
chords.
246.
fe^=F*=«
I^a^^a 4.
Seventh of three septime and two nonachords.
247. -TT
5.
*
lo
"
F
—"g—F—
"~ I
^
—^
1
F
Ninth of two nonachords. 248.
,si
w.
:M b!
We have discovered, monies
*
according to the above, one and thirty har-
for every single tone, independent of the different inver-
177 Application of these means
C.
We have now ascertained
to
indigenous or digressive melodies.
how many
chords can possibly be
used for every tone of a melody, and the question arises which of
them we have to choose, or which to exclude. Our general rules wUl be sufficient for the present. No chord should be chosen, the introduction of which would cause faulty progressions the connection of the harmony must be retained, and each, must be con;
ducted conveniently (fluently) and intelligibly. develope
The
rest will
of our labors.
itself in the cdurse
Our first care next to this, will be to preserve the unity of key, and the turning points of the modulation. We .shall, therefore, end with the dominant chord and the tonic triad, and generally ,
begin with the vyith
latter,
we
shall
mark
the thesis of a phrase
Finally, in the course of a composition
of the dominant. shall
while
the triad of the dominant, or with a modulation to the key
always think
first
we
of those chords which belong to next-re-
lated or near-related keys, in preference to chords of keys.
-
more
distant
•
Let us attempt now to apply our new means to one of oui former melodies (No. 195).
^f^fe
i
255.
n
S
6 f6
fcl
b5 6
4-7
6The first chord remains unchanged. The second tone we consider The d immeis fifth of a triad which brings us to A minor. 9
diately after, [g\-b-d-f)
we
consider as
fifth
of a diminished septime chord,
which forces the tonic triad of
sixth chord brings us back to Cmajor.
chord
g-h-d.
We
can either consider
A minor upon us. The The thesis closes with the
it
as dominant triad in
C
we accompany the preceding e with the or we can consider it as tonic triad chord c-e-g, {vide No. 195) of G, in consequence of which we have to modulate into it. Accordingly we treat the tone e as ninth of the chord (i/|-a-c-e, or major, and in that case
;
as seventh off-orc-e.
We have preferred the former, because it is
easier for the bass to proceed from c to
d, than from c to /|. and dominant pi-incipally in the parallel the occupied Having
178 first
part
we
turn
now
some other
to
related keys into which to
There remains for us the parallel of the dominant,
modulate.
It would require the chord its parallel. some harmony derived from it to get into the first of
the subdominant and 6-rf|/|-a, or
the above mentioned keys
but
;
these chords are too foreign
all
We are limited, therefore, F major and D minor, if we insist upon introducing
to the last four measures of the melody. to the keys of
modulations into foreign keys. Therefore, (i-c\-e-g,
minor,
chord
its
consider the second tone
o-c-e ;
but since
is
it
the
as fifth of the chord
Being once in
modulation.
D
of the sixth measure with the
e
our object to go with the next
F major, we prefer the chord
c this
e
modulate into J) minor.
we might accompany
tone into
by
we
in order to
a-c-e,
because
The remaining chords
it
prepares
require
no
further explanation.
The chords which we have chosen trary.
Thus, for instance,
No. 255, as at
256 or continued
a,
here, are
by no means
arbi-
we might have treated the fifth measure. it
as at b or
c.
The reasons for
our present selection will become apparent at a future time.
256.
THE COMPLETING OF OnR WORKS.
We will now place our
phrase completely before us, in order
to attach our further remarks to
present a form
somewhat
it.
No. 255 would perhaps
like this
257.
Looking at the harmonic contents of our phrase, we cannot but observe, that
we
devote more space and time to the foreign keys
than to the principal key.
We cannot justify this, proceeding which
179 takes
away
the unity and firmness of the whole structure, except
with the plea that
it
was our object
many keys as
to introduce as
possible.
We must further remark that in finding these foreign chords we have observed a two-fold proceeding. At first we enquired which chord was suitable to
this or that
particular tone of the
melody, and retained the key into which we were led by the lected chord.
we had
keys
Then again
we
in the antithesis,
se-
consulted what
already employed, and selected those harmonies
which woujd bring us into the other nearest-related keys. Finally, 'it is clear that the above treatment is by no means
With
the only one possible.
inversions, the harmonization It is
not easy to introduce a
the aid of foreign chords and their
might be varied almost to
new
the treatment of the whole phrase.
infinity.
chord, without its influencing
Here, for instance
treatment which does not even begin with the tonic
we
give a
triad.
259. 1
I
I
I
I
!J
j
it^zMizat :tT=^:
1
I
I
3ti^--
IPW^m^^Gr-
:d.t::-.
t^
I
2
6 3
tl
m \,1
mm
Jalii--
bbY
b6
'^
Ul^-d iW
i 5
No
sooner had
we touched
the keys with
flats
than our whole thoughts turned to these.
(2d measure),
The
thesis closed
upon the dominant it is true, but not before a chord from C minor found room, and the antithesis touched upon G minor, minor, and JF major. The third tone of the second measure has two chords (and consequently two figurings) beneath it. This is no fault, for we can rhythmically dissect every tone and treat it as tone-repeti-
F
tion.
The penultimate chord had
necessarily to be a triad, becai.ise
the resolution of the preceding chord required such a one.
order not to lose the dominant chord for our
final
But in
cadence,
we
180 have led one of the intervals of the triad into the seventh (/), and thus satisfactorily ended the phrase. Figuring of two or more chords.
How
can
harmonies
we
douhle or triple
distinctness sake the triads,
(by
two or more For
indicate that a bass tone contains
By
?
figuring
in succession.
on such occasions, are also indicated
^
5 3, 3,
5,
though they do not absolutely require
We have already,
at a
it.
former opportunity drawn the attention
of the pupil to a false relation, which, with foreign tones often finds its It is
way
into our harmonies.
(Page 166.) (mi contra fa), and has
technically called cross relation
given ample opportunity for the writing of volumes.
Though the pupil who follows our
principles in the conducting
of his voices need not fear the occurrence of such relation,
not pass this subject without devoting to
it
we can-
a few remarks.
Proceeding from one chord to another which has one or more notes in
common with the
first
one,
it
has generally been our rule
to retain such notes in that or those voices in which it or they first
appeared.
Thus, for instance,
we
consider
it
better to write
as at A,
I
E r than to write as at
Now,
if the
r
r
b.
succeeding chord brings us a degree which already
existed in the former chord, save that
pressed
by
^ we
-*
I
^
it is
now
raised or de-
accidentals,
r r
f
'
r
also consider it best to give such
r
^^
an altered degree to that
voice which had formerly the original degree.
For
this reason
181 the notes alto)
and
e
/|,
e}),
c|,
appear in the same voices (treble and
which formerly had the notes
e,f,
But the moment we deviate from
e\)
and
c.
proceeding, and
this natural
give the altered degree to a different voice from the one which
had the
original, -
J
i^ !
mi rt rr i--^r-r
Mz
l^z
=F=is
the voices have no longer a flowing and natural progression,
and stand to each other in an unnatural relation. Thus at a and B the treble seems to stand in C major, while the bass is in C
At
minor. in Z> or
D
c the treble stands in
G
At d
major.
minor, while the bass stands
the treble indicates
while the bass stands perhaps in
G
Such equivocal relation of one voice to another
Former
cross relation.
D
C and
minor,
major.
theories have laid
much
called
is
stress
upon
matter and have earnestly and anxiously warned against
We,
it.
however, need attach no such importance to this matter
not
;
merely because our manner of conducting voices avoids such lations of itself, but also because
may
we never
a
this
re-
decide one-sidedly, and
have reasons occasionally to permit such cross-relation
These reasons
we
will
A cross-relation is
now
point out.
disagreeable, because the voices do not pro-
gress flowingly and naturally, and because the key of the one contradicts that of the other voice. case, or
when
design, or, finally, when
advantage,
Whenever such
is
not 'the
the harshness of this relation corresponds to our
we shall
In pointing out
by
the passing annoyance
we gain a greater
unhesitatingly permit such cross-relation.
the admissible cross-relations,
we meet
first
those cases in which the degree to be altered exists in two voices at once, tion.
and consequently can submit in one only to the
Here,
at A, the
altera^-
for instance.
upper voice cannot go to /| with the lower voice, withHaving once admitted the doubling of /in
out making octaves.
182 the
first
we must of necessity lead the two fi The same is the case at b, c, and d. But
chord
directions.
in different it is exactlj'
because ol this necessity and because the voices are led as natueasily as possible, that this progression is permitted
and
rally
and can hardly be counted among the cross-relations. This relation is also covered or smoothed over, when the contradictory tone has the appearance of a
newly entering
voice,
as at A,
fe
-£3.
:d^i-4-
3^;
^=0=F+=if I
when
or
two opposed voices indicate
the
I
different,
but near-related
we can see how easily such crossbe avoided and how much milder and flowing the At
tones, as at b. relations can
c,
however,
modulation can be made.
A
similar state of things
when
is,
the cross-relation occurs in
chords which belong to different phrases or sections.
W-Si
S
ir
u
m
--^
first
rrf-
ff
I
Here, in the
j^_
example, four and four chords constitute a phrase,
and consequently the cross-relation of
c
cause they belong to different sections.
we the
two and two chords
and
c| is admissible, be-
In the second example
as different links,
and permit
of the second link as a newly entering voice.
If in either
consider cjf
I
case the rebellious tone
more
only to
is
conceived more distinctly,
plainly distinguish the sections.
it
serves
The same occurs
in the following phrases
I
„l
fe^
ip-jz
-J-
r^UT¥
We have now proved ness, can
J
5S
fe^ T
r
that a cross-relation, with all its harsh-
be even desirable, as the only right expression, when
it
183 is
our object to introduce a voice decisively.
we quote
tion,
As
a further illustra-
G major
here a passage from Mozart's Quatuor in
which of late has been the theme of earnest discussion among
German and French
Mozart commences thus
theorists.
s; m^
:
r
OES
-
^- p-rrf~f
^^^
gloomy manner, before entering the fresh C maThe second entering voice leaves us uncertain whether c-f-a\) {F minor), or c-eh-a\, {A\, major) will appear. The succeeding
in a mysterious, jor.
voice decides for the latter, and with the next voice (the treble)
Mozart breaks
this
harmony
at once,
and keeps us in anxious
uncertainty, until with the sixth quarter-note he turns decidedly to
G
major, the dominant of the principal tone, and then con-
tinues.
Who
perceives not that this piercing tone
cross-relation with the preceding
—
it
a of the second voice
lutely proper and indispensable to the idea of the
forms a
—
is abso-
composer ?
If
Mozart had resigned the a\) or the a^ of the higher voice, the character of his phrase, and the analogous succession of his voices would have been lost. For the same reasons cross-relations are well applied, when we use them in slow harmonic sequences and sharp and weighty modulations, for instance.
IZt
m
m
I £22
te
i
3i -CZ-
Zisr.
^32:ja
ife
In rapidly succeeding modulations, also, particularly in a flowing
progression of the voices, the cross-relation seems to lose
its
harshness,
#==
^=#=
because the change of modulation occupies the hearer, and such
184 progressions (which are based upon the omission of the resolution-
chords) have of themselves a certain strangeness which well
^
i
t -^
^=1_
^
mz .
.
:^i
corresponds to the character of the cross-relation.
And
thus
we
dictory, but
why
understand
which, considered
by themselves,
cross-relations
which are the unavoidable consequences of a proper
and well constructed progression of the of
many
minor,
are permitted
are actually strange and contra-
instances,
we
As one
different voices.
give here a passage from a fiigue in
C
by Sebastian Bach.
^^==^=^ l^^^to m
BF¥
drf ^^^p^-
Pm^
^;
g^—
i3—
-CET
It is
^^ -^t^=^-^-=gg fes marked f, could not be upward pressure ii'om d to a, bb, b, in the lower and middle
evident that the cross-relations the
avoided without sacrificing
«K
d^
4^
W-
m
3^
«j/^/ff)
5^1
™d again
from $• toal;,
voices, or the spoiling of the
Until
now we have
upper voice.
only spoken of cross-relations between two
but tlte same relation can extend ; above the second to a third chord, and in such case it is called an chords in immediate succession
indirect cross-relation.
Here
185
h
JJ!J-JJ UJfl
we
see a series of such
lations,
at c
d,
first
I
[I
1
I
movements which
and of which the
and
'
upon us as
act
'
cross-re-
(a and b) are less distinct than those
because the cross-relation in the latter
is
in the outer
voices.
Why does
not the intermediate chord destroy the harshness of
the cross-relation 1 Firstly,
because the flowing voices
e\!-d-c,
g-f-e,
&c., are recog-
nized at once as phrases belonging together, and because
well as formerly,
belongs to
is
C major.
e|)-i^c,
as
melody of C minor, while g-f-e For the same reason the phrases b and f, in
considered as a
which passing-notes take the place of intermediate chords, make no favorable impression. Secondly, because the dominant chord tinguish major
and minor, belonging as
it
is
not sufficient to
dis-
does to both modes.
186
CHAPTER
III.
FORMATION OF NEW PASSAGES WITH THE AID OF FOREIGN CHORDS.
Every
introduction of a foreign chord can be considered as a
new harmonic design, and can be employed by
itself,
or in con-
nection with other chords, for the formation of new passages.
know
how
We
work and we require only a practice of the same, in order to become familiar with the various chords. For this purpose only we give below a few examples. already
to go to
;
We have already been made in the dominant.
Continuing
acquainted with the modulation
it,
we
259.
ascend from every
with
this,
new key
into its dominant.
Simultaneously
the chords change in positions and Inversions, and
it is
same can be done in various manners. The modulation into the key of the minor third above, issuing from C, would lead us to E\,,
260.
8va.
would lead us from C to A, iff, JE], or D and back to C. The modulation to the key of the major second above, would jj,
give us
187 In the fourth measure the dominant chord ought to have been <^|-/
tion
X -o|-c|, which would have would have been thus
led us to
G'jf
major
262.
;
the continua-
Eg f"-=*T
6^1 major with eight, A\ major with major with twelve sharps, and would have involved us in an infinity of signatures. Instead of this we have enharmonically
and would have brought us ten, B'^
changed the above chord into
keys with
less signatures.
e])-g-i])-d\i,
which has brought us into
The same occurs
in the modulation to
the sub-second
263.
The beginning of No. 263, and the ending of the remind us of our first harmonic lesson ascending and descending major scale.
moved
voluntarily into any key,
we
;
last
passage
the accompaniment of the
While
until
now we have
can now consider the degrees
many tonics into which we modulate. In we go from C major to D major, jE major,
of the scale as just so other words, i''
major, &c.
264.
or, vice
versa,
either in the
from
C
upper voice,
below
a 265.
B
to B,
A, O, F, &c., placing these tones No. 264) or in the lower voice, as
(as in
A
a
F
&a.
^^^^#ii Tf ripf
188 or into another voice, and regulate
Or,
cordingly.
we
the remaining
voices ac
take the ascending and descending chromatic
scale,
m
G
D
E
Eh
and write our chords now with sharps, now with
be most convenient to It is clear that
exhaust them
is
&Z.
flats,
as
may
us.
such exercises
ca^be extended
infinitely, and to But we recommend the
almost impossMe.
much as pos on paper and (improvising) on the piano.
pupil to practice these- m^odulations and passages as sible in all positions,
The
different positions will often
present
difficulties
to him, be-
some of the tones strive downward, and vice versa. Thus No. 261 and 264 were comparatively easy, because we always returned to the same position, and a cause in ascending modulations
In No. 265, too,
single design sufficed to carry us through.
could have finished as
we
began, and
we only changed
tion (2d measure) in order to get along with one stave.
was
No. 266
it
position,
we
different.
Placing the
first
we
the posi-
But
in
triad in a different
are absolutely forced to place the second triad again
in a different position. I
267,
±
i
Ai
ld=
%\
list
r ^ w-
T r
If our former advice (the consistent continuation of
now heeded, the very furnish new designs. As an
design to a well formed whole) ing of those difficulties will tion
268.
we
is
give here No. 266 in other positions.
every masterillui-tra-
189
Here are the beginnings of the same
in dispersed harmonies,
^ ^±ir^^L^dS=^ F¥g=J Q^ T'-¥
which, like all the former,
ztzi
^
we
leave
=*
to the pupil
to
carry-
through.
The to the
practice of these passages
must not be
dominant chord, but should include
all
limited, however,
the other transition-
chords.
Thus far, though we have discovered extended combinations, we have obtained nothing essentially, new. We will now pro-
new
;eed to the actual
formations.
PASSAGES OF DOMINANT CHORDS.
1.
We can consider the dominant chord as a major triad with added minor seventh, and consequently can change every triad into a dominant chord. Here 270.
^,
P
=g=fe=^-'&:t|
Z13Z
-&-
-&-
fo-
we have
regularly resolved every dominant chord into the triad of
its tonic,
and every triad has been changed into a dominant chord
a passage
But a triad,
which we owe to the introduction of foreign chords.
since every
we can
dominant chord contains within
reject all the triads of
itself
already
No. 270, and have the
dom
inant chords follow each other immediately.
=^
ds _£2I
:fe --^
:te
z\S2Z
271.
m
JZ. 3SZ.
'-bzsn
-y&-fe-
§&-
190
#fi=*=#=,^
T=^=^^ES^f^:^2~=^.
-&-
gg~
Here we
see every tone follow its regular progression, with the
exception of the third, which descends a semitone, and becomes the seventh of the following chord.* for five voices, in
We have written the above
order to avoid the irregularities which
we
en-
countered on former occasions, and yet to obtain perfect chords. If it
were our object to have the above passage tetraphonous,
would be best to omit
2.
it
either the third or fourth voice.
INDIGENOUS PASSAGE, DERIVED FROM THE ABOVE.
drives us from dominant chord to dominant from one key to another, in rapid progress, but without unity of key. Strictly speaking, it is nothing but the foreign tones which occur at every new chord, which destroy this
The above passage
chord, and with
it
Let us attempt, then, to retain the passage, at the same time voluntarily rejecting the foreign tones, by omitting the acunity.
cidentals.
* The above resiilts of the analogous development of the harmonic ment are already indicated in the natural development of the tonic
ele-
ele-
ment.
Already (page 75) we noticed that after the first six tones which nature had given us, and which stood in the simplest relations to each other, (1, 2, 3, 4, 5,)
for instance, ',
e g,
c,
7,
g,
a seventh tone made its appearance, for which then after which only, the other tones, c,
a,
e,
we had no
name,
an(J
made
their appearance. This seventh tone, (the tone relation
6, 7,), though lower than our 6b, an must and can serve us as 61;. that the second harmonic mass, or the dominant chor-l g-h-drf, has a predisposition to resolve into the first harmonic mass, or the tonic triad, c-e-g. But in the same instant, by means of the just mentioned ib, the chord becomes anew a dominant chord, (c-e-j'-Jb,) which resolves into a new tonic, (F-c-a.) Thus the nature of the tonic element strives of itself downwards, in the same manner as we have illustrated it in No. 271.
higher than
a,
Now we know
I
191
1227
272.
.._-J-_i_-J_iJJ_
^F^ ^m we
Here, amidst familiar chords,
No.
1
some new ones.
also discover
us, besides the final chord, are
Familiar to
and
8,
dominant chords, with major
third,
major
fifth,
and
minor seventh. No.
4,
a chord which at a
first
glance might be taken for a nona-
chord with omitted fundamental tone.
would have resolved
into
c-e-ff,note-g!lj-b,
has taught us already that
it is
dominant chord, and as such No. 272 is perfectly- proper.
If such
were the
or e-g^-b-d.
case, it
But No. 270
nothing but a voluntarily-altered its
progression, as
it
appears in
JVew, beside this one, are
No.
2,
and
3,
two chords with major
third,
major
fifth,
and ma^
jor seventh, and
No. 5 and 6, two chords with minor minor seventh.
third,
Aajor
fifth,
Being nothing but voluntarily-altered dominant chords,
and
theii
progressions are those of dominant chords.
SUCCESSION
3.
OF NONACHORDS AND SBPTIME CHORDS, OR NO-
NACHORDS ONLY.
ff*'
According to the above, nonachords
also, instead
dominant chords.
273.
or even into nonachordi
it
requires but the mentioning, that
of resolving into triads, can resolve into
192
11
I
i^--^. 274.
^
bp:
z^trtfa
•F=t=^
The
latter
can take place, either in major and minor nonachords
alternately, (as in the above) or in a steady succession of either
major or minor nonachords, which
is left for
the student to prac-
tice.
INDIGENOUS PASSAGE OF NONACHORDS,
4.
same manner
In the
in
which we formerly gained an indigenous
succession of septime "chords, dentals,
we
can here, by omission of acci-
form an indigenous succession of nonachords.
I
--i=l=l
m
--^—f—r^--
•275.
3E^^ Amidst two
familiar nonachords, Nos. 1
and 8 we
find here
^ ^
several new. ones, vis.
Nos. 2 and
3, consisting exclusively
No.
4, exclusively
No.
5,
with minor
of minor third,
of major intervals.
intervals.
major
fifth,
minor seventh, and minor
ninth.
Nos. 6 and
7,
with minor third and seventh, and major
fifth
and
ninth.
These chords require no additional rules. major and minor nonachords.
They
are treated
like unaltered
From each of the above nonachord 5.
successions,
we can
SUCCESSIONS OF DERIVED SEPTIME CHORDS.
Thus from No. 274, we gain
develops
193
276.
the passage
B
—from
a
—from a succession of major nonachords the passage —and
a succession of minor nonachords the passage c
from the indigenous passage No. 275; we gain the following
277.
^E^dfe ^m
which, however, as
How
is
=^
be seen, brings us nothing new.*
easily to
to despoil all these passages, and particularly those of
the nonachords, of their superfluous tones, and
through their various positions,
is left
how
to carry
to the student's
them
own indus-
try.
But the
us consider once more that
let
many
all
that might be developed from
chords have
the above passages, and
them with
so
many new
all arisen
* Here, at last, we have an opportunity to introduce an appendix to the passages discovered. (Page 119.) Then, particularly in Mbs. 134 and 136 we took the step into the dominant as basis ; now we take the step into the subdominant as design. Here,
278.
and
here, reversedly,
& 279.
is::ai
S>-)g-
:pi^=f±t
fetEzgx
r
i^:g=:-4-
r ri-p
-p-
But is it proper at .\, b, c, carried the design straight through. and D, to deviate from the rules of the dominant chord and the dominant triad! to omit the resolution of /J-a-o into g-b-d? to have the seventh c ascend to d! to double the third, or to lead it now above, then below ? These deviations, too, like those in No. 271, and similar ones formerly mentioned, are hidden and justified by the analogy and the firm progression At a and b the actual resolution-chord occurs merely of the whole passage. and we shall soon learn that this, is tl e later and in a diflterent position
we have
—
case too at c
and
D.
—
194
FROM A SINGLE DESIGN,
—
from succession of two dominant chords or more properly from the passing over a single tone that, in No. 271, instead i.
e.
—
of taking
280.
c
as at a,
b\,
we have
taken Sb at once, as at
b.
^^
$
-33:
^C2.
r
I
I
and we have again an illustration of the infinity of that tonical development in which every step hrings us a new series of formaConsidering again that so many septime and nonachords, tions. together with the diminished triad, obey
A SINGLE LAW, which, though given only with the dominant chord, was already mass and the second position of
indicated in the second harmonic the scale,
we
cannot but acknowledge the intrinsic unity which
runs through the whole tone-development.
We
can, therefore, justly call the ,.
THE origin of HARMONIC MOTION.
Its first inclination is
nachords and
dominant chord
all the
towards the
tonic, to
derived chords
;
appendix from one key into the other nouncing the return into
its tonic, its
which
then,
it
it
drags the no-
leads us with its
finally, after its
;
motion
each of the passages originating from
it,
is
once
unbounded
;
re-
for
finds in its elements
neither rest nor end, but drives us incessaptly through all the
degrees of the scale, until
mony.
Equally just
is
we
arbitrarily rest, or seize a tonic har-
the designation of the tonic triads
AS SEAT OF REPOSE.
They
are the goal, the actual end of all harmonic motion, as
they (particularly the major triad) were the beginning. for themselves, have no stimulus for motion
by
itself,
;
They,
each stands there
without the necessity of moving into another chord.
Therefore, with the exception of the dominant chord, they pro-
duce no sages
;
new their
chords, and no necessarily connected harmonic pasmost flowing combination, the sext chords are merely
mehdically (by the parallel direction of
all
or
most
voices), not
19S harmonically connected
mon with Now,
;
for
none of its chords has a tone in com-
the next succeeding one.
for the first time,
we
can fully appreciate the
name
DOMINANT.
The tone
so called reigns over,
and tone-motion;
it is
and leads every tone-combination
the centre around which from the two
first
harmonies to the end of all tone-motion, harmonic sequences and modulations turn.
The greatest motion of the triad we can oppose to it and harmony would be a succession of sext chords, diatonic as No. 167, or chromatic, as here
its
in
281.
But
c-e-ff
has no relation to f'a\}-d]) ; consequently no inclination to
into or towards
or chromatically lar
moThe chord
in the latter case it is evident that the stimulus of this
tion is not properly harmonic, but merely melodic.
manner
in
it.
The separate
voices only
move
move
diatonically
up and down ; but exactly because of the regu-
which
this is done, the chords
at least melodically connected.
which they form are
196
CHAPTER
IV.
VARIABLE MODULATIOirS.*
By
this
name we
shall designate such
means of modulation as
can lead into more than one key, according to the view which
we
take of their relation.
ticularly to
two
A.
Of
this
chord
we
est designation of a
cause
it
We
turn our attention here par-
chords.
The diminished s^time
chord.
said already, (page 169) that
key
it is
the clear-
dominant chord be-
clearer than the
;
designates even the species of key, (major or minor)
while the dominant chord leaves the species undecided.
But owing to a peculiarity of which we very chord becomes what
we
shall speak
just designated a
now,
this
means of variable
modulation.
The diminished septime
chord, as
we know, consists exclusively
of minor
thirds, for instance, in
When we
invert this chord, (for instance, place the b above ah),
minor of
b-d, d-f,
and
f-ah.
the two tones form the interval of a superfluous second, which equivalent to a minor third.
Now, when this
enharmonically changed into a minor third succession of three minor thirds,
consequently a
d-f, f-a]),
new diminished septime
tinguished from the inversion of the
name of one contents.
tone, but
And since
1.
like 2.
by no means
this
inished septime chord,
first
it
inverted tone,
c
and
we have ab-cl>
is
b is
again a
instead of b ;
chord, which is only dis(quint-sext chord)
by the
in the actual pitch or tone-
proceeding can be applied to every dimfollows,
That the inversions of the diminished septime chords sound a fundamental chord.
That every inversion of it can be considered as a new dimin-
ished septime chord. 3.
That every diminished septime chord contains
in its tones
three others, that consequently there are only three tonically
dif-
ferent septime chords in our system, while of every other species
of chords can be found twelve. * See Appendix
(J.
197
The
first
can be said of no other chord ; the second causes that
by merely changing a name, we
with every inversion,
new
Here, at
key.
arrive in a
a,
282.
Dh
£],
we At
see the diminished septime chord,
we
B
diminished septime chord
b-d-f-a},,
first) is
But
which leads us to ^|j minor
chord,
(or the terz-quart
which would lead us to
/ialj-cb-ebb,
e{{-^|-5-rf,
we change
and arrive thus
in
take the quint-sext chord, g\-h-i-e\, (sounding
like the second inversion of our first chord)
change the
and thus obtain the fourth septime chord,
us to
en-
assume the form of a new
in order to facilitate the writing of it,
F% minor. At d we
minor.
by the
d-f-a\)-h,
new septime chord
the whole chord enharmonically into
f,
leading to
again (at c) enharmonically changed into a
new diminished septime minor.
6 in ct,
(ci^ab-cb),
quint-sext chord of this
chord of the
Q\3
Cjj
see the quint-sext chord of the same,
harmonic change of a single note
The
or
g\-h-d-f,
e|
again into
which leads
A minor.
Now,
since neither
change of name nor inversion alter the
actual effect of the chord,
we can
represent the
same
results at
once, thus IlJ
I
J" I
283.
We need hardly mention that these modulations can be efiected in every inversion
and every
and that each of these sep-
position,
time chords can lead to major as well as minor. student will practice
To
The industrious
all.
the above three observations
we
will
now add a
fourth one,
equally simple and productive
"The seventh of the diminished septime chord of the nonachord), has
its
(the
minor ninth
position a half step above the octave
therefore, if it descends a half step
it
would
fall
into the oc-
tave."
Consequently every diminished septime chord can, by means of
198 the descension of the seventh, be changed into a dominant chord, (or rather a quint-sext chord of the same), for instance
b-drf-a)}
in h-d-f-g.
This gives us the above four modulations with a circuitous course of the dominant chords,
Here we have obtained the above
by lowering one tone
results
of the chord, consequently increased the distance of
much from
But the same
the other tones.
retain one tone
and elevate the three
is
otlftrs
the case
it
just so
when we
a half-step.
This
gives us four modulations,
to D\), E, Q,
and
B\)
major or minor.
Here we have led upwards will
now attempt
it
with
all
of the chord;
three tones
Ac.
&e.
286.
i "^^
iffi^E2^
%
it
tions.
Here, be
it
-^
observed,
it
:fe
%
i^
to the student to carry
leaving
we
four tones down or upwards,
:^MP^-
out through the various posi-
we meet
again upon harmonic pas-
sages or sequences, the single chords of which have as little relation to each other as those of
No. 167 and which are admissible on
ac-
count of the then-mentioned m.elodic connection.
With every this
were the
we arrive here at we can repeat the
step
chord, with which
case, the
a
new diminished septime
operation of No. 281.
If
seventh would twice descend a halfstep,
(once according to No. 286, and again as in No. 284), the other tones would follow as in No. 286.
Let us do
The seventh may descend a whole
step,
step
;
this gives us four
major or minor.
this all at once
—
and other tones a half
new modulations
to
.5,
D, F, and
A),
199
Of course direction
;
the
same proceeding can be
one tone
cend a whole
may
ascend
others
as-
step.
i^^^
288.
Here we have again and
carried out in an opposite
a half-step while
it
four
new modulations
remains for the student to carry
to it
B, F,
A\),
and G,
out in other,
per-
haps more favorable positions.
Thus the simple diminished septime chord leads us immediby means of an assistant chord into all twelve major or minor keys, and to most of them in more than one way. ately, or
B.
The dominant
chord.
Already in Nos. 154, 155, and 188, our third and seventh of the dominant chord have risked, under cover of the remaining voices, some deviating steps ; at No. 271 we have arbitrarily changed the resolution of the third, and thus have arrived at a inant chord, and consequently at a
new key
new dom-
(that of the
subdom-
inant).
Let us now pursue the opposite. one dominant chord into another, vis.
We ;
proceed (at a) from
that of the dominant.
-59289,
$
li^
^S©;. _£2_
fro^-.
The third pursued here its natural course, but the seventh was elevated, and the fifth and fundamental tone have also pursued a different course. This proceeding is based more upon our pleasure than any law of nature, and is only admissible because of the near relation of key. of the same (as at b)
But we
It is
but rarely that a continuation
is applicable.
will attach to these
some other nearer
deviation.
200 291.
At A as
of
which,
tiial
the
tonic
c,
we
of
c-e])-g.
we have
triad,
A
resolve the
C
minor.
c-e-g,
to c or e ;
the
c-e\)-g,
seems
and
perhaps causes an
In the
same manner or
c-e])-a\)
as illustrated
in-
of a before
triad
excuse these deviations or
it
a,
major-,
dominant chord into
We might
as omissions of
d
c,
But g goes to
c-e-g.
perhaps, remains
modulation to
6 to
e,
were going to be
instead us,
goes properly to
/
if it
at b
a,
ac-
and
instead
by imagining them by d but the near ;
relation of the keys justifies this proceeding in itself.
We will now add to these deviations
a few free resolutions of
the dominant chord and the diminished septime chord, which
might have been mentioned
comprehended
earlier,
but will certainly be better
here.
-&-
-iS^
•292.
:iES^^=g=± ^g=~
E s-
.a.
^^ -&
m.
At A
W
5
s
-e-
s-
the seventh of the dominant chord remains,
other tones pursuing their regular course, form with
while the it
another
chord, until finally in the last chord the seventh obtains its due.
At B we
neglect even this
nor, while in reality
At
c,
for g-l-d-f apparently proceeds to i?' mi-
to the
subdominant of
C minor.
D and.E, the fifth/ (the seventh in the nonachord) does not
pursue
its
natural course
fundamental tone. it.
;
we merely go
By
to
this
e,
but goes
means we
far
beyond
into the
are enabled to double
(k)* * See Appendix H.
201
CHAPTEE
V.
GENERAL ORDER OF CONSTRUCTION. The
last
and most important use of modulation into foreign
keys, consists in its enabling us to form
tended constructions, than single key.
Though
tions which require a
we
this is rather too
more
more
more
firm and
ex-
could formerly, in the compass of a
soon to think of composi-
firm and extended modulation,
take the opportunity of exhibiting at least
we will
its principles.
The harmonies of one single key permitted us in reality nothmore than to form a period of thesis and anti-thesis and coda
ing
In the duophonic composition
or codas.
and
anti-thesis to a first
and second part
mere extension of compass. cally satisfactory
The
;
we
elevated this thesis
but
this, in reality, is
a
was only rhythmiin tonical respect it was by no means so well end we had merely the half cadence on the
;
constructed, for its
first
part
second harmonic mass.
But
this
second mass has long since become the triad of the
dominant which reminded us of the key of the dominant and served as close of the thesis. There remains now for us but one step
;
we
take instead of the mere triad of the dominant, the key
of the dominant for the close of our
we have
Thus
first part.
anticipating,
No. 257, closed the thesis with a modulation into the dominant but the close was rhythmically imperfect. already, in
;
Here we have then The first perfect
A.
The
first part, as
cadence
is
a whole, ends with a
full
cadence
;
but
this
not in the principal tone, but altogether in another key
and thus with end
construction of a two-part composition.
all its
satisfactorily,
completeness at the close,
it
still
;
does not
and leads us to expect a return to the principal
tone.
And now comes
the second part as something expected, and
leads us back to the principal tone, in order, there to end the
whole
satisfactorily.
202
The
first is
progression, elevation into a higher key
;
the second
It is therefore
part has the return to the principal key.
again the
fundamental form ot page 81, though carried out with higher and richer means.
The above est,
and
Thus the first part of
the general rule for major.
is
a composition in
C major
suificient
will
end in
and
until larger
G
major.
freer
This
is
the near-
formations
lead
us
further.
In minor,
gloom is
to
modulation from minor to minor would add
this
gloom
;
for the
minor
we have
triad, as
seen already,
neither clear nor sure like the major triad, but as
has been developed from the latter
by
were,
it
the depression of the
That which characterises the triad is characteristic of the key also. Nor is the minor key so intimately connected with its dominant as the major key. major, the For instance, in third.
dominant triad g-b-d indicates at once the key of G major. Not so with minor ; for the actual triad of the dominant in minor, (for instance in A minor «-5'|-S) by no means indicates the minor ,
mode
of the dominant.
Therefore, the modulation in minor
does not generally turn
minor mode of the dominant, but prefers to go into the nearest-related major key for instance, from A minor to C major. This is the regular progression of the modulation, which we into the
;
shall follow until
weighty reasons and more extended formations
from this rule. Our first construction in two parts would therefore be represented in the following sketches For major justify us in deviating
I
293,
$
e-&~P-
gd-
Sp- —
-s-
1
-s?
-ig-
^^E
f^
^-
f and
for
minor-
S-&-
203
294.
_ss_
i
tp=^±y
rw
-p-
$¥
SSSl
The two sures each
The
;
parts appear here in the original length of 8 mea-
the
first is
we know
second
i
i:
divided into thesis and antithesis, of the
not yet whether to give
it
such a division or not.
harmony begins here the first part: it is needless repeat that we might also commence with another. The the-
to sis
tonic
of the
according to rule, ends in the principal tone.
first part,
After that
we
leave the principal tone and
key in which the part
is
move towards
a higher
to end.
Second two-part construction^
B.
We have now, by means of a full cadence, made a whole of the first part.
But
this whole, in its nature, is
—a
uous elevation
start, as it
one-sided
were up to the final
the second part brings a second motion
i.
;
;
point.
a continIt is true
back to the quiet
e.
But the second part is to a degree separated from the first. Thus the character of the first part disagrees with the meaning of a close, which ought to be quieting and soothing. of the
first
How the
can
first
beginning.
we now
unite these
two
—the
essentials
part and yet a satisfactory close
?
elevation of
According to the fun-
damental principles of all tone-motion, the close ought to a tone lower than the one in which the
we
movement
led
fall it.
into
But
cannot alter the close, without falling back upon the principal
tone.
Consequently the alteration must take place in the move-
ment of the
first part.
We lead the
movement BEYOND
ITS
ACTUAL GOAL,
C major, for instance, to Z* major; aud now we can fall upon the actually wanted key of the dominant, and have thus from
204 united elevation and depression, and gain a perfectly quieting, soothing close.
same proceeding should be applied in minor, the modulamust first be led into the dominant of the parallel key, and finally into the latter ; in A minor, for instance, fij-st to G major and then to Cmajor. But this impulse seems here to be less forcible for the felevation in minor rests less upon the elevation into a higher key, than upon the transition into the clearer and more If the
tion
;
vigorous major. In the second part, also,
ment towards the
end.
we discover now an unsatisfactory move-
The second
part follows its original des-
tination, to the quiet of the principal tone.
ter
and
if,
as the actual ending of a whole,
decision.
It
it
But
it
would be bet-
had somewhat more vigor
ought to contain an elevation and stUl
fall
upon
the principal tone. In order to achieve this low, in fact)
pal tone. in major,
we
and now we can
pass on to the subdominant, (too effect
an
elevation into the princi-
Below we give a modulatory sketch
tor constructions
205 the dominant, or with the parallel key, as the nearest and
appropriate steps.
we
Afterwards
most
introduced the dominant key
of the dominant, or of the parallel, and the subdominant. If
we were
related keys
;
to go
we would
further,
still
again seize the nearest
these are the parallel keys of the principal tones
and of the two dominants.
But we know already that we
can choose more distant keys without touching upon the nearer ones.
Our present means
are
by no means so profuse that they should The second manner
require a further extension of modulation.
of construction, or even the
first,
we
shall
in passages (sequences)
be perfectly sufficient only be able to use richer and more
will
;
The unity of our well-rounded phrases would be destroyed by too great an abundance of modulation extended modulations.
into distant keys.
But
if it is
our object to give to these phrases a richer and more
extensive modulation, at the
we have but
vagueness,
to
same time avoiding the danger of remember the already mentioned
CODAS, (page 86) which might repeat the
By
without alteration.
final
such a proceeding
we
phrase, with or
not only
gain
on space, but the very repetition serves to strengthen the ending. In that case a
more
because whatever in
made harmless by makes the
digressive modulation it
leads
Formerly we had
more
is
conspicuous.
The interrupted
D.
to,
objectionable,
principal tone,
the repetition of the ending, which of course
principal tone again
connection than
is less
away from the
cadence.
for our codas (page 86)
represent the
first
no other means of
ending imperfectly.
the licenses of the dominant chord give us
new means
Now,
to avoid
the actual close in the principal tone, and to introduce the coda,
we end with a full and perfect cadence. For we make use of one or the other of the free resolu-
or codas, until finally this
purpose
tions of the
dominant chord.
paration of a close in
c.
Thus, for instance, after a
full pre-
297.
^
206
-^=$=f=^^^
we could go bring with
A
or ^b, or to any chord which would know a coda, and finally a principal cadence.
to the triad of
it
We
already (page 86) that cession,
'P-'P-
we
can apply two or more codas in suc-
eflfected by renewed avoidance of Such preventive cadences are called " Interrup-
and that they can be
the final cadenoei
ted cadences."
The imperfect
merly (page 118)
cadences, too, which
seen, belonging to this category,
we have
for-
when they take
the place of a perfect cadence and cause the addition of a coda.
207
CHAPTER
VI.
ABEUPT MODXILATION. The thus
diflerent
far,
manners of modulating which we have learned
are fully sufficient for all the constructions capable of
being formed with our present means. the
present
is
more extensive formations, we daries
But
since our object for
prepare means and foundations for future,
to
will pass our self-proposed boun-
in order to produce such
new
can easily
formations as
be derived from what we have learned. Until signified
now we have more or
modulated into another. as it were, the key which at the
modulations by chords which
effected our
we had left the one key and we renounced,
less distinctly, that
same time our
By the
transitive chord
until then
was the
transitive chord
connection with the preoeeding chords. first piece,
field
If
instead of modulating into another
begun a second piece
of modulation
had always more or
less
we had ended the key, we could have
any other key without the necessity of a
in
modulation.
From
the above
—when a phrase
we
conclude that
were, a succeeding phrase, as if
it
were a new one,
ends, as
can,
it
without
transition, begin in another key.
Here we have a phrase
298.
M
^
1
which ends in
G
r
major.
rhythmical form or other the end, a continuation, a tion of the former one,
voice only retains a tone in
in other wordSj
new
some
we have to expect after
phrase, or perhaps a
mere
repeti-
and the retained tone is the connecting link
between the two phrases.
mer harmonic
One ;
This tone, without reference to
relation, can
now become
its for-
a fundamental tone,
208 third, fifth, seventh,
nachord
which
in
it
major or minor ninth, of any septime or nois
inherent,
and consequently can prepare
SIX different modulations, each to major or minor
C
299
D
F
Ab
At No. 298 we manner. ;
for the fifth considered as
inant or nonachord leads into
But
since
we
;
become fimdamental
new
;
.B.
but we could
it
in the
same
fundamental tone of the dom-
no new key.
considered the phrase No. 298 as concluded,
require no transition
a
and applied
fifth,
or
This gives for the three tones eighteen modulations,
one
less
or
retained the fundamental tone
have retained the third or
also
Bb
or
we
the retained tone can immediately again
tone, third or fifth of
a
new
tonic triad, in
key.
E minor
G minor --^
i O minor
^
5 major
:&«
5 minor
G
E major D minor D major.
^eB\>
W%-
¥,
«
E
Git
lis=F4IL-
»E
C
E\)
-s-
M
This gives us again twelve modulations (not counting the repetitions of those already counted) into
In all these cases,
it is
true, the
major or minor.
remaining tone was the con-
But we have depended more on was closed, and that the har-
necting link of the harmony.
the fact that the previous phrase
mony had
ceased.
We will now in reality depart for a time from We will change No. 298 into the following, 301.
>-a»-
—"J—tl t-^
d
J
1
the harmony.
209 and
after the perfect, ending of the harmony we continue^ in a monophonic or octaye passage up to. any particular tone, in this case it would perhaps.be/. This/ can again be part of a domi-
nant chord, a nonachord, or any chord derived from the former thus, we could
two; and
into six different
303.
Or
the
B\,
E\,
o\,
same tone.can major
J*"
303.
have after the above passage transitions
major or minor keys.
at,
once. be. part of a
J minor
Vt major
i
new tonic
triad,
jyxaxaax
^ ii
I£2I
m
%%.
and, therefore, again lead into three major or minor keys,
we have
•which there are four which
we
A
A\,
among
not reached in No. 802.
And
bound to attach our new phrase to the tone/ since we can stop at any tone of our tone-system, it is evident that there exists no key which could not in this manner be attached to the preceding one. But all these harmonies and keys, at which we arrived in Nos. 300 and 302, have not the since
are not absolutely
slightest
harmonic connection with the preceding chord
They are
justified
by
this
g-h-d.
very disconnection, by our •purposely
resigning the harmonic connection, and they are connected with what preceded by the mere thin thread of the melody. At last we have arrived at the point where we can resign even this last connecting link, and enter a foreign key without any mediation..
Here
is
an
illustration.
The second measure closes in C. The cadence is full and perfect And immethe rhythm only leads us to expect a continuation. diately
we
continue,
without preparation, in a foreign key.
By
210 -what right
Because
?
this continuation is a phrase
by
itself,
as
were ; a new piece which takes up the thread of the previous phrase at a different place, and perhaps in a different sense. And it
it is
exactly because the continuation in the third measure is con-
sidered as a at
new phrase,
that
we
consider the
new chord
once as a tonic chord, though the key of
cated by the dominant chord If the continuation
we should
b\)-d-f-a\>,
H\)-g-b\f
only
indi-
which occurs three notes
later.
JE}}
is
should not correspond with our expectation, if
continue thus
305,
feE $ fT^
and turned to
h-^f^
5 b major, we should still consider the first chord as
tonic of ^\)f and major.
the second as a second modulation into £\>
211
CHAPTER
VII.
ORDER OF MODULATION FOR MORE EXTENDED COMPOSITIONS. One more rule
can be derived so easily from the previous prin-
we retain
though
its full
im-
portance will only become evident in more extended forms.
It
ciples of modulation, that
it
at once,
has reference to the order of modulation which should be observed
which combine several phrases in various keys into one is a continuation of the fifth chapter, in which we men-
in forms
whole, and
tioned the order of construction for compositions of two parts.
At
that time the transition in
major into the key of the domi-
nant or parallel was the means and sign of the close of a part.
The or
and combining of various keys gams additional im-
seizing
portance,
when
when
several phrases are to be connected in one piece,
In such
others have to be repeated in a different sense.
a case every key mentioned in the laws of construction becomes in
time the field fOr a new phrase, and influences its relative keys. first appears the actual principal key, and demands room for
At
development. necessary
If the association
we must
with another key
is
absolutely
take the subdominMit, for the dominant will
soon be a principal sphere. After this comes the dominant as principal sphere of modulation,
pal
preceded by
key
itself,
its
Its
subdominant
is
the princi-
and consequently would be altogether unnecessary
at the
end
here.
Therefore, if
;
dominant.
which has just been passed, and will return again
we must extend
our modulation
have to select the parallel of the dominant, as
its
we
shall
nearest re-
lation.
The third
principal sphere belongs to the
key of the subdomi
An extension of modwould lead us to its parallel for, its dominant would be the principal key, which must follow soon after under any circumstances, and its subdominant would lead us off nant, which prepares (page 200) the close.
ulation in this third sphere
too
far,
allel
without bringing anything new.
;
And now
occur before or after the subdominant.
shall this par-
212
We allel
would prefer the
latter,
because
we
cannot reach the par-
without passing through the subdoi/iinant, and can only be
comprehended as belonging to the latter. But this analogical powould place a new key where we want it least where the elevation from the subdominant to the principal key is of imporAnd this must decide us to have the subdominant precetance. sition
;
ded by
The
its parallel.
close, of course, is
made
in the principal key.
but one relative key which
There
is
—the
parallel of the principal key.
far
attach
it
we have It
forgotten thus
would be proper to
to the principal key, either at the beginning or at the
close
between the subdominant and the principal key.
place
it
would stand
in the
way of proper
elevation.
At Its
either
best po-
be where all the parallel keys meet here mass of minor modulations which, by the intervention of the principal parallel, becomes first duly organised. As a summary of all the above we give now a diagram for the
sition would, therefore,
we
;
find a
order of modulation in major.
Cmajor, JD major,
Major.
Minor.
Major.
G major,
jF minor,
A minor, 3 minor,
i*"
major, Cmajor.
Everywhere we have' an analogical progression, sufficient connection, and, in the combination of major and minor, a simple and vigorous distribution of masses. Were we tobreak up these major and minor masses, and intersperse them at random, none of the keys would achieve its full efficacy, and the modulation would become unstable and restless.
The order of modulation
in minor, naturally resists such a sure
and simple combination, corresponding thus perfectly with the
gloomy and undecided character of the minor keys (page 202.) The cause of this lies in the fact, that, immediately after the principal key, the second sphere is occupied by a key of a different mode. To this parallel key we could attach the dominant, (or rather the parallel of the principal key's dominant) and afterwards
the dominant of the principal
key itself. Then the key of the subdominant and its parallel would naturally follow, and we would have the following diagram :
A minor, in
major,
G
which we perceive
major,
E minorf, F major, D minor, A minor,
at once that the parallel
of the sub-domi-
213 nant this
(at f ) does
not attach
itself as
easily as the others
;
might be obviated by placing between them the principal
by omitting
key, or
altogether the disturbing key, or in various
other ways.
Both these orders of modulation have another property, which gives freshness and decision to their
Uach
key,
effect.
with the exception of the principal key, appears but
once. It
follows from the whole tendency of our work, that these or-
ders of modulation are
by no means
absolute laws, but that other,
deviating orders can also be attempted.
remain the same throughout.
The
we
If
any key a
different
deviate, therefore,
we must
position,
other keys accordingly. first
will
be neglected without serious disadfrom the above, and give to
petition of a key, can rarely
vantage.
But the principle
last particularly, the non-re-
If,
take care to adjust the
for instance,
we
concluded to end a
part of major in the parallel instead of the dominant of the
principal key, that parallel
must not occur again
afterwards,
though the dominant would find a position at some other place. The following order would perhaps come into existence :
C major, A minor, D
minor,
Passages, whose object
is
G major, E minor, i^'major, C major.
merely to touch the harmonies of
dif-
ferent keys, as a matter of course, are not tied to this order of
modulation. at
any
place.
But
let
we have
Keys, too, which are merely passed over can occur
now from a different point of view what by our order of modulation. Not merely the
us consider
achieved
passages lead us through different keys, but the actual spheres of
modulation are different keys, and each one
fills
part of the composition
and the
of the it
first
were,
is
:
the thesis of the
first,
an important anti-thesis
The whole composition, merely an extensive passage simply its aim or
second part,
&c.
—
as is
fixed.
PASSAGES OP PHRASES. In reality. No. 266
is
already such a passage
;
it
consists not
No. 270), of a series of well connected single chords, but of two and two harmonies the dominant chord like others, (for instance,
:
and the succeeding
triad.
In like
manner each
phrase,
by
repeti-
214 tioii
on
different degrees, can
Here, for instance at a and
be made a passage, or a phrase chain.
b.
306.
we have
such chains before us, each consisting of a combination
Phrases of greater length, as a matter of
of four chords.
course, can also serve as designs for such chains.
Thus we have
here
307.
i^i_4ifMJ:
^^m^
a passage before us, the phrase of which originated from the design,
No. 306
even here we
—
A,
and which regularly descends a
see, already, that
third.
But
phrases which are well rounded in
The phrases and only the repetition made them a more significant whole. The phrase in No. 307, however, is in itself more rounded and satisfactory the first repetition makes it moie vigorous, and accidentally represents it in minor ; the second repetition will already be conthemselves, do not require a frequent repetition.
(No. 306
—A and
b),
were
insignificant in themselves,
sidered superfluous, and in order to invigorate
placed
it
in a higher octave.
It is
it
anew,
we have
also apparent, that passages, if
formed of more extended phrases, are apt to get too broad and expanded.
215
CHAPTER
VIII.
THE PEDAL-POINT.
We have now developed a mass of
harmonies, and perceived
the possibility of combining any keys with
modulations
all their
into a single whole without destroying its unity.
But even making
but a limited use of these means, there comes into existence a balance of motive power against the calming mass of the principal tone, which
is
much stronger than that of the At that time we found in
the tonic (page 72).
scale against
the
first
har-
we now find a similar succor for the principal tone. Where is, in reality, the beginning and origin of all motion ? we have perceived this in our deIt is in the dominant chord
monic mass a succor
for the tonic.
It
is
necessary that
should
;
velopment and have distinctly acknowledged
it
(page 194).
But the dominant is not merely the basis of the dominant chord, the nonachords and the derived septime chords, but it is also the fundamental tone of that triad which we consider at one time as a harmony of the principal key, at another time as a tonic harmony it can be fifth of the tonic triad of the principal key, or the basis of a quarUsext chord. chords
It
could bear, at least, the following
:
308.
Such an accumulation of harmonies would weighty
return to
the principal
key,
fiirnish
a
much more
than the mere domi-
nant chord, however long continued. But we must proceed. The dominant chord itself is nothing but an issue from the tonic (page 76)
91
we have
resting
upon a tone of
already learned
to
its
harmony.
At page
express this origin in tones,
and to introduce the dominant chord simultaneously with the tonic:
216
309.
But
since
$
every tone can become a
sider our dominant, too, as
new
tonic,
new
tonic,
we
and build upon
it
can con-
a domi-
nant chord.
310.
i
^
Only now the dominant has reaUy become a tonic, and we can combine it in this capacity, and in its original capacity {g as tonic of Gf major, and ff as dominant of C major,) in the following harmonic formation
311.
or with the addition of the already
known septime and nona
suc-
cessions in a stiU richer formation.
312.
in
which the most essential of all modulations,
The tonic triad as quart«ext chord, The dominant chord of the principal key. The dominant triad as harmony of the principal key. The dominant triad as tonic harmony of another key have been combined.
But we have seen already in our order of construction, how when it becomes the tonic of a new key, (page 163) brings with it the key of its own dominant ; and having just now considered the dominant G, as a new key, we can open
the dominant,
the
way
for its
dominant.
217
313.
And
i
r-
=«:
f
thus, chord after chord is
drawn into the whirlpool of the dominant chord, and ascending and descending
314.
passages which are a condensed recapitulation of the whole mod-
upon the single dominant, and harmony of the principal key.* Such chain of harmony is called a
ulation are built
are thus led
into the tonic
PEDAlj-POINT,
and
is
the last and strongest
means to make a
decisive
and vigor-
ous return to a principal key, after a rich and extensive modula tion has led us far from
While
it.
in the pedal-point the chain of chords returns to the prin-
cipal tone, the sustained bass serves to connect the chords built
upon it. Thus we see in the pedal-point, in two respects, one of the most energetic tone formations ; firstly as the basis of a wellclosed series of chords, working towards a certain aim, and sec-
ondly as the connecting link and support of these chords. It is exactly for this, tha,t the pedal point is only then in right place,
when
it is
its
intended to counterbalance a rich and ex-
tended modulation ; then only the sustained bass serves as a rest
mind and for the tones. But as every dominant can stand as tonic, every
ing place for the
as dominant'; consequently the tonic.
we can
tonic can stand
develope a pedal-point upon
Uniting, then, the pedal points of dominant and tonic,
* can we explain the chord a-ci-e-g in No. 314? By, itself, alone, it certainly does not agree with the pedal tone ji; we can, therefore, only speak of its position in the above modulation. have considered the first chord as the tonic of
How
We
&
We
218
315.
ISl
BE
flre
have at once the
fullest
and most majestic end.
In the above
example, in consequence of the profuse employment of the dominant harmony,
we have
called
on the harmony of the subdomi-
nant for aid. This reminds us of that deviation from our principles of modulation (page 211)
on the strength of which we placed the subdomgood foot-
inant at the beginning of a phrase, in order to obtain a
hold for an elevation and a richer tone development. pedal-point, too, can for
Thus the
be placed at the beginning of a composition
which we have a rich modulation in view.
We will now set aside
object and origin of the pedal-point and
confine ourselves to the analyzation of its contents.
take a two-fold view of
it.
It is, firstly,
and successively developed chords, and
a
it is,
pendent, sustained tone, which at one time
We
can
series of analogically
is
secondly,
an inde-
an essential of the
219 chords while at another time
it is
Since,
not.
when standing by
an independent voice, we can also double it by means of octaves, without regard to the web of the other voices.
itself) it is
316.:
All these octaves are independent of the harmony, but stand
merely as a duplication of the
original fundamental tone, which,
as tonic, reigns quietly over the
whole movement.
And thus is the inversion of a pedal-point also fully justified. By inversion we mean here that combination in which the original fundamental tone resigns
its
position in the bass, and occupies the
place of a middle voice, I
ItJ
1
J
I
1
I'hJ
or that of the upper voice.
|_ q-
I
I
,
g'.
m tPr'S-^-
318
The pedal-point can be employed less extent,
in every
the place of the tonic or dominant, and pedal-point. will
be
form to more or
and in such a case every tone of the
Below
will be found a
scale can take
become the
basis of a
few such applications, which
suiiioient to serve the student as guides.
^"^"-^TTTTj III' 4-'^^:^319.
320.
* See Appendix G.
220
CHAPTER
IX.
RETKOSPEOTION. A.
Devehpmenf of Harmjony,
We stand again at the boundaries of a vast field. A rich and important part of tonical development
The two
and
tone-species
is
their scales
spread before us.
have been firmly estab-
lished.
The melody has been developed upon a diatonic and harmonic by means of rhythm and the first principles of musical con-
basis,
struction.
The fundamental forms of musical construction have been
in-
dicated.
But most important of all is the development of the chords, it was effected by the triple structure itself, or by such alterations of degrees as were originated by modulation. This development of harmony led us to modulation into foreign keys. as far as
The two together engaged us so much that the melodic element, the guidance of voices, had to become subordinate and also the further development of rhythm and construction had to be ;
neglected.
Let us
now
glance at our results.
Our rapidly increasing richness has furnished us with innumerable means and ways for the most manifold objects. We should not like to lose any part of them. But the power of our first formations the meaning and importance of each exist still.
—
None
—
of all succeeding harmonies
and strength to that
first
is
the parent and
equal in clearness, dignity,
harmony,
321. f)--
which
is
gz
modeTof proportion
for all the others.
221
The depression of its third has given us the minor triad. Its was the basis of the dominant chord with all its variations
fifth
And
and descendants.
thus, gradually,
have
we been ied
to the
modulation into foreign keys, and have gained means for more extensive compositions. It
now
remains
on paper as well as
for the student to practice
at the piano-forte, everything
he has learned thus
far.
Having arrived at this point of harmonic development, we must look back once more and consider the relation of voices in their progressions
We
with each other.
have already observed that two voices cannot well pro-
gress in octaves or fifths with each other, without injuring the
At
proportions of the whole tone- web.
we have
the
same
time, hovvever,
indicated their admissibility for particular objescts.
order to arrive at these objects
we must
first
ascertain
In
what such
It is not enough Such principles would degrade music to a mere slave of the senses, while it would prevent mind and soul from taking any but the most superficial interest in it.
consecutive
fifths
to say they
do not sound well.
or octaves in reality express.
If the progression is
idea then,
intended to convey an idea to us, that
must be interpreted that
consecutive
able in their
effect,
either rightly or wrongly.
octaves
or
This proves,
however disagreeone place, and wrong at
fifths,
can be right at
another.
In order to ascertain where such progressions are rightly or wrongly, stated, first
we must
know what
such
therefore,
momentary
as
employed
we have
alreiady
parallelism of voices in
general expresses.
This
is
for us to
not the place to exhaust such a subject.
know
It is sufiieient
two voicef makes establishes a unity between
that the parallel progression of
those voices resemble each other,
them, to a greater degree than progressions in difierent directions. Therefore,
two or more voices progressing in octaves
i
M^ Ff
222 are considered as a
monophonic mass ; and
for the
same reason
have consecutive octaves in tetraphonio phrases been condemned.
For the s*me reason are the parallel progressions in sixths or thirds (as we find them often in duetts) so well calculated to cement the unity of voices. In polyphonic phrases, too, these parallel progressions preserve
the same characteristics.
Thus we perceive
in the following, for
instance,
^ two upper voices seem to lean on each other, as if they were determined to be reckoned as but one. Therefore all paralthat the
lel
voices are capable of leading ns past such progressions as
by themselves would be offensive. Thus are the following progressions justified by the parallel directions of two or more of the voices, I
J
-^ -r-frrTT But
On
this unity
the contrary,
Kl
fl
and similarity cannot always be welcome to us. we would probably prefer, particularly in the
outer voices, a characteristically-different progression of voices.
Besides
this,
a too great extent or accumulation of parallelisms
is
apt to produce monotony instead of unity.
For
former theorists established the
bass and treble, or
rule, that
this reason
have
lower and upper voice in chorals, should not progress in parallel sixths or thirds.
Thus much of the parallelism of voices in general. We have to consider the effect of two voices, according to the intervals in which they progress. The first of these are
now
the
Octave Parallels,
of which everything most necessary has been said, (page 101, ex-
ample No.
93.)
223
We
convinced ourselves at that place, that octaves as mere
mere reinforcement, as it were, are admissible was quite a different affair when the octaives were
duplications or
but that
it
;
formed by such
voices, as, according to their position,
were
idently intended for an independent path in the harmony.
the alto in No. 92, took
place between the essential voices of
its
the harmony, and though until then an essential voice
came merely a
ev-
Thus,
duplication of the bass
;
itself,
or ia other words
be-
made
consecutive octaves with that voice.
Here
11
)
I
1221
e
.
—=p~i
I
I
'
I
r~
is
FtF
r
i
.
r^^—r^
'^
a phrase in which the third and fourth voices proceed in oc-
The one
taves throughout.
is
a mere reinforcement of the other
both in reality form but one voice or melody, and answer their purpose full well if it was the composer's object to obtain a broadness of volume which could not be effected
by mere
stronger enun-
ciation of a single voice.
From
we
the octave parallels
turn
now
to
the Fifths, or Quint-parallels,
of which, too,
we have spoken
and
already, (page 102)
select ot
them the succession of
Two
We remember
or more
Major
54 the
that in No.
Fifths.
fifth
was the
first
new
tone
developed from the fimdamental tone, and that the interval of the
fifth,
for instance, c
was the
first
and
dawn of harmony
;
g,
the, as it were, still
uncompleted
triad, c-g
Without teristic
entering
and
e.
more deeply upon the meaning and
of this interval,
we
perceive at least that
" the triad" to a certain degree.
it
charac-
represents
Consequently a succession of two
^134,
fifths
represents to us, a succession of
manner of the
ing exactly in the
two
This hollow repetition
must be already displeasing to us when we couipare normal development of our harmony,
with the
it
3
8
321
$ ^ in
one appear-
triads, the
other.
-&-
which no triad appears in the same position as the imme-
diately preceding one repetition,
instance,
when
its
;
more,
still
when we meet with such
so,
ingredients belong to non-related chords
dominant and subdominant.
This explains, then,
;
for
why
one quint-succession can be more disagreeatl^ than another. Fifths, indicating or belonging to non-related chords
(like those at
a and
b), are
more conspicuous
and'
more
disagree-
able than others, indicating or belonging to related chords, particularly
when
the faulty chords are separated
belong to different rhythmical links (b). tion of the delinquent voices, is for their progression.
Even
by a
(c, d,)
pause, or
the contrary
mo-
sometimes a sufRoient excuse
Thus has Haydn introduced them in the
Overture to "the Seasons:"
?t.
^ai.
^
ti-
Ete^
when the
two., lower voices. have the
notes
—a and d—g
e
— d and g—
a
c.
^
±3
225
An
interruption of the quint-sucoession
Jinatead of
I
!
by means of
rests,
^
=lzE_lir=4:g:
i
r
f—
I
tends also to indemnify us for the fault, as in a degree the connection of the
f-
interrupts or hides
it
harmony.
Intermediate tones,
too, tend to mitigate the effects of such succession,
iL-i.J-J
i
«P0
r
and particularly when the
fifths fall
the measure, as in the following
on the unaccented parts of
:
i^f^^P^ J-
i
)f
Another
liind
of mitigation
that not the chords indicated
nected, succeed each other.
sures
A and B of the
is when the other voices insure us by the fifths, but others, well con-
Thus, the unpleasantness of the mea-
following.
^
It
T
r is
considerably softened
when they appear
^^
-A
—
I
thus
—
*\-^-'
li-
?2Z .01
-iB-
f Still less
unpleasant are such successions when they are hidden
226
by a flowing progression of
the voices (a), or when: the
can be considered as essentials of one chord
^ i rj This,
we
B
two
fifths
(b).
I
-*—Ti
r
hope, will be sufficient for a subject which for years
has set our theorists at loggerheads, and has caused the most con-
We
tradictory rules.
have perceived that the prohibition has
good reason, and that we are always able to avoid consecutive fifths, if we wish to. But we must always remember, that an abstract rule can spread much mischief, and that quint-successions are not only sometimes admissible, but actually the only righ1! its
way of
We shall,
expression.
therefore, attend for the time to
these prohibitions, if for no other purpose, merely to practice the
But
avoiding of fifths. fifths at
not prevent us from using these
this shall
a later moment,
when we have some
particular expres-
sion in view.
SUCCESSIONS OF MINOR FIFTHS,
(a),
and SUCCESSIONS OF MIXED
FIFTHS, i.
e.
of major and minor, (b) or minor arad major
included
A
m
I
B I
M:
in the prohibition,
U i"
I
are not
I
n from the very
fifths, (c)
"I
minor
fifths
do not des-
when a major
fifth
succeeds a
fact that
ignate any original chord, though,
minor, the succession partakes, in a degree, of the disagreeable character of major.fifths.
The inversion of a
fifth results in
a fourth.
It is
sequence, therefore, that fourths, too, should share
the inconvenience of quint-successions.
made use
It is
true
a natural con-
somewhat
we have
in
often
of consecutive fourths, but never without hiding the
obnoxious tones between the parallel progression of the outer voices.
227 Successions of sevenths and seconds can only occur
Sep time chord leads into another
when one
for instance
;
Pis^ Successions of thirds and sixths are the most unobjectionable. But we must warn against a too frequent and too long use of
them, as they are apt to give to the music an effeminate character.
A succession
of major thirds, as
we have had
monization of the sixth and seventh degrees of the
it
in
our har-
scale,
iESE^
-Sh
-iS-
r
has also been thought objectionable
cannot be denied that there
is
by former
theorists
something harsh in
;
and
it
this succession.
But if the chords are otherwise well-connected, this harshness becomes much less perceptible, and often, too, such harshness can be the very representative of an In short,
we
will
artistic idea.
always guard against that effeminacy of mind
which makes us hesitate at every full and vigorous expression, and which always deceives itself, because the anxious listening to every strange tone or chord leads us to suspect something wrong or bad, which in reality does not exist.
228
Eigrhth Fart. Displacement of Chords.
CHAPTEK
I.
SUSPENSIONS FROM ABOVE.
However
richly our
there remains is
still
harmony has been thus
far
developed,
a certain monotony in our compositions, which
owing to our close adhesion to regularly-built chords.
Every
tone of our melodies belonged to such a chord, and every chord
The consequence
stands there, independent and well rounded.
we had
of this was that zation,
to resign all free
and animated rhythmi-
which enlivened our monophonio and duophonic composi-
One voice was chained to the other, and when one entered new harmony, the others were sure to follow. It is clear that the invention of new hatmonies does not remedy for each of these new chords must again be constructed this evil But we must take a different view of the harof three tones. monic element we must look upon it as a combination of diftions.
a
;
;
ferent voices.
our
From
this point of
view
we
discover the cause of
difficulty in the fact that
All our voices progress simultaneously from one chord to another In the following phrase, for instance,
zssz
322.se
as soon as the first
chord, too, enter
g goes to
upon an
/, all
the other tones of the
interval of the second chord,
first
and thus
it
continues to the end. It is
now our
object to attempt the reverse
;
the different voices
229 shall not progress simultaneously. shall not progress
The upper
voice, for instance,
with the others.
-J_; '-i-
323.
-&-
The succession of chords remains here third,
first,
and
fifth
lower voices are the same throughout. voices progress from the still
first
But while these three
chord to the second, the upper voice
holds on to the &st chord upon g.
to the
same
The The three
essentially the same.
chords are absolutely unchanged.
This g does not belong
chord, is absolutely discrepant to
then the discrepancy ceases.
and must,
there-
But we should not have introduced
ha4 not remained from the
this discrepant tone, if it
and thus become bearable. has prepared us to find
it,
the proper tone of the chord /; and
fore, finally resolve into
it still
Its
existence in
in the second.
the
first first
chord
chord
The same can be
said of the e in the fourth chord.
A
tone, thus stretching
does not belong,
»
from one chord to another, to which
it
is called
SUSPENSION.*
Thus the nature of the suspension suspension
is
itself teaches
us
when such
admissible.
Firstly, the suspension
must be prepared ;
i. e.,
the discrepant
tone must exist in the preceding chord, and must be given to the
same voice which forms the suspension. Secondly, the suspension must be resolved ; i. e., the discrepancy between it and the chord must cease, the suspending voice must finally enter upon the proper tone of the chord.
/
Yet the discrepancy between suspension and chord is not justified; in spite of preparation and resolution, we still hear a strange tone instead of the proper tone of the chord.
Strictly
speaking, the discrepancy exists between the suspension-tone and that interval of the chord which has been retarded fore, in
order not to
make
it
too harsh,
it
is
by
troduce the suspension and the retarded interval ously.
If,
for instance,
we were
it.
There-
advisable not to insimultane-
to represent the above phrase
thus: * See Appendix
1
230
J—r^ 324.
m
W -f=^
TT
ei^
^^
22=
the octave of the fundamental tone (in the second chord) -would
be suspended, while the same interval would be introduced simultaneously with
its
suspension, in the upper voice.
In the
manner, in the fourth chord, the upper voice has the fundamental tone, to if
d,
same
of the
while the fourth voice has the suspension
The discrepancy of these tones would be
it.
fifth
still
e
greater,
the disagreeing tones were close together.
^-^=^=4=^
'''$
r
2221
^^-
r
We have to make a distinction here between fundamental tone and octave.
The octave can be suspended, without
interfering
with the simultaneously-entering fundamental tone.
Where, now, can suspensions be employed? Everywhere and with observation fulfil the above conditions
where we can
;
of these conditions 1,
in every voice.
2, in 3, for
every chord.
every tone of a chord.
The preceding attempt (No. 323) leads us pension which
we
to one species of sus-
shall call
Suspensions from Above.
This suspension-tone
is
one which must descend a degree, in
order to resolve into the proper tone of the chord.
Consequently every tone of a chord which descends a degree, can be employed for such a suspension.
Let us attempt the upper voice.
this in
our descending
scale,
and
at first with
231 326.
^J-J
I
I
t:
-^
-e-
W\\usi :
I
And now we
will introduce all the suspensions possible with
these chords.
327.
^U-
I
^
I
g—
^-FS
—g—
SI-
^
e
-s'-
p^r^f J-
QE
:23i
The bass could nowhere become a suspension, because it nowhere For the same reason the alto had to wait
descends a degree.
until the seventh measure.
We perceive into existence as, for
here harmonic formations which, though called
by
suspensions, resemble
some of our former chords
instance, the second chord, which resembles a quart-sext
chord, while
we
intended quite a different harmony
chord or triad of
It is
d.
such formations as chords or suspensions.
we know them, and can
;
quite immaterial whether
call
them
It
the septime
we
consider
sufficient that
is
into existence
whenever we
want them. But there are other suspensions which, though resembling still treated very differently. Thus we might consider the first tone-mass of the fifth measure as an incomplete former chords, are
nonachord, f-a-c,
But
c-e-g-h-d.
in that case
instead of resolving into
need not stand in our allows us
way
;
to consider this
c-e-g.
nay,
mass
it is
it
ought to resolve into
Here, too, this ambiguity
an actual advantage,
for it
either as one formation or as
another.
The introduction of because
all
suspensions, thus
far,
gave us no trouble,
our voices descended, and were
preparation and resolution of suspensions.
cending successions
?
Here, for instance,
all
appropriate for
But how
is it
with
as-
232
ki
328.
sr a suspension from above seems impossible, because none of the voices descend.
But
if
we merely
look upon the contents of the chords, suspenIn the second chord is
sions are quite practicable.
be suspended by fortunately
it is
in the treble,
we
Here, as formerly in No. 95,
The
voice.
alto,
We have now two goes to
rf,
Leading
which might
and the treble goes to d instead of h.
same manner we might suspend the but the d is again in another voice.
In the e?,
6,
This c exists in the previous chord, but un-
c.
c
of the third chord by
two tones to one g and then goes to c.
give the
for instance, takes first
voices which have the tone c ; but the one
and the other forms the suspension and goes to
this h again
up
to d,
we
d goes to into c. Here
suspension, because the one
suspension and resolves
make
are again enabled to e,
J.
a
while the other forms a
is:.
1.
3F 329. 2.
s.mm.
^^^»lJlij^Md: f fe-
is
an illustration of the proceeding.
ing scale, harmonized in the sions
first
Here, now,
mamier, with
is
the ascend-
all its
suspen-
:
330.
im
P Ps-\ 0-
BE -Ai The If,
&-
f^VfT
;A-^-i
-022r
alto, alone,
was able
221
in this succession to
we had changed
f
1-^
sr
P2-
in the third measure,
-e-
221
form suspensions-
the triad into
a domi-
233 nant chord, the tenor would have had opportunity to form a suspension.
1: 331.
BE In the penultimate measure, too, the tenor could have
made
a
was not already in the upper voice. What have we now gained by these suspensions 1
suspension, if the b
First of indicate
all,
many new harmonic formations. If we wish to figures, we must write the suspension and the
them by
resolution under the bass.
marked thus «rt^
r
V
:
The above
succession
would then be
234 It is
now
necessary, above
all,
to acquire the greatest facility
of constructing suspensions, such as eroise
we have had
may
or
first
and No. 195
togethei'.
finally
—
B, (2),
all
Every ex
one voice after the other in
be advisable to treat ner,
we know now.
write, can serve us as basis.
As an example we
with simultaneous suspensions in
It
this
give
will
manhere.
the voices,
all
as far as they are possible without change of harmony.
335.
j-^gi
.r-i
m f^ J-
I
z3tji=Mziz
^.^
-TjJr
BE
=^
fZ:
But, however, great the mobility of our voices, and however
extensive our means, like to be,
wherever
and
we
by no means as free as we should we had to introduce the suspensions many as we could, without having it in
are
for this reason
we could and
as
our power to obviate the harshness of one, or the meagreness of another.
mand
But on the whole we have gained considerably
in
com-
of our different voices and their characterization.
Suspension of Fundamental
tones.
The suspensions of the fundamental tone of a chord in the bass seem so harsh, that we must enquire whether it is at all admissible to make use of them. The suspension of the fundamental tone in the bass shakes, as it were, the
upon
it.
which
is
Nor does
the bass at
all
necessary for the other voices.
cisive steps, particularly
when
whole formation based the melodic finish
require
The bass
prefers de-
progressing in fundamental tones.
235 But
in this
very consideration
above question.
When we
lies
the proper answer to the
wish to express a deep emotion, &c.,
the harsh suspension of the fundamental tone in the bass will be just the thing.
Or,
if in
an excited, agitated mood, the bass
should happen to take charge of the melody, as in Beethoven's Finale of the
I^ ji
li
m^ it
C| minor
Sonata,
335.
—^^33—1^—
^^B
f
KB.
gEE^=i«^=?:
would be cowardly
to retreat before a
g=
momentarily harsh com-
bination.*
* See Appendix
IT"
I
J.
236
CHAPTER SUSPENSIOK-S
We only
II.
FROM BELOW.
when we attached our suspensions to was not in this that the nature of the
acted arbitrarily
tones which descended.
It
suspension lay, but merely in the fact that a tone of one chord stretched over into another to which '
But
this can also
pension-tone
lower,
is
it
was not indigenous.
be the case when the preparatory and
sus-
and resolves into the next higher degree.
Here
336.
we see the b of the first and third chords resolve into the higher c ; and again we see the h and d of the penultimate chord resolve These are the suspensions which, in into the higher c and e. we call suspensions from They require no further explanation. The ascending with employment of these suspensions would present an
contradistinction to our former ones, below. scale,
appearance like the following:
387.
The necessary
figuring
has been added according to
known prin-
ciples.
In the descending scale, too, sions,
we
can introduce these suspen-
with proper regard of the necessary preparation, as indica-
ted in No. 330.
237 i^
338.
238
And now we must
return to the heading of the whole part,
DISPLACEMENT OF CHORDS.
Formerly we have looked upon the suspensions in a literally melodic point of view, as the most important, and have acciden-
some new harmonic formations. Now that we can them fully, and observe their effects upon the harmony, in them
tally acquired
reconnoitre
we
can see
A
new means, and
Next to
the strongest
means of harmonic connection.
most general connection which chords have on account of their intervals belonging to one and the same scale, there were two means of bringing them in a harmonic relation to that
each other. Firstly, the mutual tones. are actually the
most
But as
ineffective in the
far as
new
we have
seen, they
For, on ac-
chord.
count of their having been in the previous chord, they are less
new
conspicuous than the
tones.
Secondly, the necessary progressions to another chord which nature has given to the dominant chord and
all
sub-species,
its
though we have occasionally permitted some deviations from the natural progression.
;
The Suspension combines both The
ens them too.
the previous chord chord, its
it
;
suspension-tone, also, has been retained from
but since
decided progression
—
the resolution
new
absolutely disagrees with the
The
suspension-tone, too, has
but in consequence of
;
new chord
as far as
the nature of the suspension ;
it
monopolizes the attention.
with the whole
poned
of these means, and strength-
its
we can judge
—
this progression
disagreement
at present
from
cannot be post-
must follow while the new chord
is still
in existence.
Thus,
by means
of suspensions,
we
can form harmonic succes-
sions firm, unseparable, soldered one to another,
city they will
be of vast service to
and in
this capa-
us.
In the course of our instruction we have only spoken of what was absolutely necessary for the occupation of the student we have not even drawn attention to the fact, that the tone of a melody need no longer be considered as an independent tone of the ;
chord, and that, now,
it
might be considered and treated as a
sus-
239 pension. But now, that we have done justice to the nearest and most practical object of our instruction, we must not fail to draw thelattention of the student to some peculiarities. The resolution of the suspension was necessary, in order to explain and justify the discrepancy
the
new
But
chord.
between the suspension-toiie and
this justification can
be postponed, by
cing between suspension and resolution another, or
more
pla-
chord-
Thus, here
tones.
at A, the suspended e reaches correctly into d, but not before the
new chord found its way between suspension and resAt B, in the above, we find even three tones between
third of the olution.
the suspension and its resolutions.
Op. 101, has gone even
Beethoven, in his Sonata
farther.
A t^^i=H i -fi
@W
^^^^Ih&^ The
first
measure closes with the quart-sext chord
ceeding ineasure begins with thS dominant chord the a of the
first
chord
is
retained,
before doing this the a goes
and
finally to
If
^^f.
it
first
were at
«-a-c|
the suc-
;
e-g\-b-d, in
and must resolve into
which
^ff.
all
is
J,
important to reduce every
new formation to fundamental forms, we might easily explain above by imagining the chord /|-(i-c|-e, but the explanation that/jt
But
to the foreign tone/|, then to
the
of
here of minor importance, the retarded resolution of
the suspension
is
our chief topic.
The whole reminds us of the retarded third, seventh,
and
ninth, in the septime
resolution
of the
and nonachords.
Thus much of the resolution of suspensions. * See Appendix K.
In regard to their
240 preparation
we must remember
that a succession can only be un-
derstood, inasmuch as its tone or tones have appeared as harmonic
tones in a former chord, and have stretched over, as we'said before,
new
into the
mitted that
This was in fact, its resolution, and we adhad to take place in the same voice preparation^
one.
it
;
suspension, and resolution are in reality nothing else but the pe
But now we can derive from
culiar progression of a voice.
many new and
freer formations.
ii
Here
iE^^^^m^^^. m ~^' ^ ^
BE at A, first
we
±z
see the chord g-b-d with a suspended
chord, even in the
?ame
same
suspension-tone at sis not even in the
At
lower one. first
was
in
the
The
octave," but in a
c the suspension-tone does not even exist in the
chord, but our experience
the chord
c ; it
octave, but in a different voice.
and sensation lead us to imagine
c-e-ff.
It is easily
seen that in
all
these cases the preparation of the
suspension does exist, though only in imagination.
We
say that such formations are inadmissible or wrong
;
cannot
but
we
must admit that there is something estranging m them. And, finally, we might allow a suspension without any preparation.
-^
^
F=F
f
'ff
m^
II
'
y^
c^"
jr~s
ff
BE
r
2?".
we aimed at all at a decisive, startling combination of tones. These unprepared suspensions might serve also for a milder, if
anxious expression
;
for instance,
341
P
But often the apparent writing
^
w
-zsa
w manner of
irregularity lies only in the
Phrases like the following,
it.
J^^^^P^— 1=
1^0 ^^
O^^g ^^s-
-
containing apparently unprepared suspensions, might have been
written thus
221
E=^ ^i=:
J2—-S.
3
-G-
and can in that manner be easily explained.
But we must return again It
to the resolution of the suspension.
ought to take place while the chord into which the suspension
has found
its
way
is still in
-&-
W-
existence.
y=^
Here, however,
-^-
-19-
Y i
P
we see the resolution take place on a
different chord.
the treble ought to resolve into the
of the chord'
like
manner should the
Both tones pureue
But there are
their prescribed course,
still
We know already
and in
resolve into the d of the chord g-i-d.
but in the meantime
c-e-g
chord does not influence
The /of
e-e-^r,
and g-h-d have changed into- cb-c-e and that the resolution is effected on the proper
the chords sufficient
e
e
h-d^f.
It is
toTie.
The
it.
more peculiar formations.. of two ways in which to retain a chord while
one or two voices progress:
—
1,
the suspension, and 2, the pro-
gression of a voice from oi:e chord-tone to another, (Nos. 59 and ft5.)
We need not hesitate to
employ the two
in succession, as
242 long as either of them, particjilarly the su»pensioiif obtains its due.
Here, for instance,
the suspension of the treble at a,
solved into the next tone
;
b, c,
and
but immediately
d,
after
is
correctly re-
the resolution
the voice passes through several tones of the chord.
responds perfectly to our rules, but since diffiised,
we
P E /
it
This cor-
might often be too
will here
i
Jtt
ty^ * ^^ i -^-:
243 contented with the
still
the resolution-tone, has
sounding chord, which though containing it
the discrepancy between
But
in another voice.
serves only to isolate the suspension-tone
still
this
very defect
more, and to
make
and the harmony either milder or
it
stronger.
In the above
it is
not only better to introduce the suspended
chord-tone simultaneously wtth the suspension; for instance, tn
make
the accompaniment of the above thus •g--g--
^^
but the chord-tone
^?#
:
-^V-fi-
m. m
another voice can serve in a degree as the
expected tone of the resolution.
Here we
see
We
pension.
agdn a
deviation from the
one and the same time, though
-'(2-
i
first
niles of the sus-
see the suspension-tone and the suspended tone at in diiferent voices.
I
-&-
1 "^
jG^Tn
^
^^^
=F=f=
-e-
Z2=
BE The ate
distance modifies the disagreement, if
Finally logically
we
it
does not obvi-
it.
we must mention an ambiguous form which
from the suspension.
arises ana-
Here
The g of the treble remains same manner does the b remain with
see this form twice before us.
with the chord the chord
c-e-g.
OrC-e ; in
the
Were we
to consider these tones as suspensions,
they could only be from below into
c,
;
g would
resolve into
a,
and
h
though the resolution of g would be an octave lower, and
244 that of b retarded
by two
intermediate tones.
But in that case
these suspensions
i I
would be nothing but octaves of another voice dragging after it, and suspension-tone and suspended tone would meet in the same
moment.
A regular explanation of these tones
possible.
But w6 need not bestow too much time or thought
upon these
formations..
It is sufficient if
is
absolutely im-
we have a perfect control
over them.
Thus much of the suspensions themselves. that in all their fornis they have the effect of
But we have seen making the single
chord less clear and distinct, because they unite or solder
as,
when given
able
it
to
Therefore, they serve as modifications of such relations
another.
effect.
in their nudity, as it were, produce a disagree-
This last remark reminds us of the reputed octave-
and quint-successions.
Let us glance
first
at
FIFTHS MITIGATED BY SUSPENSIONS.
Here
we
at a,
see an evident quint-succession
;
it
belongs to the less objec-
tionable class, on account of the seventh therein contained, and at B
it is still
less objectionable
on account of the suspension. The
following succession
17"
i PT'if^
I
I
I
f
would be absolutely wrong,
if
written as at a ; but the suspen-
245 sions at b, soften it to such a degree that
employ
we need not
hesitate to
it.
It is different
with
OCTAVES COVERED BY SUSPENSIONS. Here, worse.
it
may
Thus
often happen, that suspensions
make
the evil
if here.
1
i
I
r
I
i
at A, the octaves are objectionable
I
;
i
those at b, on account of
the meeting of suspension-tone and suspended tone are
more
so.
still
246
CHAPTER m. ANTICIPATION (ANTICIPATED TONES).
What made The
fact
the suspension comprehensible and sufferable?
of its having been a part of the preceding chord. In other
and
justification in another chord,
words,
it
and
one that has already been heard.
in
finds its explanation
/ To attempt the which
it
reverse, let us
now
lead a tone into a chord to
does not belong, and with which
it
disagrees.
But the
tone has not remained from a former chord, but has been antici-
pated from a future chord.
341,
m
% i^
±:
-^
m
We see here that the tone c appears in
total contradiction to
the chord g-b-d, without any justification of
tone
d appears
in like
its
The The succeed-
appearance.
manner with the chord a-c-e.
ing chords, only, /jf-o-c and g!^-b-d explain the contradiction. clear that such discrepancy,
which
duce a more harsh and decisive
is
It is
not even prepared, must pro-
effect
than the prepared suspen-
We
have to consider well, therefore, if the introduction of such effects corresponds with the object we have in sion.
view.
Sometimes voices,
it
is
the consistency in the progression of our
which leads us to anticipating tones, as for instance in the
following
where the upper voice pursues
its
own
course,
and thus blunders
247
upon the tone e, •which belongs to the succeeding chord, c-e-gi, instead of the dominant chord which accompanies it. Sometimes the anticipated tone is merely intended to add rhythmical vigor to the succeeding one, and cannot be considered as belonging to the chord in which
it
appears.
Thus, in the
ancient cadences,
343. ~i\
f=
which the anticipatory
in
r c acts
merely rhythmically.
Or,
by
means of anticipation, the figuration of a melody may become more animated, as in the following
^
:
— —^—# i^f=f^
344.
g.
r
And
r
Pis'-
again these anticipated tones are used^
makes a his opera.
La
Vestale, after
D minor, anticipates a tone
when one
voice
Thus, Spontini, in the overture to
decisive entrance.
having closed in
F and modulated to
(6),
345.
full
two chords, and only justifies is no need of searching
There
covering
all
possible liberties
it in
the third chord.
for such formations, or of dis-
we might
take with these tones.
is best to trust to our inspiration for their development.
It
248
JVinth Part. The Pass.
The
suspensions and anticipations were the
first
step towards
the liberation from the triple nature of our chords, and the de-
pendency of every tone of the melody upon the harmony beneath it.
But
Tor
if
neath
have
in reality this
dependency of the melody has not ceased.
melody does not belong to the chord be^ it or after it. Yet we a choice, and this new liberty has arisen from the
the tone of our
it, it
now
belongs to either the one before
at least
harmonic element
itself, or,
to speak strictly,
FROM THE CONNECTION OF THE CHORDS. But we know that in every single chord lies the element of melody ; that we can introduce its tones in melodic form, one after the other. »And this new view of harmonic formations must open to us a new melodic sphere. Here 1
346.
we
f
see the treble pass through all the tones of the chord.
It
pro^
But knowing that the third is in degree, and that another degree lies
ceeds, consequently, in thirds. reality nothing
between
it
but the third
and the fundamental tone, can we not include
termediate degree in our melody
this in-
1
347.
We go from e through d to Thns we see
*.
at once the nature of the pass.
does not belong to the harmony
;
the preceding, nor to a future one. stance, a filling of the (c
and
e).
It
The
passing-tone
neither to the present, nor to It
is
simply a melodic sub-
melody, a mediation between two tones
agrees with the harmony, because
harmonic tone to another harmonic tone.
it
leads from one
249
CHAPTER THE DIATONIC
We are already familiar in
with
it.
I.
PASS.
We might
No. 346 a second passing-tone, from
348.
have introduced
e to g.
m
Instead of the prolonged tones of the chord
we might have
re-
peated them thus
349.:
We see that melody. the
Tf=f the chords
fall
Thus we are led
always upon a harmonic tone of the upon one and
to place the whole scale
same chord
.^^ n
350.
the repetitions of the chord have also been here employed.
This leads us to something entirely new. last
chord does not
fall
but upon a passing tone,
We
see that the
upon a harmonic tone of the melody, h.
This
is
not as satisfactory as the is in reality nothing
former arrangement, though the fourth chord
but a continuation of the same harmony which did not displease Still more strange would this form us to the tone d,f, and a. be, if a
new chord
should meet with the foreign tone
351
^ff
:
250 but the immediately following harmonic tone
(c)
balances every-
thing in either case.
A
passing tone,
chord
itself, is
when happening upon
the entrance of the
called
a Participant Tonei^itl'-'
Thus
Sa.'
*
''^
in the following example.
the twoy^'s are passing-tones, while the tones, a distinction, however, which
Had we
we
two
e's
tried to avoid the participant-tones,
achieved the same object
by a
are participant-
consider as unessential.
we might have
different rhythmization, perhaps
like the following
353.
sM ^ ^ P Tf w^ *=f
This has led us to employ two passing tones in succession. reality
we have done
this already in
trast the repetitions of
355,
it is
i
No. -349.
Let us
In
now con
one and the same chord
iS^Eg^
nothing essentially different from No. 350, and
we
see the
whole scale accompanied by one single chord, in which we consider d, f, a,
and b as passing tones.
confined to the tonic triad.
356.
^MM=i i I.a.
is
But we are by no means
Here,
23
1
the ascending and descending scale with the accompaniment of
251 the subdominant and dominant chords, in which
we have
only-
taken care to begin and end on a harmonic tone. Thufs far
we have
taken
our passing-tones from the reigning
all
These are called
scale.
Diatonic Passes,
and well deserve a thorough practice before we proceed.
Above we
voice
all
we must remember
introduce the pass.
that it is immaterial in which Like the suspensions, they can
occur in every voice, and consequently in different voices simulta-
The above tells us that every third can be filled up with one passing tone, and every fourth with two, or, to speak strictly, with one passing-tone and one participant-tone. neously.
Let us
now employ them
as often as possible,
our melody of No. 255 as basis, harmonize at
B we
it
as
We take again A simply, and
'
introduce our passing-tones.
357. A.
dz
^.^M^
IM
.i-
f'^mw^F^--^^^ 11 — V=^tMi ^^ fSEi^ tt Fi 1
1
iJ-J-
I
^ -0-0
-»-0:^
'i
D
i
i^
I
J
j#-*— aL
1
y=ri
^ l^§fe ? Why, at A, have we not filled out the bass have produced a peculiar kind of octaves, 358.
i
12*"
t==|:
?
'^J
Because
it
F would
252 (1) which are even worse than the open octaves at 2.
case
would have happened
Why,
at B,
have we not
at e filled
A similar
between bass and
alto.
out the bass
would not have
1
It
been wrong 359.
f but the seventh-succession between alto and bass, and the accu-
mulation of passing-tones in the three voices, would have given a dragging character to the whole phrase.
Why, the
first
treble
at c
case
and
and a have we not filled out the alto 1 Because in should have caused consecutive fifths between
we
alto.
360.
and
in the latter case
^^w
between
alto
and tenor.
253
CHAPTER CHROMATIC
PASSES
ASSISTANT-TONES.
The Chromatic Pass.
A.
Our
AND
II.
present means enable us to
fill
every third and every
larger interval with passing-tones.
But
With
let
us attempt to
diate tone d, rfj
fill
out a smaller interval, the second.
we seized between c and e the intermewe can now take the tone c| between c and or
the same right that
rf,
between d and
e.
-^^ much
This gives us Firstly,
we
to consider.
see passing tones employed, which are foreign to
the key.
Secondly,
we
see the small space of a third filled
by
three
passing tones, and thus are led to take the whole chromatic scale
upon a
single chord.
362.
Thirdly,
we
see
among
the passing-tones raised degrees which
are in the chord in their original form
^1 against
g.
Of course we can
;
for instance, c| against
c,
also introduce depressed degrees
against natural, or natural degrees against pressed or raised degrees.
254
iiitS33=
363. t)-
i
a=1=
S>^ -& i^
:fe
II
I
I
X
^^
iatfl :^
73SZ
These formations remind us of our former
cross-relations.
But
such a momentary oross'relation, appearing in an analogical succession, can produce
of the hielody, and
no disagreeable
by
effects
;
it is
merely a part
it justified.
This teaches us also the proper manner of writing passing'tones.
A passing-tone, for instance the
c| at a, is
Bd=^&:j P =5F ^
'''$
I
i
but a leader from one tone say
it
nothing
(c) into
the next one (d);
raises itself until it reaches the d.
the passing-tone
harmonic tone, sequently
should, of course, be called accordingly.
c raised
-^ame manner,
we might
according to
this,
nothing but a continuation of the preceding
is
it
If,
at b,
to
cjj,
in order to lead to
d descends
to
d\,,
d; and
in order to lead to
Conin the
c.
But why, in No. 362, have we written b\> instead of a#, as it ought to be according to the above rule t or why in No. 363 have we taken /j) instead of ^rj,, or e?K and c| instead of eb and d\)t Because the strict observance of this rule would lead us to tones too foreign to the original key, and would notes
more
What we have done
make
the reading of
difficult.
just
now shown in the upper voice can also be But we must look out, particulaiiy
in every other voice.
in the middle voices, whether there
And
is
room
for these passing tones.
since these passes are practicable in every voice, they
must be
practicable also
365.
'^^m
:^=^^^^^^B3E&=| M\
255
m
two voices
simultaneously,
or
even
in
three
more
or
voices
366.
But, of course, the more passing tones we introduce above or below the harmonic tones, the more are the latter placed in the shade, and the more danger is there of causing confiision.
And
again
we
return to our phrase of No. 357, in order to in'
troduce the chromatic passes too.
i
JEEJ^^fei^ '^0-t-f^i—-
rr-fi
seIe
i
w¥^=-y
-f-
f^f^F S
F-
?^|:
>J.#
-&-
-J-.
^E£ :f:
r
make this phrase richer, we have introduced some but we have by no means exhausted all possible
In order to suspensions,
For this would lead us into false progressions, and would overload the phrase with foreign tones. The treatment of passing-tones.
the thesis
may
serve as an example.
m^ 368.
i-
^^^s
256
With
the introduction of the diatonic passes
spoiling an originally correct phrase
ran the risk of fifths
and
The chromatic passes add another danger
other bad relations.
that of accumulation of foreign tones
and cross
relations.
The Assistant Tone.
B.
A pass
we
by consecutive
supposes always a vacuum, a step in the melody wide
Between c and e we d we had room at least for cj( no vacuum to be filled, consequently
enough to admit of an intermediate tone. could place the d; between c and
between
c
and
e| there is
we can have no pass. And yet there may be a tone ; the very
effects
at such places a necessity of interposing
of the pass would lead us to think of
We gain by the pass, as we have just of filling up larger intervals'
But these passes serve tion.
by
this.
explained, the possibility
interposing smaller ones.
also to increase the rhythmical
anima-
Here, for instance,
i a are resolved into quarter-notes at b, and into But between e and / we can gain no such animation by the mere passing-tone, because there is not room for
the half notes of
eighth-notes at o.
one.
It is true,
we might avail
a harmonic by-tone
370.
But use.
for
=>^ many
^
ourselves of tone repetition, or of
reasons neither of these expedients might be of any
The first might seem
poor, and the second might be preven-
257 ted by the progression of the bass, which, too, might go from
ciof. For such cases we require a The phrase a
We derive
particular aid.
it
thus
371. !
1
^r*i
I
372-9-
up by passing-tones at b. But must we absolutely go to e 1 is filled
return before
made use
we
The d led
We
get there, as at c and d.
of half steps.
to e
and back to
c.
can change our mind and
At e and
f
we have
Such tones are called Assistant-tones.
They can be either steps or half steps, ascending or descending. Half steps are generally best for ascending. We shall have more use for these assistant-tones at a future time. At present it will be sufficient for the student to practice chromatic passes, with the occasional introduction of assistanttones.
258
CHAPTER
III.
THE KESULT3 OF The
PASSES.
results of these passes consist principally in the additional
means acquired ; then in the capability of making our voices more connected and more flowing than we were able since we deserted onr monophony. It is true that by a too frequent application of the passes, our melodies can now become too round and polished, as they were formerly too angular and rough. But our only object, for the present, is to practice these passes, and at a future time we shall be able to to judge to what degree we can make use of them.
But the greatest advantage obtained
is
that
we
are no longer
melody yoke of harmony.
forced to construct a chord for every tone of the
we
thus
are liberated at once from the
harmony
now
is
and
Our
dissolved into four voices, each of which devel-
opes itself melodically to
;
;
based upon harmony, but not chained
it.
This melodic relation can even sometimes be predominant over
Mozart, in the " Magic Flute," in a and animated triphonio phrase, writes thus the harmonic element.
373.
^
i:
i
I
It is easily
If.
f
light
?~K^>
Z!'
perceived that the two-eighth-notes of the second
measure are in reality nothing but the chord ffJ>-d, suspended in the upper voices by a-c and the lower voice passing from b to the
d of the next
chord.
374.
r
The
phrase, originally,
was
i^^^fc r ^ f W
259 at A, and according to rule as written at b or c but Mozart wanted a more flowing progression and he mixed up suspension, and harmonic-tone and passing-tone, A similar proceeding has ;
been applied in the following
s
375.
W-
r f
tr
-r
?2I
where the simultaneous application of suspension and pass has preserved the flowing progression of
all
the voices and the dia
tonic progression of the bass.
But in the
since the passing-tones
harmony
itself,
now
actually begin to play a part
to which, originally, they did not belong,
they are also applied, though merely pseudo-harmonic
as suspension-tones,
1,
by making of the at B
376.
tones,
We use them
as real harmonic tones.
passing-tones at a, for instance, suspensions as
and c
fegM i&t^ r r
P
lU^UM^i:
IZ±
^:
"rT
u
--^
r
the preparation of which suspensions does not even exist in the
choii tions.
377.
It
c-e-g.
will not
Two more
Ei
be
difficult to
construct similar illustra-
illustrations here.
^
-e>-
H-ge
-yri&—
\-^
-^
-cr merely to remind us that even cross-related passes can
suspensions.
"cr
The passes can 2,
or,
they can at least
also
new
disfigure
become
become
chords,
well-known chords to such a
260 degree, that
we
can use them independently, without regard to
their origin.
The
378.
new
of these
chords arises from the pass of the
fifth
triad.
Eti^d=^
3E
:|bi-
m
The '
first
major
in the
f=
triad has
now
stance this chord
is
a superfluous
fifth,
and owing to
r this circuni-
called
THE SUPERrLTJOUS TRIAD. It is
It
the only passing-chord which boasts of a particular name.
can be introduced whenever
its
superfluous
fifth
has not ap-
peared as a previous passing-tone, 379.
and
it
new
,..,1,.,1,
can be used in
b^J,,U..
all its inversions,
and
for the
formation of
sequences.
380.
rrr^' Since the dominant chord
nothing but a major triad with
is
added seventh, we can embody with (a),
and use the new chord
ff-b-d'jf-f
it,
also, this superfluous fifth
independently
(b).
It fol-
lows, as a matter of course, the rules of the dominant chord, with
the exception of
its fifth,
which, owing to
its
origin,
must
as-
cend.
S81. '
'.J
MM.
-^ tiP'e—-
f Knowing,
further, that every septftne-chord is nothing
i^ but a triad
with added seventh, we might apply the same proceeding to the
major septime chord.
Here
261
382.
I'^m^-
we have made from by adding (•-e-jijf-6,
it
to
it
the chord
the seventh,
which we might
were at
all
-i
M. c-e-g,
i
the passing-chord
we have
call
ES£
c-«-^|,
and
obtained the septime-chord,
the superfluous septime chord,
necessary to have a
name
for
if
every new forma-
tion.
Formerly in No. 378, we altered the dominant chord by fifth. Let us now attempt it by depression.
eleva-
tion of the
383.
ibAi
ibA.i
W--»-
E^=^
We have done
m^ f^^
f-
it
at
a
;
at b
we have
placed the passing-tone at
once on the place of th^ proper harmonic tone, and thus formed a
new
chord,
depressed interval.
which differs from the dominant chord by its and by the absolutely necessary descension of that as we formerly made a diminished triad from the
g-h-d\,-f,
fifth,
And
dominant chord, we can now make a triad from our new septimechord (f) which is even smaller than the diminished triad, and which might, therefore, be called the double-diminished we were in want of a new name.* If this new chord
triad, if is
to be
* The chord d\i-g-i-f (o) boaBted formerly of a high-sounding name. Jnst because the superfluous sixth, ck-b attracted princapal attention, it was called the chord of the superfluous sixth, or some similar name and not satisfied with this, the same name was given to another chord, d\>-f-a\i-b, which had altogether a different origin, and thus, sext-chords, terz-quart chords, and This name is not quint-sext chords wei'e all thrown into one category. only superfluous, but it is absolutely unsystematical and confusing. ;
262 used tetraphonically, ssventh, as at
But
g
can only be done by the doubling of the
can easily be seen that not every position of these chords
it
All those positions in which the conspicuous
appears favorably.
tone
it
in the above.
(c?l))
close to the third (6) are unfavorable, because after
is
once exciting our expectation by
its
strange appearance,
resolves
it
which has already been obtained otherwise, and thus
into a tone
deceives us.
Chords like these, which take their intervals from can become ferring to
new means
them the
different keys,
of modulation, or mediation,
freer resolutions of the
by
trans-
dominant chord ;
for
instance, thus
384.
The minor
triad, too,
to it the elevation of the
we
fifth,
and by transferring
obtain a new chord
$M
385.
which resembles a well known sext chord
{g-byd!^)
which
has a major fifth,
differs
from
septime chord
it
in its progression,
{g-h\)-e\/),
but
and even leads to a new
:
^-^
^
386.
Ife
^ -&-
r Finally,
we
are led to harmonic formations, in which the for-
merly unlawful quint-succession appears purposely and with good effect.
387.
$
^V5
"ST
^
t^-
fe
-e-
We know that the
fc
^-
'!fn-
"C3"
f
iZ-
1'^^
-xsr •ST
diminished septime chord (b) arises fronj
263
We
the dominant chord (a). cession of heterogeneous
have also submitted to the
Here now,
fifths.
at c,
we have
suc-
intro-
duced the passing-tone ab, and at d follows the chord, /f-ab-c-e^, formed by it. The lower voices form here consecutive fifths, which are by no means disagreeable or inapplicable nay, which can even be used, as Mozart has done, and with good effect, in slow movement. ;
388.
E
*;
:^-
m^^
i
fe But we are led here dent has probably
to
made
.-&-
an observation which the attentive before us, viz
tion of the chord-tones does
much
:
stu-
that the peculiar posi-
to favor the admissibility
the comprehensibility of these successions.
If the foreign
too close upon another tone of the harmony,
if
and
tone
is
the two resolve in
one and the same tone, the resolution of the chord brings about something so forced and confused that it can almost become incomprehensible. admissible.
T
TJie successions of
But the same successions
j
quite correct at A and
But
Thus,
E^tlli
F=> let
in a different position
T"^
are useless and wrong.
389.
No. 383 and 386 are well
b,
is
the passing-chord d^-f-a
T-r while at o
it is
ff & spoUed by the position.
us return to No. 388.
Why are we justified now in making use of progressions which we formerly denied ourselves? Not merely because we now
264 consider
them agreeable and
fit
been led to them consistently,
for use,
but because we have noTf
ailalogically, instead
of owing them
to accident.
Here
is
the point whence arises often the greatest error.
say the greatest, because active minds often seize the
We
new and
ir-
regular instead of the nearest, and thus cut off at once every fur-
But we must warn,
ther development.
also, against slavish obe-
Every artistic nature has within it the impulse to free itself and to become independent ; but reason must decide how &r a deviation is admissible. And, finally, we see in the passing-tones dience to the letter.
3, the
at
or,
means of modulation, and preparation of
the introduction
least,
transitions.
Here
390.
we
Jfl
P
^
--F
1^
see a phrase beginning decisively in
measure into
in the third
G
major.
C major,
w but modulating
But already
in the second
measure does the passing-tone major, so that
/jf indicate the subsequent hardly requires the dominant chord.
it '
!
Here we
that
J
I '
J_J_ j
\
.
4
see both dominant and subdominant defend and main-
major, and yet, from the sixth measure, everybody
tain the will
J
G
imagine himself in G major, though the dominant chord of key does not make its appearance even at the end. The
passing-tone
key of
C
/t]
would have as surely indicated and retained the
instead of G.
This leads Us to a very importa,nt observation.
taken the passiflg-tone f,
we
If
we had
should not haive been prepared for
265
Q major we
but rather confirmed in
C
major.
In future, therefore,
will construct the pass before a modulation, so
pares rather than contradicts the subsequent key. reason, if
been
we
intended to remain in C,
unfit,
i :*=*
392.
r^ and the tone
/ti
'f the right one.
that
it
pre-
For this verythe tone f\ would have
266
Tenth Part. The Treatment of More or Less than Four
Voices.
Latelt we have limited ourselves to the tetraphonic composi and only occasionally represented one thing or the other with more or less voices. It requires now but a brief considera tion,
tion of the more-or-less-voiced composition.
CHAPTER
I.
THE TEIPHONIC, DUOPHONIC, ASD MONOPHONIC COMPOSITIONS.
We
have perceived that not even four voices were sufBcient to
by making use of harmonic bye-tones. Complete nonachords were altogether impossiSeptime chords could only be carried out completely with ble. five voices, and faults could only be avoided at the expense of give us always complete chords, unless
the completeness of the chords. It is still
natural that this incompleteness of chords should happen
more frequently with
oftener
make use
less than four voices, or
of hannonic bye-tones.
we
should
These, however, if
still
we
wish to avoid a certain emptiness and superficiality, will force us to
make
use of passing-tones
;
and
it
may
not always
suit,
our
purpose to overload our voices with harmonic and non-harmouic additional tones.
must
first
What The
Before making use of the latter, therefore,
harmonies
triads require
we
can best represent without imperfection.
but three voices, and consequently can some-
times be better applied triphonically than tetraphonically.
we know
we
consider
But
already, that the progression of the voices often pre-
vents our directly reaching those tones which seem desirable to
267 Therefore, even in triads,
us.
we
shall
many
have to resign
a
position, in order to represent our chords as completely as possible.
If,
we were
for instance,
accompany the
to
tones of
first
the scale with triads, the position at a and b would be preferable to that at c.
393.
$ P=f
&
2
:
-JF I
though
we had
But even
to introduce sext-choi'ds in the former.
this
we
precaution will not always/ be sufficient;
must, for the sake of flowing progression, leave some chords complete.
It is
best be omitted.
now
necessary to
We
know what
have given
all
in-
tones of a chord can
necessary information on
that point.
The dominant-chord cannot be represented completely without The fifth is the interval in it which can best
harmonic bye-tones.
We know, too,
be omitted.
omitted, in which case
that the fundamental tone can be
we have a
diminished triad
gression of the voices will often force us to
left
the pro-
;
make use
of this
chord.
Let us now attempt the accompaniment of the scale according to our first
manner of harmonization, with employment, howev-
of the inversions, wherever they seem preferable.
er,
We
perceive that the final chord of b has lost the
th.rd, unless
we
fifth
and
prefer to end with a sext-chord.
The duophonic accompaniment would be We could employ the natural harmony,
still
more meagre.
395.
or,
take a mere succession of sixths, or pursue any other course.
268
The nonaohords would have to resign third and fifth, unless preferred to exchange them for derived septime-chords, in
we
which
latter case the third
had best be omitted.
According to these principles, No. 217 would be harmonized triphonically, perhaps thus
m-wri 1
1
In duophonio composition to the
and
we
should have to cling
model of natural harmony, and
sixths, for instance
still
closer
to successions of thirds
:
397.
^^m
^m w
rnffT^^Tf-
We know, tones the
too, that by means of added bye-tones and pa>.i--ingharmony can be completed, and the voices made more
flowing or animated.
Instead of all further explanation
we merely
give here a single illustration, -yy—h 398.
^
—
d
"
i
^^-^ :?-*! :?=^i F-^a-
CCj'
:^^^ Li'j ^^ 1-5=
^^m1
269
may
which the student
analyze for himself.
way in which the And, finally, we must return
not the only
This was our
tion.
possession the
This, of course, is
phrase can be carried out. again to the monophonic composi-
first lesson,
but
we resume
it,
having in our
means of a fully-developed harmony, and the
tone-
foi'mations attached thereto.
We must now confess that the mere scale, though the first and most necessary, is but a meagre basis for melody. Our phrases have long broken through the limits of a single scale will
no longer end upon the
nant, or has
harmony and the
parallel,
;
we have
latter strives again for
sions, passing-tones, all this
&c.
the thesis
;
but strives tqwards the domi-
become a separate part and ends
dominant, or the
Can
tonic,
in the
key of the
a continual longing for
embellishment by suspen-
&c.
be done
in a single voice
?
Beyond doubt.
We know already that chords can be melodically represented, in part or entirely,
by a
single voice.
Then we can
easily see that
suspensions, passing-tones, &o.
399.
^feg^
can easily be mixed with the harmonic tones. fore in reality, the
means
for every
-S t£?;
^--^^ i -f:^
We have,
there-
harmonic form, and conse-
quently can distinctly express every turn of the modulation.
Thus we see
in the following
monophonical ritornel of a concerto
by Sebastian Bach:
400.
^^J^E^ m rn^Mm^^^^
gfe^^-
^±itijiqc
that
it
contains
all essential
points of an energetic modulation
tonic chord at the beginning
sure 2 to 5)
;
;
the
the turning to the dominant (mea-
the modulation into the subdominant (measure 5 and the modulation to the dominant. will be suiHcient for us to indicate the means and possibility, ;
to 6), It
as the student of illustrations.
harmony
will
have no
difficulty in writing such
271
CHAPTER
II.
THE MOEE-THAN-TETEAPHONIC COMPOSITION.
Wb
must here
distinguish whether all the voices belong to one
two or more bodies, which, though form separate' choirs among themselves.
single body, one choir, or to
connected,
still
The
first is
In
the necessity of leaving harmonies incomplete will occur
in preference called many-voiced, or polyphonic.
The Polyphonic Composition.
A. it
less frequently,
ble one or careftil to
but instead of
more
tones, in
it
we
shall often
be forced to douwe must be
consequence of which
arrange our voices so that they are not in each other's
way.
Above
we must
all,
think of those harmonies and those re-
sources which permit each voice to pursue
ent course.
Nevertheless
it
the voices clear through the throng.
all
its free
and independ-
be possible to lead We shall have to choose evil, and we shall even
will not always
occasionally between a greater and less
be forced to employ duplications and progressions which are contrary to rale the greater number of voices forces them upon us ;
and covers them.
""
think of procuring more space for the The bass must go lower, must take the fundamental tones more frequently, in order to give a firm basis to the numerous voices. The middle voices, in turn, must cling to one
Next
to this,
we must
middle-voices.
position as long as possible, and only progress in small steps for,
when a numerous mass of voices once happens upon
harmony,
it is
very
difficult
to control
it
;
dispersed
and to avoid confusion.
we must always remember in the right place, to extend chord internally, {i. e. to make of the triad a septime chord,
Finally,
every
and of the tity
latter a
nonaehord) in order to find the greatest quan-
of matter for the
many
voices.
All these rules are so clear and consistent, and have been pre-
pared so much already, that they require no particular practice,
272 save a few attempts to apply our acquired information even
under
diiBculties.
We
add the subsequent remarks, but warn
expressly against a too-great extent of these attempts, as this manis of but little importance, save in extraordinary and leads the student to ponderousness and affectation.
ner of writing cases,
The polyphony ^upon entirely
in the orchestral composition is
The student ought to begin with very simple of how
test
something based
different principles.
many
voices they admit.
successions,
and
Hfere
401.
w^m we have written a simple melody with an a<«iompaniment of At b we have arranged it ootaphonically, and have introduced a somewhat richer modulation. At o and d are two, at A,
six voices.
for seven voices. We have everywhere taken as many voices as we could introduce without diffi-
more treatments of the same culty.
It is
we have
practicable enough to
here
•
add
still
more
voices.
Thus,
273
B ^^^^
g^
i ^ i^i^ -°-#-
402.
BE
1
B=
m^^^
^m^
-•.9^ -4
e=
^^m^-
*=(:
^
arranged the melody of No. 401 for ten voices, or eleven,
it is
if
we
But, independent of single inconveniences,
count the pedal-tone.
undeniable that the ninth and tenth voices find their
way
only with diiBculty, and even then have to cross between tones
which have been much better represented by other voices. In order to obtain the greatest
polyphonic compositions,
it
is
amount of clearness and care
in
always best to have two or three
voices progress in thirds and sixths, and to place these parallel voices so close together, that they form
independent, separate choir. voices
1, 3,
and
4,
among themselves an
In a, b, and d of No. 401, the
formed such a choir; in c is a similar choir There is another in a, formed 1, 6, and 3.
consisting of the voices
by
the voices 5 and 6
in B.
Wherever such
;
and the voices
8, 5,
and 6 have another
choirs occur they ought to
be placed as
Soon as possible after the upper and bass voices. In No. 401, after having written the bass,
we have imme-
diately written the voices 3 and 4, which, together with the upper voice,
form sext-chords and appear as a well-closed mass.
this it
was desirable to have a second mass, proceeding
trary direction, which formed itself in the voices 5,
After
in a con6,
and
7,
though much less connected. The other voices were added as well As a matter of course, we cannot always finish one as we could.
374 )r two voices before beginning the others. It can only be done where a voice seems particularly apt to such treatment, as, for instance, the voice 8 in No. 401, or, when the general arrangement
of the voices permits
it,
as in the following
-i.
i:
w
-4-S& -3-g —
403.
-e-
i=s -J-
zz^sz
r-*In conclusion,
we
will
ment of No. 396, with
^W
^
now gite a
Y
hexaphonic (six-voiced) treat-
slight alterations of the
upper voice.
--^
J-J-^
3t=t & e^ f--^BJ.fi^'.^J^.J_J_,gj. ^rff-r*=nfTi^
^^
275
rm~im It
r
cannot be denied that the whole appears overloaded, and
though at some places
we have obtained a greater volume of tone, is by no means an improvement on the
the phrase, as a whole,
But
former treatment.
this is
snuch less owing to the manner of
execution, than to the forcedness of the task. ject to
make a work
and the manner of writing polyphonically. that the phrase
It
was not our ob-
of art, but simply to illustrate the possibility
had been treated with an
But even admitting
artistic object, the result
would teach us that even in the
number of
voices
simplicity and
ciency are always best, and that every excess
Not
easily will a
composer overload
his
suffi-
is injurious.
work with voices,
with-
But even under the
out a particular and sufficient reason.
exis-
tence of a reason, he will not treat everything polyphonically,
but only appropriate phrases, or parts of phrases, particularly in simple, slowly-developed
harmony and
while the remainder will have to be of voices.
ferent voices,
less
manner ; sometimes employing
sometimes forming
times dissolving two or is
steady melody,
with a
number
Handel, in his oratorio "Israel in Egypt," has treated
Several choruses in this
There
quiet,
satisjfiied
more
different choirs,
eight dif-
and at other
voices in one.
an apparent or pseudo-polyphony which
is effected
by
doubling some real independent voices, bass or treble, or perhaps have had such cases in the double-duophonic all voices.
We
composition, (page 90) and have decided that these duplications
cannot be considered as actual voices. consider the following phrase
For
this reason
we
can
276
405.
merely as pentaphonic, though
it
selves, the phrase
would
still
Even if among them-
contains nine voices.
these assistant-voices should exchange their parts
Not even
be pentaphonic.
the em-
bellishment of one or the other of these assistant-voices, by-
means of bye-tones or passing-tones would change voice ; and if
we were
it
into a real
to write the highest voice of the above,
thus,
406.
for instance, it
wovdd
still
be a mere duplication of another voice,
(page 72).
The Double-choired, or Polychoired Composition.
B.
This cal
is
and
the
more customary manner, because
it is
more
practi
useful.
Dividing the voices contained therein into two or more masses,
we we
can employ one or several of these masses can unite them in real polyphony.
The
by themselves,
first
or,
manner, particu-
which is not limited to periods or phrases, but which can be employed in even the closest interchange of choirs, gives to the whole manner a mobility, transparency and clearness, of which larly,
the real polyphonic
manner
is
absolutely incapable.
There are various ways in which ployed.
We
this
manner can be em.,H,
can form two or more choirs of voices.
277
The
choirs can have equal or unequal
number of voices and
position.
The different connected choirs can be employed differently one choir can be treated simply, another can be more figurated, &c.
All this demands no eration,
new
law, and requires but a simple consid-
which then, of course,
refers to the real
polyphonic com-
position, also.
The united
choirs
must appear
as a whole ; not merely all to'
gether, but each choir separately, and at every separation of the single choirs, the fact of each one being a whole, even
are
all
when they
combined into one grand whole, causes us to conceive
each one separately, as long as
we can
distinguish
it
from the
others.
From
this it follows that
pendent whole, characterize
and make the harmony
we must treat each choir as an indeit by good upper and lower voices,
as complete
and clear as possible, while
we
are at liberty to permit between
two voices of different choirs
all
those relations and progressions which the real polyphony
upon us. But as soon as we consider every choir as a separate whole, the most manifold applications are open to us. While we give the hai-mony to one choir, the other can proceed in unison, octaves, or take the pedal-tones, or contribute in various ways to the effect forces
of the whole. All these formations will be reconsidered in the orchestral and They do not, for the present, require even a vocal composition. particular practice.
It is suiiicient
to have indicated them.
SECOND BOOK. THE ACCOMPANIMENT OP GIVEN MELODIES.
281
INTRODUCTION. first book we have acquired the means which the and rhythmical elements offer us for artistic objects.
Jn the cal
shall
now proceed
to the application of these
means
toni-
We
for artistic
objects.
Though we have already constructed compositions with the mere natural harmony, which in their sphere were probably satisfactory, sitions
also
we were always restricted in our means, and these compoOur fiiture labors are
were merely the means of practice.
merely devoted to the practice and development of our
means, but they can already be considered as independent works of art.
Beginning again with the most simple task, we are led at once to
THE ACCOMPANIMENT OF GIVEN MELODIES. There are two species of melodies, the accompaniment of which can be demanded of the composer 1,
:
|;
the choral melodies, and
2, the secular
melodies of the people.
Other melodies are generally provided with an accompaniment
by
their composer.*
* [The chorals and national
melodies, or melodies of the people, form a music peculiar to Germany and to German composers, and, owing to their importance, German theorists have attached to them all those rules of composition which perhaps could have been attached to other musical The translator had no alternative before him, but either to give the forms. information embodied in these important branches as he found it, and to style of
give a literal translation of the
work
before him, or to reduce this informa-
tion to mere principles and to adapt them to other cosmopolitan forms. The translator of this work has chosen the former, because, independent of the correct conveyance of the author's ideas, he thought it too good an opportunity of acquaiating the student with these peculiar musical forms, to let it pass for mere brevity's sake, or for other equally unimportant
reasons.]—-Ed.
283
First Part. The Accompaniment of the Choral.
The
choral melodies, as
embodied
at present into our
worship, fiirnish us, because of their simplicity, the est task for the practice of erally, is
accompaniment.
first
quiet and steady, and their measural construction
is
is
generally
very simple,
a few passing-tones, their melody pro-
gresses generally in measural parts,* interrupted but rarely
notes of longer duration.
of
easi-
Their compass, gen-
not too extended, their melodic progression
for with the exception of
mode and
The
by
division into single, short strophes
(phrases), each of which, as it were, forms a whole, facilitates their internal arrangements, the treatment,
and the survey of
them.
Even
the adaptation of words to
them
is
very simple ; each
syllable has, generally, one tone, to which, occasionally, a passing-
tone
is
attached.
Thus, in every respect, the choral forms one of
the simplest lessons for accompaniment.
But in other respects it can also be called one of the richest. For the noble simplicity of its melody makes it appropriate for the most manifold harmonization and accompaniments aye, most ;
of the chords have so general a destination, that from various points of view they admit of various accompaniments, which each in
its
place and for its object can be considered the best,
while none can be caUed the only correct one.
Added
to this is
the lesson.
The
now
choral
the religious and artistic importance of was always, and is now an essential part
of Christian, particularly evangelical worship, and will remain so Many of these melodies have been transmitted to for all time. us from our fathers and forefathers ; for centuries past they have been the voice of the people, their consolation and their strength
* Measural
parts are such parts of a measure as are indicated
rhythmical bythmical signature of a piece notes,
;
by
the
thus, for instance, in ^ time, all the half
in 4 time all the quarter-notes,
284 they have been the armor of the church at the time of the Eeforma-
and with
tion,
all
these reminiscences, with all this power, they
on to posterity, perhaps for centuries to come. Even now, and ever after they are mixed up with our
will pass
by
as people's song, led
life,
the organ,
as OBGAN-piECB, of deep significance,
and
as CHORUS, in simple majesty.
Thus
our ideas connected with the choral are elevating.
all
But besides of the
this the
treatment of the choral
is
an important part
duties of every organist, a highly productive matter
official
for sacred music,
and even
for secular music, a highly important
form.
Points of View for the Treatment of the Choral.
We have already of
many
said that one
and the same choral can admit
from its respective But there^e three points in par,from which we have to* consider our lesson and to decide different treatments, each of which'
point of view can be correct. ticular,
upon the treatment of the Firstly,
melody
it
may
choral.
be our object merely to accompany the choral
in the simplest manner.
In this case
such harmonies as are most easily attached
to,
we
should choose
and best support
the melody.
Secondly,
it
will soon
be perceived, that every good choral
melody expresses a more or has a typical significance. character the
less decided character,
To make
and therefore
the exposition of this typical
aim of harmonic treatment,
is
an
artistically higher
task.
Thirdly,
we can make
it
our object, not merely to have our
treatment correspond with the general character of the choral and the words, but to take into consideration, also, the character of
each single verse.
From every point we can accomplish our object in various manners. We can make it 1, more or less voiced we shall generally prefer tetraThus much
as
an explanation of our lesson.
of view, in material respect,
;
phony 2, 3,
more more
;
or less rich in
harmony
or less melodioally developed
285
CHAPTER
I.
GENERAL CONCEPTION OP THE MELODY.
A.
Confirmation of the
Key and
the Principal Points oj
Modulation.
As soon as we have selected a we have, above all, to decide upon
choral
melody
it is
We know, already, that the signature and close are the teristics
of a key ;
we
also
know what
treatment
for
the key in which
written.
first
charac-
are the nearest modulations
of each key. '
us safely. chorals.
These marks, in moSt cases, will be sufficient to guide But we have to encounter a peculiar difficulty in the Many of them originate from former centuries, (or are,
at least, conceived in the style of those centuries,)
neither to our major nor to our tirely different
from
either,
minor keys, but
and which we
and belong to
keys en
shall call ecclesiastical
keys.
All our former principles are by no means immediately appli cable' to these ecclesiastical keys.
We
meet with
chorals which
have no signature, and which according to our former ideas would be either in
major or in
^ minor,
and end accordingly.
But
they end upon G, begin, perhaps, with G, and yet do not belong to
G
major, because, instead of /jf,
/t|
predominates throughout
and instead of closing with the dominant chord
(d-f^-a^), they
close with the triad of the subdominant.
Other chorals, again, seem to belong to
D minor, but they have
not the signature of that key, and instead of 6b out, to say nothing
chorals, which,
keys,
still
of other deviations.
we find it| throughwe meet with
Finally,
though having the signature and close of our modern
demand a
different treatment,~if
we would produce
a
characteristic efiect. It is clear,
that under such circumstances our present informa-
tion will not suffice for a proper
conception of these chorals.
286
They demand a in
better information on the character of the keys
which they have been composed, and
it
is
exactly this in-
formation -which will form the .contents of the second part of this book.
But
it is
formation,
also clear, that before having obtained the
we
shall
above
in-
not always be able to decide whether a choral
belongs to one of our modern keys, or has the mere appearance of
it,
and
is in reality
written in one of the ecclesiastical keys.
Ve have, therefore, annexed a few melodies, which can be treated as belonging to practice.
modem
keys, and which will serve at least for
287 Ima.—
,
^
3da.
m^hnn^rr^^
m
s
r^. it*jt
^
Y=x:s=i
S^^^S^feEfEgfe
m^-
/TS
m
• rJ
/Hitv^.
i ^
»-
•
-*
:^
^o^-n/i^ Ojttu
^e^,
JPE -& -0-m-^'-
is ^a^F^fTflPq^^j^^gEi *-T
^twv,e;i,
Jtf/-
>t^*^
,
J'^^^w.^it^
^^^i^te r M^-g ^ Bst |g^F^
^
i
-•
—•—-
F;=p=?^ i
^S^ii
m^m a—p-
<'/
2S8
iifi'-^*-
i ^£g
zfr.
f f r
-0-m-
'-¥
cl^cJU.f^'y^
jE3ri:=pitf:^
^
i
m
nr^¥T^¥=f
^r^^^^^t-d^CUkM
Ol^
^^^^^^ a
*—m-
^,P,,,,^„./de;fe6-»*v
,
HCyrr€^t dJiu^ CA/ frV^ o«-^
^s^gfe
^
i^S3
^Tt^
gg^F^a
B^^f^fPs
* ^^^^^p^^iil ,^^^, Je//*^!^'^»-^''^«^*^*^ i^^S -1^—
i^
i
=#^
?=P=f=
289
Having once decided upon is how to arrange the
the key of a melody, the next
question
general modulation. The rhythmical construction of the chorals, must be our first guide.
Many
chorals are actually divided into
stance, the first four of the above. is
not distinctly marked, but
the whole.
$
This
is
it is
;
as, for in-
by
indicated
the arrangement of
the case here
=t -%--
zgpi
two parts
In others again, this division
zzt
-&-
^^^
'^-
f±:^^
-i :ri
» d
^p&ir^ M
^
F-F
^^^^_^|lpJ^ :^tj:/^^. d=
^
Oh
^p=
T
3E
ff^f^Ff l-X P=f
tJEPfei €—-§f— .d.
:^
^
I
'Sl
it^z -^-J¥
>
.^_f2:
T m :'?:
1
fe=-Hfe=grL=:g|
i=S:
^=3
.
f^ !
iEgre
:^--4
.d..^_
.is^^sd:
f-V"
•^^-?^3e&e^ f-^: .<:1
^-
:«:
:?:
l^r=^M-T^
J.
tP2-~
290
The second
part repeats the
first
two strophes of the begiimingy
and thus causes another beginning, while
it
indicates at tmce a
division of the choral into twice three strophes. If a choral has this two-part form,
mits
we
close, if the
melody
per-
the major melodies in the dominant, the minor melodies
it,
in the parallel.
Each single strophe of a choral has again its close, which by means of pause or interlude, or voluntary retardation, separates Thus we have to treat each that strophe from the remainder. strophe as a separate part of the whole, and to close it with either a half cadence, or a full cadence
;
we
consider, therefore,
the end of each strophe as a resting-point of the modulation upon
which the
latter breaks
off,
We must reflect well,
more
or less satisfactorily.
therefore, at the
end of each strophe
:
what conclusion of the modulation is possible and which is the nearest and most natural, and most appropriate for the progression of the whole ; and, finally, which conclusion would be most ;
with the character of the choral, and consequently the
in keeping
most
preferable.
Summary
B.
The importance which
of Cadences.
these strophe-cadences, as chief
ful
preparation
demand
choral
What
the
so
more
many
cadences have
The
1.
;
full
so, since
moments
demands a carethe numerous strophes of a
and end-pomts of the modulation, have
for us,
different cadences.
we now
at our
command
?
cadence, from the dominant chord to the tonic triad.
Instead of the dominant chord
we might
also use the
major or
minor nonachord, or the derived septime chords, (these, however, form but imperfect cadences) even the dominant triad is admis ;
sible,
2.
except in the last strophe.
We
shall require occasionally another species of full ca
dence, which passes from the triad of the subdominant to the tonic triad.
G major. 407,
and
i is
=F
called "ecclesiastical cadence."
It is
evident that this
291 cadence closes not as satisfactorily as the piv per the
full
two chords do not even designate the key with
cadence
decision, (the
F major), and the
forms of No. 407, could also be half-cadences in
triad of the suBdominant does not so well prepare the final chord,
because into
it
it.
has not the impulse of the dominant chord to resolve
Yet, in choral treatment
we
cannot well do without
and we need not care how much or how -
little
it,
satisfactory
it is.
Full cadence and ecclesiastical cadence, can at
ployed for single strophes, in an imperfect form of the whole, and of the
first
part (if there
is
events be em-
all ;
merely the end
any) demand a per-
fect full cadence.
The
3.
half-cadence.
This, as
we know,
is
formed by the
progression of the tonic triad into the triad of the dominant.
But we cannot always employ or replace
it
by another
it
astical keys, or the will of the
in this form, in the chorals.
The
cadence.
after-effect
of the
ecclesi-
composer, necessitate occasionally
a second species of half cadence, which
is
formed of the triads of
subdominant and dominant
408.
i -F
"ST
r consequently of two chords which are not even harmonically connected.
However, imperfect such cadence may
ployed occasionally; we have employed
when
the periodical construction
it
be,
it
must be em-
already in No. 105,
was of minor importance, and
we have employed it on different occasions to close the thesis. All we have to remember is, that the final chord of the halfmust be a major
cadence, whether in major or minor,
triad, be-
cause both tone-species have upon their dominants a- major triad.
And now we have to enquire at every choral, which of the enumerated cadences are possibly applicable in it ? Most of the choral strophes end by ascending or descending one degree of either a step or half-step.
would go from
c to d,
or from d to c
In ;
major, for instance,
from c to
b,
or from h to
it c.
292
The
last
tone of the
final strophe, at all
major or minor triad half-cadenoe
;
events,
and we know that the
must be major.
Let us
cases, considering the last tone either as
must be part of a last
chord of the
now survey
all
possible
fundamental tone, minor
or major third (in the half-cadences exclusively as major third)
or
fifth.
409.
p
E.C.*c ==
1
293 There are other closings of strophes which exhibit a repetition of the last tone, or the descension of the third
;
in such case it
depends upon the student, and upon the adjudging of each particular case, whether to treat the last two tones as belonging to the final chord and to place the preparative chord upon the previous tone, as here
i 411.
i^^l^
^^^m
BE ^-
t %FM^^F^ goai=gjJ
m
J
J
a
m
f^
at A, or to attach the
whole cadence to the
last
two
as
tones,
at B.
And now
only,
we
ask which of
all
the possible cadences
is
preferable in each particular case.
Let us
now
analyze a few chorals.
fc:
412.
W=3k±jt^r=^
?^
J/j^ ^
.
"^<
j^ .^_^ ^
=t "t
^# —PSignature and end-tone indicate here the key of
P
f
^
5b major
;
the
stands for " fundamental tone ;" 5 stands for "Fifth." The formula is thus If we take e as fundamental tone, we can make a full cadence with g-b-d-f Instead of the indicated nonachords, we can to c in C major or C minor. also take derived septime chords, and instead of fundamental chords we can :
.
take inversions. As a matter of course we need not absolutely use the triad c-e-g or ce\>-g to go to (^ but we can also substitute the sext chord e-g-c or eb-{r-c. Whether all these cadences, as enumerated here, are appropriate or not, is a question to be decided in future.
294 close can be accomplished with the
We
manner.
signature interfere with
it
would be imperfect, and
in the
with
;
instead of the /)( of
/,
dominant chord, in regular
Q
might also close in
minor, without having the
but in that case the
Gf
The above choral contains
final
cadence
melody we should always meet
minor. four
two of which
strophes,
semble each other in length as well as in tone-succession.
since the second strophe admits of a close in the dominant,
can consider the two
The
first
strophes as the
first
first
re-
Now,
we
part of the choral.
strophe admits of a like close in the principal key.
It
might also end in the parallel {^G minor), and it would matter but little that the cadence would be imperfect. But, according to our principles of modulation, this digression into the parallel comes too soon.
The second strophe
closes, as
a
first part,
nonachord f-a^c-e\i-g would enable us to close pal key
;
but, apart
satisfactorily,
in the dominant. it,
The
too, as the princi-
from the opportunity to end the second part
a repetition of the close in the principal key would
have been lame, and would have confused the harmony, which evidently inclines towards
^ major.
The third strophe, too, might be ended with a full cadence in F, by means of the nonachord e-g-i\)-d, but here, too, it would be a mere repetition of one and the same cadence. We might close in
C
minor, or even A]) major, but for so small a phrase this
is
far too distant.
But have we not already considered the first strophes as a whole, which ends on the dominant 1 Consequently we
as a first part
can consider the last two strophes as a second part which returns
from the dominant key into the
principal.
The beginning of the
third strophe corresponds to such conception.
We perceive now
that the third strophe, as thesis,
makes a half cadence from the
upon the dominant ; the more satisfactory. Here is another ex,ample:
full
tonic
cadence at the end will be
S-rMjdUtXu^^,
• p -0—0F-*
413.
% —F— ^
r-
-»
—^-
i
^^'^
irz^zs
i
i
295 "Ehis choral is really constructed in
whole
is
evidently
would be the
G
minor
parallel, B\,
to the ending of the
;
two parts. The key of the the nearest modulation, therefbre,
major
and such modulation corresponds
;
We
have now decided the two most important points of the modulation, to which everything else must be subordinate. The first strophe, too, might be led into B\, major, but this would be anticipating and injuring the effect of the just-mentioned first
part.
cadence of the whole part
full
;
and we
em-
prefer, therefore, to
ploy the half-cadence from the subdominant to the dominant.
The third strophe can make a full cadence in D major, by means of an actual modulation, or can make a half cadence upon the triad of the ^minant.^ The followipg chora,! » g ^2^
«
^
W:^^ 3
414.
-&
3F
*
i
may
— s •-
i^zp:
Ij-jj-
::izz±zd
bizfz
serve as third and last example.
This melody offers some
slight difficulty, because five of its strophes turn in the tonic,
and always in the same manner, by
retain always the
ually in
G
major
it is
towards a close In order to
a, g.
most simple, we should have to remain ;
even the penultimate strophe
for a half-cadence in G,
But
1
*:
is
though inclined to modulate into
clear that simplicity
would here lead
contin-
appropriate
to
D major.
monotony.
Let us admit at once, then, that the penultimate strophe leads to
D major
;
and the question
in in in
is,
how
shall
we make
the other
The ot, g can be employed for a close G major, by means of the dominant chord d-f^-a-c ; C major, by means of the nonachord g-h-d-f-a ; minor, by means of the dominant chord h-d^-f^-a ;
five cadences
t.
^
and consequently gives
us, in addition to the principal
key and
the dominant, the keys of the subdomin9.nt and the parallel. are
now
prepared for
all
the nearest modulations.
We
296
We close the first The
latter.
strophe in the principal key, to confirm the
last strophe
We place
belongs already to this key.
the cadence of the subdominant, according to its
character, as near as possible to the
end ;
—consequently
in the
fourth strophe.
The second and
third strophes, consequently, belong to the
parallel. It is
seen that more than one deviating arrangement
easily
could have been
made
for instance, in
E
again in
E minor
;
;
we .might have ended
minor, the third in or
C
we might have closed
the second strophe,
major, and the fourth the third in
Q major.
would have been the steady mass in E, which we gained in the above ? And where would have been the decisive juxtaposition of subdominant and dominant ? But in return we should have fallen again upon former keys But where
in that case
E minor, we
G
major,
E minor,
G-
major,
E minor,
G major,
should have modulated in a vague manner, and deadened the
of former keys by returning to them. For two strophes we might have chosen,
effect
the key of the But in that case the decline of the modulation in the subdominant would have been too conspicuous ; and with five major strophes, we should have had but one minor strophe, while in the above sketch there reigns abetter symmetry, i. e. two minor strophes against four major strophes or two strophfes for the principal key, two for the major, and two for the minor modulations. Thus much of the sketch of choral music. But when we re-
subdominant,
also,
E major, instead of E minor.
;
consider the principles which have led us,
we
see that our actual
aim was merely a general appropriateness, a
natural, fresh,
and
analogically-developed modulation, without regard to the single
moments of the melody, color which
we would
to the meaning of the words, and to the
like to give to
one or the other phrase.
We must remember, therefore, that the above sketches or plans of modulation are subject to priate they
We
many
alterations,
however appro-
may
have appeared from our present point of view. must permit such alterations, nay, consider them as ne-
when the melodic contents of a strophe would not agree with the harmonies of the pre-destined key. cessary,
297
CHAPTER
II.
DISPOSITION OF THE HARMONY.
As
soon as the strophe-cadences are decided upon, the harmony
of each strophe has received that destination,
with due regard of
we
therefore,
chords,
has
it
and, according to
and
steadily,
Again,
of the nearest and most appropriate
first
look then to succession and connection, and without
losing sight of our aim,
every wavering.
when
;
decisively
the principles heretofore mentioned.
all
think
destination
its
now to be arranged
the
We
we
avoid every unnecessary repetition and
bear variety in mind, too
melody might lead us
erally prefer vigorous
to religious dignity
and
and
to
;
particularly
monotony, and we
shall gen-
dignified modulations, corresponding
elevation, to those of an effeminate, triv-
ial character.
We shall sext chords.
also avoid too frequent inversions, particularly quart-
The
latter,
which formerly seemed so appropriate
would here make the harmony monotonous and weak, in consequence of our having so many • endings and such short strophes. for the preparation of the ending,
For the same reason we
harmonic
shall generally avoid those
successions in which bass and treble progress in thirds or sixths, for instance
415.
i 1=
s
^f^k^i^.
^
=M
T-
f^^= '^:
r
r
mi r
f
For, owing to the preponderance of the outer voices, such succes-
298
monotony and effeminacy in the harmony, however vigorously the latter may be organized in itself.
sions are apt to produce
We need not here repeat that, in the proper place, we
may
devi-
ate from this rule as well as from every general rule.
The whole
disposition of the choral
that each tone of the
melody ought
melody
tells
us already
own chord, But we must add
to have its
other words ought to be a harmonic tone.
in
to
this the follovring 1.
To
simple,
give each tone of the melody
it is
true,
own
its
chord
is
the
most
but often, as in No. 417, a chord can be
re-
tained for several tones of the melody. 2.
A tone of the melody can also be considered as
and consequently as a part of the preceding chord. stance, the last strophe of the choral.
treated in this
manner
No.
1,
suspension,
Thus, for
in-
page 287, might be
:
J=L=i A i
.
416.
m
BEl 3.
tone.
The tone of the melody can be considered as mere passingFor instance, the ending of the third strophe in No. 414,
might be treated thus
417.
^t ^^9\ A J.
A
5S m
I
Neither of the above are, however, as vigorous as the employ-
ment of a separate chord for each tone of the melody. 4. We meet occasionally, as in the third and fifth strophes, of No. 414, instead of equi-long measural duration for one syllable.
It
parts,
notes of longer
depends then upon us to give such
a tone one single chord, or to give a separate chord to each mea-
299 sural part therein contained
;
for instance, the third strophe of
No. 414, which might be treated thus
^^^
418.
1=
w-
or thus.
SSfg ~cs-jitp=rz:5=l I
rrr-r
I
I
e^d^P^I^EfePE^^^Ei ^ i f^ When a
syllable has
two measural
parts, but different, tied notes
first and second strophe in No. 414,) these two tones can have a single chord. But it is more customary and vigorous, to give a separate chord
(for instance in the
penultimate measure of the
to each tone.
We iind occasionally
5.
sure of the
members in such
we
a
same
penultimate mea-
(for instance in the
choral) a measural part divided into
—two-eighth-notes instead of a quarter case, treat the
can give a separate harmony to each of them.
The just-men-
:
^^^8p^^^3 s
,Ji5,^
I
I
?=FK
r
?*£F=
Each of these conceptions can be is more common
right in its place,
treatment as at a or b
which of the tones
monic tone
?
If
shall
;
sion of our
though the
but the question
is
be the passing-tone, and which the har-
the progression of the melody does not indicate
the one as essential, the other as added,
harmony and consider
we
follow the progres-
that one as harmonic, which,
according to the connection of the modulation, for
We can,
one or the other tone as passing-tone, or
tioned instance might be treated, therefore, thus
419.
two measural
note.
is
most appropriate
it.
It is less
usual to treat each measural
member
as harmonic,
300 because
it is
mony and
apt to interrupt the steady progression of the har-
to overload the modulation.
determined to employ two chords, connection of chords, as at
c,
we
Therefore, if
we are once
ought to prefer the closest
though the treatment at d
may be
appropriate for a particular expression.
After these observations, let us
Its first
strophe
now turn
to the task
itself,
i. e.
No. 412.
to our first choral.
we have
We know, therefore,
decided to end in the principal key.
two tones must be accompa; it is also most natural to begin with the tonic chord, and to the first /of the melody that the last
nied with the dominant and the tonic chord
we
shall take, therefore, the chord
And now we
bh-d-f.
have
harmony between these fixed points. Three times more does the / appear in the melody, and we shall find the mere repetition of the same chord too monototo find the
nous
:
J. 420.
or
its
duce
.1
A
1
HF¥
r '-^
inversions too trivial for the chorals.
new
We must then intro-
chords.
The nearest, and, therefore, best, is the triad of the dominant. The nearest step, now, is the chaflging of the dominant triad into the dominant chord, which, then, leads back to the tonic triad.
We have now found
the following fundamental bass,
421.SEd2:
^
but shall prefer a more pliant inversion.
422.
Bq±
Qfc,P=i=tt
fe£
6
probably the one at
c,
2
6
because those at a and b end with the same
tone with which they began.
There remain now only the tones
6b
and
c ;
the former might
301
be accompanied with the tonic chord,
with the subdominant
01-
We prefer,
that chord.
triad, if
therefore,
we
had that
just
if it
And
us at the same time of the parallel. reminiscence,
we had not
were not too soon for the triad of ff, which reminds
e\!-g-b\),
exactly because of this
attach the subsequent chord to this
harmony
and accompany the following tone of the melody with the triad of
the subdominant of
c,
ff.
Thus, the
form
this
r 423.
=^^ 2
6
We
6
first
strophe would have
^^ m 6
3=
7
see here, in addition to other observations, that the bass as-
cends and descends in a decisive direction; the elevation or ascension
is
accomplished by quart-steps, therefore uniform, and
would be an additional reason for choosing no other chord for the tone JI7. The subsequent sext-chord gently prepares the descent of the bass a triad would cause here a stiff progression
this
;
in that voice. If in
the bass,
this
harmonic disposition we have specially
we have
a good reason for
voice, consequently
We
in its
regarded
being an outer
more conspicuous and more important.
why the beginning could not have been made with a quart-sext chord, or a terz-quart chord on the can
now
it,
understand
second tone of the melody
424.
Obtr
r
:t
How
weak and inappropriate would the succession at a have and how insignificant at b the two inversions of one and But the greatest loss would have been in the the same chord been
!
!
sacrificing of the consistent progression
tained
The next strophe we intend to end ural to turn towards
the
of the bass, as
we
ob-
it.
new key with
it
in
F;
it is,
therefore, nat-
as soon as possible, in order to introduce
decision.
Its first tone,
c,
yields under
any
302 cii-cumstances no nearer
which
we employ
harmony than the
triad of the doinmant,
as sext-chord, so as to avoid the repetition of
/ in the bass. But we consider this dominant triad as were a tonic harmony, and follow it up with the dominant
the tone if it
triad of the
new
key,
c-e-g.
It
sufficient tor the transition,
and
is it
clear that this
triad is quite
enables us, besides, to preserve
the freshness of the dominant chord for the cadence of the stror natural that the dominant triad, like the dominant
phe.
It is
chord
itself,
should lead to the tonic triad, /ac.
One more chord
The
tone, g,
demands
its
harmony,
for the
"What can
the dominant chord.
longs to
other
g be
this
g
be-
any
in
?
new dominant
triad of the
have but just employed
it,
is
again the nearest
;
but
we
and the subsequent dominant chord
Would appear weak and a mere repetition. The triad of e|j, which we might choose, lays even beyond B\> major, while we are proceeding towards F.
But we have the minor
strengthen the modulation to
F
still
triad of g, or to
more, the major triad or sep-
time chord of ^.
But in
is it
worth
while,, for so short
a strophe
^ major, to go as far out of the way
ticular reasons
we
shaU. avoid the
?
is
intended to be
In the absence of par
modulation to
C;
it lies
now
nearest to change the foreign chord g-h-d-f'vcAo an indigenous one, g-b\)-d-f,
as
we have
learned already, (page 190.)
strophe of our choral would
now be
The second
thus
i
'25.
i
fe^=r
msE Here
are the last strophes with three diiferent basses,
303
=*—•^
'i=F^
$
=P=F=
s^
^
2
6
6
7
5
-©-
426.
6
S
4
3
4
5
7
^=E » 7 6
6
S=E r which
-vrill
i^i
rtF
require
some few remarks
;
that there are
still
other
harmonizations possible need not here be added.
At
A, the
preceding
secunda chord
final chord, f-a-c,
e\,-f-a-c
issues
immediately from the
in accordance -with the nature ot
and
inversions gives a greater mobilty to the harmony.
Simultane-
has been the means of our returning most rapidly and most decisively into the principal key. The subsequent harmonies which seem as if conceived for horns, or a more frequent ously
it
and untimely employment of them, might easily disagree with the religious dignity of the choral, and we must consider how far otherwise, the treatment of
the words admit of a
more
it
upholds this dignity, and
how
far
light conception.
the return to the principal key, in the first part of the general rula strophe, has remained undecided, contrary to the decided, bemore the now here is it But 301. page given on
At
B,
we modulate into the subdominant, £}, major, and thus ascend to the principal tone. It is only in the penultimate meacause
sure,
At
when c,
this principal
key becomes decided.
the bass tried to avoid the return to
its first tone, {/,
g,/)j
would have been nearest, now, to therefore the sext-chord. case the bass would have proceedthat in but of take the triad 5b, It
ed in thirds with the upper voice, three or four times in succesintroduced, therefore, an actual modulation into the sion.
We
parallel
of the principal key.
This has caused a cross-rela-
304
by means of a
tion in the harmony, which, however, tone,
^^
/—fi-
^
:^=i ?'=F^
f~^'~f~r~
437
uJH'
or
1
I
I
I
J
3E5
;^E
could be easily mitigated.
by an have
We
might have avoided
it
alteration of the bass {//|, instead of a/j(), but
lost
by
altogether
we
should
the symmetrical progression of the bass.
it
We
might, also, change this obnoxious /| into /, or, in other words, change the major sext-chord into minor ; this would give a more serious turn to the whole strophe, and in the
we might
triad,
thus
manner of
a,
than that of
also turn to
C
c.
would be better concluded
Prompted by the
:
b:
428.
foreign
minor, and conclude the choral
-&-
I
3
OEfc
^
:^=t3p:
-&-
3 5 if this
foreign and serious ending corresponded to the
any particular
intention.
In that case
we
words or to
should have
made a
modulation into the parallel of the subdominant,' and at a point when foreign modulations, accordhig to rule (page 211), are not in
their place.
This makes
it
advisable, in the penultimate
measure, to touch once more upon the key of the dominant, and thus to return gently and quietly into the principal key to end there.
305
CHAPTER
III.
SIMPLE TREATMENT OF THE CHORAL.
The tory.
same time and
indicate that
method which has proved
itself the
best
safest.
The following of the most slight
moment
7f
choral,
insignificant
illustrate the
49.ft
were merely preparaharmonize one or two chorals, and at the
reflections in the preyious chapter
We will now
which
we
to us, as long as
method of our r-
select for this purpose, is
and unchurchlike melodies, but labor.
it
one
this is
of
gives us an opportunity to
306
We are not must hasten Yet,
us.
we
shall find that the
of the melody makes for instance,
we
it
distinctly-expressed character
difficult
for us.
C
If,
major
the above,
in
triad,
which
zMzziL
should disfigure, or
^= Tl6
6
mask the key
in the
6
very beginning
;
the further harmonies would be placed in the shade, because
have
first
and
we
introduced the distant chords and afterwards turned to
the immediate proximity.
is,
is
m
tfEfclHE=E|
6
we
at least, as it will permit
by the melody.
i m
very
far,
should try to avoid the
so forcibly indicated
430.
But we
responsible, however, for the melody.
to its assistance, as
therefore, preferable.
This treatment
We
have here submitted to the har-
mony, as indicated by the melody, at least for the first four steps, and have confirmed the principal key in the first strophe with such harmonies as the melody admitted of The second, strophe, minor
triads re-
parallels, and, finally, confirms the
dominant.
too, clings to the principal key, but
minds us of the two
The
with
its
third strophe turns again towards the tonic of the principal
key, but leaves us ample
room for other harmonies.
The arrange-
307
ment of the harmony
as simple. as possible, only towards the
is
end we see the voices beconie more'animated.
The monotony of by the suspensions even
the cadences could only be mitigated
the
quart-sext
chord,
in
this
;
could not well be
connection,
avoided.
As 432.
second illustration,
will take the following choral,
\v«;
* ^P^
3
A^-
-^-d=^\-t=i^*=-*^^-
III.
t ^ i the
first
61,
e\,
II.
61,
eb
-e
—
-»—*- icipz -&IV.
/
I.
61,
two strophes of which form a
first part,
6b
«b
-
and are repeated
as such. _
,
We
the key, ^1» major, and in accordance with
first fix
the close of the whole. the
first
part at
and
II.,
After this fix it also in
we
it
at
I.,
decide upon the close of
For
the principal key.
it is
impossible to have the cadence in the dominant, the subdominant
would be out of place, and the parallel would appear strange and But we now discover that the same cadence is requisite for the first strophe, and we shall consequently fix upon the
gloomy.
parallel after
433.
We
all.
decide
now upon
K n^liM I
S
1
1
)
I
.
.
1^
jc:p:
the third str6phe
I
I
d_d_
*:
'
;
if
the
I.I
'^M=^
t=f=,^F=F=iF*F=*=^ff=r
r
te^E^ti
3=* g^h*—*— - ?="Pl^
m
308 principal key had preceded it, instead of the parallel, it would have been best to end it in the dominant, but under existing circumstances, it -will be best, perhaps, to adopt the arrangement
of No. 433.
Here, in the
first
we have
place,
liberated ourselves, in a de-
from the close position of the harmony ; the chords are clearer and more dispersed, and for this reason, already, the voices are
gree,
and more mobile. The observations made formerly upon the monotony of the cadences have not been made without results they have prompted us to enrich the modulation intrinsically, to touch upon the subdominant in the very beginning, and the parallel of the same in
freer
;
would have been equally easy to enby touching the dominant chord might have been a-c-e\,-g, instead ib-ff-b],. The fol-
the second strophe, &c.
It
hance the modulation in the beginning, the
fifth
lowing choral, by Graun,
is treated in this manner. Graun repeats two strophes which form a first part, with different harmonization the words of the last strophe, too, are repeated in a coda, and in both repetitions the composer clings to the harmonic
the
first
;
system of the
ecclesiastical keys, to
belongs, and with which
we have
^
which
his choral in reality,
at present nothing to do.
But
the remainder confirms the just-mentioned principles.
$s
r
;r^^^=F^=-P
^E± ,^j^^£La
-A
-0-p^
W^.
p=^
"
^
Thou, whose tears were flow
--^hd
&
SS=^ was
F sight,
-
ing,
When
Zi
'A
on
:i
zt
-&
in
J.
—=^ ?f
Re - solved on deeds
of
e
vil,
Ap-
309
h
rJ
^sA
rJ
J_J. proach-ing
J-
J SJ
its
Wliere
^^
i
-^-
-i
^
OEE
:te
ley
That
.£2_ -JO-
f^
de-cline.
£
J :J J-
is
the oBve, the
val
-M: d=
f=^E|g=f^=f-
M J :^
.J-
J
bus,
Lord?
fiP=
hides thee,
Je
-
I
I
^
And ye
I
for
«
i
fe=^i=-i:
ffS
2^=
^S
J
A. M:
blood
now
thirst
-
Is
:?2=
his
P¥^^?%=f=-^ soul!
blood
f-=P= your on
g^^^
H-
^S
zL_d_J_^
?3I
ing.
Is
his
blood on
your
-S>
soul?'
310
CHAPTER
IV.
THE HIGHER TREATMENT OF THE CHORAL. we have
In the preceding chapter
executed our task in the sim-
The voices were employed, almost
manner.
plest
exclusively, in
the representation of the harmony, rarely in suspensions or passes
the harmony, as
it
itself,
kept as close to the requisites of the melody
possibly could, without becoming meagre and weak.
The
principles of modulation will of course remain the same,
even in a higher conception, for they are based upon the very elements of harmony
we have
already been taught to power of the harmony, becombination the harmony is formed. Suspen-
but
;
consider the voices as the motive
cause
by
their
have also furnished us
sions, passing-tones, assistant tones, &o.,
with the means to give to our voices the necessary melodic connection, flow,
And chorals.
and pliancy. what we miss in the former treatment of our
this is
Let us compare,
for instance, the
treatment of the last
(No. 433) with the treatment below,
g^^i^^l
g 434.
11*1,
I
1
^
I
.
M^
KJ
J U-U
h^
1
^m
i=J=J=iy:d=J=3=Ti
H^f-S*rrT-^r-*n*^-7?
*
fc±;
and we
*==rat£=?LjU !^
^ see,
W-
It:
m
;e^
r-
It
with almost the identical harmonies, a higher anima
tion of the voices,
and through them of the choral.
311 This
is
the higher character at which
we aim
for
We no
the. present.
longer conceive the choral as a congregational song, but conceive it as an artistic work, to be executed by four animated, i. e., melodically-expressive voices. Though our present means
do not always permit us to elevate the voices to an animate melody, without dimming the choral melody, we shall endeavor not to neglect any voice entirely, or more than is absolutely necessary.
For
this
purpose
we must now bestow some attention upon the
vocal element.
A.
we
Since
The Characters of
the
Voices.
purpose,, however, to elevate the afccompaniment-
voices to animate song,
what we might
it
will
be appropriate here, to speak of
call
THB CANTABILITT OT VOICES.
With this
expression
we
shall designate,
/«%, the
position
and
human vocal organ to exSecondly, we understand by it
progression of voices, which enables the ecute easily and conveniently.
the quality of a voice of being conceivable, comprehensible, and the quality arising therefrom of being easily represented, be
now It
it
in vocal or instrumental music. is
and representableness can and that it is absolutely im-
clear that comprehensibility
exist in a voice in different degrees,
possible to designate to hensible.
It is
what degree a melody ought to be compreto know on what basis the com-
more important
prehensibility of a voice rests. It
can have a physical or a mental reason.
A physical reason
of incomprehensibleness, or a less degree of
comprehensibility, can only
lie in
the impossibility or difficulty
which meets a voice or instrument, to reach a tone or a toneit. Thus, some tones are too high some tones cannot be reached on some
combination, and to represent for a voice, others too
instruments
;
low
;
some combinations cannot be
at least only represented with difficulty.
represented, or are
Such considerations,
however, do not belong here, but will be treated of in the science of vocal and instrumental composition. sufficient to
generally
know
difficult.
that intervals extending
For the present it is beyond the octave are
312
The mental reason of comprehensibility or incomprehensibility upon the consistency of a tone-proportion. Tone-propor-
rests
and representable as soon as we conthem and the more so the clearer and surer we conceive them. For this reason there are no more comprehensible toneproportions than those of the major scale and the first chords ; therefore, the minor scale, and particularly its superfluous second, is more difficult to comprehend. And thus we say that the latter developments must necessarily be more difficult of comprehension, for they are based upon more or less intricate suppositions. Thus, the development of the tone and harmonic system proves on one side the progressive difficulty of comprehension, while on the other side it enables him who has comprehended the connection of the whole, to comprehend the more distant and last fortions are comprehensible
ceive
;
mations as easily as the Therefore, it
is
first.
a voice most comprehensible and " singable" when
progresses in the order of t>he scale, or
in,
thirds, or
from one to
another- connected chord, particularly in its nearest intervals.
more
voice proceeds also, generally,
monies of the same latter,
scale,
than to foreign tones
;
and, if to the
sooner to nearest-related than to more distant tones.
perceive now, already, that
we need but
The
We
follow our previous rules
of harmony and progression, in order to wiite that which easily
A
connected har-
easily to
may
be sung. characterization of the voices is justly based
upon the
tetraphonic composition, as the juste milieu, which has sufficient
means
for
most and the most important harmonies, without add-
ing difficulties to the treatment these reasons that
we can
call it
by being overloaded.
It is for
the normal composition.
But the four voices are not merely
called after the four princi-
pal voices of the vocal chorus, but they are characterized accordingly too.
If
we
exceed this number of voices, one or more of
ofie, two, or more times. more than duophonic composition, we distinguish now,
the principal voices are taken In every first
of
all,
OUTER VOICES, and MinnLE VOICES. Treble and Bass are outer voices, Alto and Tenor are middle
313 and
If there are several trebles
voices.
and the lowest bass are the outer
basses, the highest treble
voices.
The outer voices, in the first place, have the most space for movements the treble above, the bass below. They are, therefore, most capable of rich development, wide passages and their
;
intervals.
In the choral, as
we
melody.
This melody
religious
service
;
treat it at present, the is
must not be
it
upper voice has the
the property of the church, and of the
and
altered,
is
therefore
called
CANTUS PIRM0S.
Next
to
however, the bass
it,
the
is
Both of these outer
portant voice.
most
voices,
eflfective and imon account of their
We
most conspicuous.
must bestow, upon that of the other voices. If any one voice has occasionally to be sacrificed, it must not be one of the outer voices, unless for some very imalso the
position,
are
therefore,
more
care upon their progression than
portant object.
The middle
voices are enclosed on both sides, the alto
and tenor, the tenor by fore, less free, their
alto
and bass.
Their character
movement must be
quiet,
sion rather in smaller than in larger steps.
suspensions are principally their property steps should not be suffered, except for
When we now
by
treble
is,
there-
and their progres-
Sustained tones and ;
progressions in large
some
particular reason.
approach the particular character of each voice,
and bear in mind the representation of the four principal voices, we voices form, as it were, two separate
perceive that the four
couples
Treble and Alto, the female
(or boys') voices,
and
Tenor and Bass, the male voices. The Treble is the upper voice of the first couple, the Tenor the upper voice of the second couple. to enter
more deeply
This observation enables us
into the actual character of the middle
voices.
The Tenor, the original upper voice of the male voice-couple, has movement of an upper voice, in consequence of the existence of a higher voice-couple, which made it a middle-voice.
lost the free
But
ofi;en,
cadences,
even
if
but for a short phrase, and particularly
it likes
to
assume the
free
movement of an upper
in
voice.
314 and instead of seizing upon the
nearest,' it departs
from the higher
more than necessary, or ascends beyond the alto. The Alto is the lower voice of the upper voice-couple, but it lacks the manly vigor of the b^ss, and the space for its free movement. Thus, it is absolutely middle-voice, and preserves a certain passiveness against the inroads of the tenor, clings more to the upper voice, and moves niore quietly and cautiously than voices
any.
The Bass, on
the contrary,
is
a
and manly, and vigorous
free,
under-voice, and loves a dignified, often bold progression.
such tion,
we have known it in and as such we have
our very
tried to preserve
its character, in bold, decisive,
too,
It,
it.
breaks in upon the other voices, but then
with
As
attempt at harmoniza-
first
done
it is
and large
sometimes in keeping
by
steps,
itself,
in
juxtaposition to all the other voices.
Thus much,
for the present, of the character of the voices.
plying the above to the string-quartett,
we would
part to the viola, the alto to the second violin, while
and contra-basso, or Applying
it
violoncello,
to bassoons
and
Ap-
give the tenor first
violin
would represent the outer
voices.
clarinetts, the first
bassoon would
have the character of the tenor, and the other instruments share in the remaining voices. It is different
with the piano forte
;
for,
apart from the general
pharaoter of higher and lower tones, the different tone-regions of this instrument
have
all
the same, or rather, no particular char
acter.
But
tically,
the listener will inadvertently transfer the character of
if
a composer has constructed his voices characteris-
the construction to the tones of the instrument.
The organ, by means of the
pedals, is enabled to represent the
bass at least characteristically.
B.
Application
to the
Choral.
In our future treatments of the choral,
we
shall
endeavor,
FiBSTLT, to give our voices a higher melodic animation.
know
that the strength
We
and the merit of a melody do not de-
pend upon the number of
its
notes.
On
the contrary, an accu-
mulation of smaller measural parts would deduct from the rhythmical strength of a melody, instead of adding to
it.
It is
the mix-
315 and contrast of slow and rapid steps, and their employment which gives significance, animation, and variety to the rhythm. ture
for designs,
We
shall endeavor,
teristically.
We
secondlt, to lead our three voices charac-
have to bear in mind here, not merely the
—
rhythm, but the tone-contents also as far, at least, as modulation and position have left undecided. The more vigorous and
moments appertain we shall give to the
quiet
ones
generally to the bass tenor,
and the
;
the passionate
alto will cling to
one or
the other of its neighbors.
Nor must we upon
it,
too,
forget the
compass of the
different voices,
depends the characteristic of the voices.
We
as
shall
lead
the Treble not lower than
the Alto not lower than
'
/>1\
My
,
nor higher than
3t:
,
nor higher than
^t or
the Tenor not lower than
Wr
the £ass not lower than
H
^_
i
.,1.»11 higher lUgLOi than
Ei
, ,
nor 11^1
,
nor higher than Hi-
T^ 22
when the bass ascends or descends by octaves, or whenever we can unhesitatingly take the higher for the lower octave, we only,
shall
also
permit ourselves to use lower tones.
This restriction will
have the advantage of guarding us against too great disper-
sion of the voices.
But
since the higher animation of the voices tends greatly to
increase the tension of the choral,
we
shall at first lead our voices
and moderate the use of bye-tones, so as to enable us to sustain the uniform movement of the whole, and to Increase the quietly,
animation rather than decrease
Por the same
reason,
obscuring the harmony,
it.
and
in order to avoid the overloading or
we
shall
but rarely give a richer
treat-
316
ment Here
to
two simultaneous voioessand
more
still
rarely to three.
ci2w^ c/^i^Oe^nf >0 I^V\J<
m
yfejj:4tuxi
'ii 435.
^ 3L
M^i i
-^JL
n Jjv I
J.
BEIEPE^^i;
the
first
p^
1
?
./j^_ jv
m
gatEEEf
J
r
chor&l treated according to these principles.
most conspicuous moment of the above second strophe, which strophe strophe.
il l!
'^
^
t
is
J
?^¥^
I
mmm ^
jrr^-i
;:
is
is
The
the end-tone of the
afterwards repeated as third
This end-tone lasts three beats, and a single harmony,
however much varied by suspensions or other means (as in No. 431) would not satisfy us; we had to employ different chords, and reserve the cadence for the last beats.
The modulation of the nearest.
first
two strophes
is
the one which was
In the third strophe, in order to avoid the
monotony
of a repetition or a halt, we thought at first of the key of A major as dominant of ; but A major being too distant from the
D
principal key, inant),
we
preferred
and resigned even
In the last strophe
A
this
we have
subdom-
minor (the
parallel of the
key
very next chord,
in the
touched upon the subdominant.
e-^-S.
317
The examination of the is least
voices
is left
to the student
;
the tenor
favored in the middle voices.
Below
will
be found two more chorals which the student will
do well to examine attentively. rules have not
The deviations from genesal been made therein without some particular reason,
and at every such point, the student should not viation has
been
rest until the de-
sufficiently justified.
1 436.
S
m
•#tfi«p:
^-^¥?
i j5;CTi;^ji
=*-«-
,_j-ji4C^
%^*^f#^^^
437.
u *Hl
m
g?3EEE*
^-
I
318
:i=^
m^
f-r-r-
'^^^^m^m^The importance of the student,
turn to
choral, as
an educational medium for the
and as a part of the religious it
service,
prompts us to
re-
once more, and to direct attention to two different
points.
TECHNICAL DIFFICULTIES,
1.
These can only
exist in the
lar execution of the
good progression of the tone or a phrase it
is
melody when
harmony, or where
it
it
The former
voices.
requires
stands in the is
a
particu-
way
the case
repeated several times in succession,
of a
when a or when
takes a turn which prohibits a dignified and rich development
of the harmony. restlessly
about,
movement
is
The latter is the case in melodies which skip when it often happens that this unsteady
communicated to the other
sion with the melody.
It
voices, or causes a colli-
be best 'to consider the single
will
cases.
A. Tone-repetition. can be
made
surmounting
—Those who know how many harmonies wUl have no
subservient to one tone, this obstacle:
difficulty in
they will merely have to care for a
consistent arrangement of these different harmonies.
B.
Phrase-repetition.
chorals,
—This
is
of
frequent
and requires an attentive consideration.
occurrence in
Sometimes the
intent of the choral is such that the modulation of such a repetition should not
be varied,
or, at least,
but
slightly.
Frequently
a good arrangement of a few near harmonies can do more than the roaming in the ipost manifold, chords.
On
the following page
is
distant,
and unexpected
the second part of a choral, as
illustration. It
can be seen at once that this phrase admits of
and richer treatments
ment
;
but
it
would be
difficult
many
to find a treat-
better in keeping with the intent of this choral.
319
438.
m
m
^m F?
-G-
f=FF
Unfavorable to dignified, ecclesiastical harmony, are such melodies or parts of melodies as cling too firmly to one single chord,
and thus threaten to exclude other harmonies.
439.
Here
^P^^^ ^^^^^m rf^f?f*^rf^^?f
cally,
At a we have treated the first measure triphoniand the tetraphonio harmony of the next measure is the
more
effective.
is
such a case.
At b
Tve
have balanced the skipping unsteadi-
melody by the calm
ness of the
2.
steadiness of the harmony.
ARTISTIC AIM OF CHOEAL TREATMENT.
Harmony and melody are merely the means of expressing what moves our soul, and what the choral is intended to arouse in the hearts of the singers and listeners. In works of unrestricted art it is the aim of the artist^of his inner promptings and conviction ^to seize what is right science cannot directly assist his prompting, and his conviction is not a subject
—
;
for a musical theory.
But the treatment of a choral
is
not a work of
fi-ee
or unre-
from the unfettered spirit of the artist. The principal matter (the melody) is given, and influences everything else rhythm and harmony, more or less. In stricted art, for it does not issue
—
such case
we
occasions.
•
Therefore,
can only express what the cantus firmus permits or
we
advise the student
first
to investigate the
mean-
ing of every single choral, to seize the current which issues from
320 the
melody and
influences the other voices
This current cannot be seized monies, but
and the modulation.
by touching upon
by a steady development.
all
possible har-
We
must consult what upon which the melody insists, and thence we
harmony
is
move on
steadily, without rest, never remaining stationary with-
the
first
out sufficient reason, or returning to something previous, but
never passing the nearest to seize something strange or new.
Oddity and unexpectedness belong to the is
that
only
truly proper which strictly appertains to the object.
This
dilletante ;
course will indicate to us the proper modulation, and the progression of the voices.
321
CHAPTER
V.
THE CANTUS FIRMUS IN OTHER
VOICES.
Until now we have always employed the upper voice as abode of the principal melody
but
;
it is
also possible to
mahe one
the other voices the abode of the melody, and in that case
of
we
have to consider two points.
The cantus firmus
1.
voices in such a
same
will not appear with the
as in the upper voice, and
we
clearness
have to arrange the other
shall
manner that the cantus Jirmus can be distinguished
'from them.
The upper
2.
•melody, will
though no longer containing the principal
voice,
still
absorb considerable attention, and
therefore, develope its
melody with great care
satisfactory as the conspicuous part of
we must, make it
in order to
In bass and
a whole.
we can permit occasionally an unmelodious progresupper voice we must not do it.
middle voices sion, in the
On
reconsideration of the
voice, as given in
quite sufficient.
means
for the formation of
we
the last chapter,
The accompanying
find that
voices
move
eighth notes, exactly like the principal melody.
an upper
they are not
in quarter
and
This similarity,
and the manner of our present treatment, (the simultaneous beginning of all the voices) give us but little hope to distinguish the cantus firmus from the other voices, as soon as the upper voices. shall
we be
But
Only with more means, and
we
it
from
in a later
form
take
enabled fully to accomplish this object.
this later
form requires some preliminary practice, and be inti'oduced here, where we speak of the
this practice can best
cantus Jirmus in the upper voice.
It
requires but little instrao-
tion. If it
depends upon
us, to
give the cantus firmus, If
a melody
lies high, it
shall first.
wiU be more appropriate
than for alto or bass, unless tone.
we
to consider the tone-region
which of the three lower voices
we have we
for
the tenor
transpose the choral to another
322
Then we have
One
to consider the character of the melody.
quickly progressing, will be
more appropriate
one be better for the tenor ; one progressing in wide steps, inclining towards below, will be better for the bass. The tenor, in general, is most suitable to take the cantus firmvs.
moving upwards,
for the alto
;
will
Having made our choice, or having a choice made for us, we fix upon the plan of modulation, sketch the harmony, and
first
attempt,
first
of
all,
to
make
new upper
the
voice as consistent
Where, with one harmony, this is not possible, we select anorther, or a more favorable position of the same, and finally we complete the work by carrying out the and flowing as
possible.
other voices.
As illustration, we
A.
take, here.
The cantus firmus in
the Alto.
i^f-^-fe^;
440.
P f=5^^=f3p
S B^ m—r»— —'-^ J—r^M
EPS
t
p—• -r»—
^ f- '
d *
323
We
perceive, first of all, that on account of its tone-region and moderate movement of steps, the cantus firmus is particularly ap-
propriate for the alto
;
the seventh and eighth measures only de-
part from the character of the alto.
Considering the whole,
what we have so lately ciency of our means for the proper
find confirmed
Jirmus in the lower voices. is -more
avoid
said,
namely
—the
we
insuffi-
distinction of the cantus
Here, evidently, every other voice
richly developed than the cantus firmus.
we were
If
to
this, for instance, thus,
441.
all
the voices would
we
mass, whether
become an
select the
indifferent, uncharacteristic tone-
Nothing
above harmonies or others.
but a doubling of the cantus firmus, or a conspicuous tone-medium Tvould serve us to distinguish it from the rest ; this, however, is
not our purpose at present. B.
We know choir,
now
is
— the cantus firmus in
the Tenor.
already, that the tenor, as upper-voice of the
more appropriate
the relations which are called into existence
of the cantus firmus,
we
perceive that
it
male
Considering
to the cantus firmus.
by
this position
separates the bass from
the other voices, while the higher voice couple, treble and alto, still
remain intimately connected.
This teaches
us,
then, that
the bass, being sole and independent, will have to be constructed care, because, its isolated position
with particular conspicuous.
The two higher
makes
it
more
voices, however, will cling to each
and mutually support each other by means of suspensions, We progressions in thirds and sixth, or, at least, close position. need hardly repeat here, that this is not an absolute law, but other,
merely intended to
facilitate at.d
Most melodies are those moving in high is
suitable
guide our invention.
for the tenor,
but particularly so
tone-regions, or inclining upwards.
a former melody, the cantus firmus in the tenor.
Here
324
s^^^^m
f-f-r-frg
1
I
442.
I
J-
J
.J
I
j
eis
i T.^
^^e
;fii
^&%=7^^
i^:^^^^^
m-r zmi
rfcl
'
-i
J-
:d^:
3=
W7" iSfT-f-
-
sP
-J-
s^E^^^i^
et-i
l^rt^^^ Jill n-^:ff^r7-*F->, J
I
I
J-
J
I
r
F=
C.
I
The cantus firmus in
the Bass.
The introduction of the cantus firmus in the bass, brings with it, in most cases, an inconvenience which can only be hidden, not avoided. The reason of this lies in the fact that most melodies are conceived for the treble
and tenor, and that consequently
they end with the step of a second c-d, c-5b,
will,
the above, for instance, with
a-g, very rarely with the step of a fourth or
therefore,
dence.
;
iifth.
It
be frequently impossible to form a perfect ca
This will be
still
more
inconvenient,
when
the imperfect
cadence occurs at the the end of a part or the whole.
How
can
we now make
aiAends for the weakness of our ca-
The nearest would be a prolongation then we have the pedal point. But of either means we must make but a limWe take ited use, or the whole will be overloaded and spread. Its high tone-region makes it a former choral as illustration. dences 1
,
325 perhaps, less appropriate for our object, and
we must,
therefore,
think of avoiding this inconvenience.
fc^
^E:Je^P^SEF^= £p#
443.
'"
JJ-J-J.
J
'
'
?^-?=
— I spppspp^i fTT F-
I
I
I
±^^ z^ W.
:*
i
¥^
=p
-
—
r
I
I
=J= p-
g
we have
^
SE
& rrr ^-F= f=Hi kSljr^
First of all
ir-
1
reinforced the cantus firmus with a lower
The plan of the modulation ;
IE
T-
octave, an addition which does not change
ter
I
M==f^ IE
•-
^^ ^
^E r-iKj
,
-© ^Efe=^ --¥
d_J.
3i
is
it
materially.
that mentioned in the
first
chap-
the third strophe only had to submit to a slight alteration.
This strophe, according to
with a half-cadence in jor.
But
this
5b
known
principles, should
have closed
major, or with a modulation to
was not practicable
F m^
in the present instance, for the
closing tone of the cantus firmus (c), would have forced us to end with a quart-sext chord. "We had to consider it as fundamental tone, and to close in the parallel of the subdominant. are now at the point from which we can give a clear view
We
of the whole proceeding. It is clear the cantus firmus in the bass gives us nothing but a melodically-regulated series of tones, upon
326 which to
we have
lead
above
to construct chords,
and above which we have
the other voices as melodically as possible.
all,
shall
we now
take the chords
Each bass-tone can be fundamental tone of a chord, and a nonachord chord,
it
What
then
first,
we
what
shall is
triad, a
septim*
can be another interval in an inverted
it
—
can be a tone foreign to a chord
cipation.
again,
;
Whence
?
we
suspension, pass, anti-
choose from the above
most necessary
for the
1
We
select
plan of modulation,
think of the nearest, or of the most appropriate for the
particular case.
Thus, our
first
strophe closes with the dominant
chord, (inversion) and the tonic triad
;
it
begins with the domi-
nant triad (apparently in JF major), then follows, with remaining bass, the
dominant chord of the same key, and
finally it passes
with dominant chord and triad into the principal tone, £\) major.
The remainder needs no explanation ; the pedal-point, indicates the end.
the beginning, resembling
Let us
now
turn to the char
acter of the voices.
The high
region,
and the ascending character of the cantvs
firmus press the other voices upwards, and limit them to a small space. cally simple.
They
have, therefore, formed themselves melodi-
327
CHAPTER MOEE AND
VI.
LESS VOICED TREATMENT OF
THE CHORAL.
We have to add a few words in regard to the treatment of the choral for
more or
less than' four voices,
though the most neces-
sary facts have been given already in the tenth part of the
first
book.
A.
The
THE CHORAL WITH LESS THAN FOUE VOICES.
choral, as
we know
at present, requires
it
fiill
harmony,
at least tetraphonic, the more, since in comparison with other
compositions,
and
it
so
much
The simple
variety.
lacks melodical
in short strophes, without
mere
thiii
volume and rhythmical
generally of equal measural value
tones,
harmonic volume would be but a
Therefore a triphonic, or perhaps duophonio
thread.
treatment can only be justified by particular reasons, and with
many
chorals
will
it
be absolutely impossible to render them
satis-
factory duophonioally.
The reasons for triphonic or duophonic treatment are either exwhen we have not more voices: or internal, when this sim.
ternal,
pier
treatment conveys a particular expression
;
for instance,
when we intend to represent the whole in a light, free, and transparent manner or when we have in view a combination of particular voices, for instance, two female voices and a bass, two ;
male voices and a In
all
treble, &c.
these cases
we must
select such harmonies as are suitable
duophonio or triphonic treatment. Many good combinations will have to be sacrificed, and many otherwise less approBut in either case the priate harmonies will have to be seized. care, because the less particular requires melody of the voices for a
voices, the
more
distinctly will the feults
and merits of each be
preserved. 1.
The Duophonic Treatment.
In duophonic composition
accompanying
it will
be necessary to construct the
voice as simply as possible.
It
is
best to keep
328
them to the most necessary inThus the following choral might be treated in this
the voices together, and to limit tervals.
W n
manner
444.
m#».
&?:
3
iy=
I1
f=lS r
I
f ^-
r
The second and third strophes hegin with a supposition that there If,
will
is
suspension, under the
but a small or no pause between.
for particular reasons, two more distant voices are taken, it be better to give to the accompanying voice a peculiar char-
two voices, under any circumstance, will not be The above phrase would, therefore, be more ap-
acteristic; for the
well connected.
propriate for treble and alto, or tenor and bass, than for treble
and bass.
In the latter case
it
would be better to construct the
bass perhaps in this manner.
445.
s?^
aiS t jtt:
s The Triphonic Treatment.
2.
This treatment
but
it
is
not merely richer in tones and harmonies,
admits also of a freer and richer development of the voices.
For the two
voices at its
sufficient to give
command
are
by themselves already we should go
a character to the whole, in case
beyond what is absolutely necessary. And since a richer development of the voices is permitted, we have also the means to make up in melodical volume and fullness of the single voices what we lack in numbers of chord-tones. Harmonic bye-tones, suspensions, and passing-tones will do justice to our hannonies,
and at the same time melodically perfect our voices. But we must not lose sight of the character of the triphonic treatment of the last choral
is
choral.
A
given here, merely to
remind us that the greatest simplicity can often be
sufficient.
329
II
E 446.
m^^^^M
is fe^^ggai
i¥
=?2::
i
m
:SE=3 fE-:^
'P?>n*^
2221
-jt=zt^zJlzjt
gE^^jE
The voices
in the following are
developed in a richer and more
mobile manner.
^:^=y 447.
BrRr-^h—'^^--hp-f--^-ff]fft»-j>
_
SF=%f
J=J=-Lt^^.jEdEddEJEJ i^n r-^^
—
»-
I
©--r
l}J_:f:_l^_^d;.d_
SS
t^fe
r The
triphonic choral
is
also well
fitted
to
have the cantus
firmus in the iower or middle voice. This requires no instruction, and simply as example we give here the above ohog^l with the cantus firmus in the tenor.
330
mEfS^^^^Pfe3?E^3E '&
P
448.
e^FJq:^fej=-FP^J=!^"PT»^j:=fc^d=i =F^
B.
P^
^Thb choeal
t^ztpz
with mobe than four voices.
We are convinced that the
tetraphonio choral
is
tory in regard to harmonic volume and fullness. shall never
write a choral for
particular reasons
;
more than
sonietimes only
quite satisfec-
Therefore
we
four voices, except for
we add
to the last strophe,
or to the last chords of a choral, another voice, in order to obtain a full ending.
For
either case the information given in the
second chapter, tenth part, of the last book, will be
sufficient.
331
CHAPTER HOW
VII.
TO ACQUIRE FACILITY IS THE HARMONIZATIOlf OF THE CHORAL.
We
have always maintained that a choral (or any melody) can be treated in various ways, and that there is no absolutely treatment possible, but that object and circumstances give
best
preference at one time to one, at another time to another treat-
We
ment.
require, therefore, the capability and the facility to harmonize a given melody in various ways. have given the means in former chapters, and can add
We
nothing new, but
we
repeat here that the practice
scious of our powers, and
we now merely
indicate
makes us
how
con-
the most
manifold treatments can be obtained from a single melody.
There
The
is
an external and internal variety of treatment.
external variety consists in the fact that a choral can be
treated duophonically, triphonically, tetraphonically, and poly-
phonically voice, the
that the cantus firmus can be placed in the upper middle voices, or the lower voice. These are the ex;
we know them at presEach of them, however, can be carried out in the most manmanners we can make use at the same time of different har-
ternal forms of choral-treatment, as far as ent. ifold
;
monies, and different construction of the voices
;
we
pose the cantus Jirmus as well in the triphonic as
phonic and polyphonic choral. forms,
we
But placing aside
in.
all
can transthe tetra-
these various
will limit ourselves to the tetraphonic treatment,
and
to the cantus firmus in the upper voice. Tile internal variety, to which is
we have
thus limited ourselves,
based upon the different modulation, harmony, and construction
of voices which
we can
give to a choral melody.
The
construc-
tion of the voices is the easiest, and therefore least important to
us;
it is
conditioned, essentially at least,
by
the choice of chords.
We shall merely remember to make them as melodious as possible.
But the modulatory and harmonic design or sketch are the
332
most important for us. How can we always find new modulations and harmonies, without trusting to chance ? The reply to this question and the necessary instruction, constitute the contents of this chapter.
In general
we
We
ascertain the key,
first
can only repeat what
and
we know
already.
upon the
fix
principal
mo-
ments, the ending and turning-points of the modulation, accordingly.
Next
to the principal
key we must ascertain of what
Here we take the
modulation the close of each strophe admits.
and pass thence to the more distant. And to these end-points we lead our harmony, employing first the nearest, then the most appropriate, and finally those in general admissible, taking advantage, however, of the slightest alteration which opens
nearest
first,
to us a
new way.
This wiU result, also, in designs and direc-
tions of the bass, at
which we have to consult how they can be
employed in one or the other manner. But now to work. We take the following choral, and simply because it contains the greatest number of repetitions in the smallest space.
yap^
*-•-
fc
Sgfefj?2=S=i cSasS
449.
-0-0.
iWe ^EfagEf: shall
m
.0-0-
merely give beginning and
indication,
and
it
remains
for the student to carry it out.
The
first
strophe
is
the
-•
most naturally
•
«
We have taken the
0- -0
a
•
f=±f
^rr 450.
in the principal key.
J-
tonic chord for the
the bass in a higher octave.
bass in an opposite direction.
first
two
tones,
and led
Let us now attempt to lead the
333
^fe^l 1 rfr'=FT=f TIT 451.
jlj =t
rf The bass ascends rather
far,
equally passionate ascension.
would have to avoid such exaggeration, exhibit a more marked direction. It
ner, the following strophe
but in
stead
its
and forces the middle voice to an we were to begin in this man-
If
we might
might, perhaps, be thus
^lf=i-
A i^
452.
i^^ £^S
m-
al
I
S^F
=F
But
us return to No. 451.
let
to ascend so high, because they
us a
new
The exaggeration of
step upwards
lies particularly in its last
1r
;
the bass
the middle voices have
have begun too low.
This gives
treatment.
^^
;fe^|
453.
Jl A- -d.J-J-d
f=F="=r=r ,iV I
1
-d
I
^
I
£
f=F The bass, from manner
I
.
.4.
the fourth tone, might also have proceeded in
this
454.
m
^^"^' It: 6
but in
all
these cases
7 it
7
6
6
7
would be advisable to employ
second strophe a less extended progression of the voices.
for
the
334 Both these fundamentiil forms exhibited a bass progressing wide
now attempt
Let us
steps.
in
a more quiet melody for this
voice.
k
fe-^E
i
m
455.
^E
:ttP=
We might
1
I
i
E^;
continue the diatonic
movement of
the bass, perhaps
thus:
456.
m^Hm^ rj
tt
g^
r
The bass descends here chromatically, and ascends again diatonically. But there was no need of discontinuing the chromaticprogression ;
we might have
*
rJ=i
i P^^^^1
ii 45T.
continued thus
m J^J
.5-^
-g**'
ipi
r
and
this
=F
would have enabled us
modulating at so early a to continue either of the
to close in the tonic, instead of
moment to the parallel. above, we should prefer a
gression, because the chromatic progression
by
the smallness of the steps, and
unlike.
by
mt 3
4
6
8
4
6
we were
would embarrass us
their being harmonically so
We should, perhaps, continue thus
458.be
If
diatonic pro-
t
:
g^fe
335
We must break off mere first two
for
here, in order not to anticipate too
chords, being the triad of 0, or perhaps an inversion of
Let us now depart from
it.
much
All these formations are based upon the
indications.
the tonic chord for the
first
this first harmonization.
tone, but
we must
We retain
find a different
harmony for the second. What now can the tone ^f be ? We have already considered it as fundamental tone, but it can also be third or fifth. The latter leads us to the subdominant of the principal tone,
and
therefore,
is,
the nearest.
Sebastian Bach
has solved the question for us in four different manners.
Here
they are
& 459.
teS^^f^ l-j&i
&
mi r^=£ff=mT
We
leave
it
to the
student to analyze and examine the
above, and turn at once to the second
of e or
eb'?
The
latter
^
ff
as third.
would not remind us of
-E'l;
Of what ? major
(be-
H
minor. It is true and soon follows), but of that this tone is rather distant from our melody, and caimot well be justified in connection with the whole. But such treatment is cause b preceded
it
not absolutely impossible or useless, and we, therefore, give here
an
illustration.
336
m^^^^ f=^¥W^
0--
460.
But such
it
1
=Wp:
m
-i
it lies
»
—
»-
^^ i.
3=p4
much
nearer
to- consider
^^.
.i
?="r^ :^
r
the g as third of
P
e.
As
Here
leads us to the parallel of the principal tone.
m
W^r^-tfT-^OLili a?=
1
461.
?^ we have ployed
it
just touched
it,
without remaining in
thus, in five treatments
it.
Bach has em-
:
462.
^^Pi^* rr-r
^i^
=1 rr—rrrtr
gai^^gi^-^gfepg I
I
Sometimes
(at a, d, e,)
he has actually modulated to
closed with the major triad.
At
'
£!,
and
other times he has merelypassed
from SJ minor to A minor. In the above we have always begun with the sext chord. might, also, begin with the fundamental chord.
We
337
r—r-
463.
mz We
'^^i^Lj-J-L-ki
^
have attempted
it
here twice.
a consistent progression in the bass.
At a we have developed At b we have retained the
tone b in the bass, and the middle voices were consequently fluenced in like manner; and from the chord i-t^|/|
led to the superfluous triad
g-b-dl^,
or rather
its
in-
we have been
sext chord.
But we have gained enough from this simple melody. A retrospection upon our work would give us the feeling of the young anatomist, who was forced to bury his knife in the most charming formations of nature.
He
followed the path of reason and
searched for knowledge.
We have
only been able to indicate rules and
body who has followed us
attentively thus
far,
facts.
Every-
will see at once
we have exhausted nothing. But we hope we have gone far enough to indicate how important this practice is, and that though that
succeeded by other exercises, practical contents of the
it is
in fact the
whole First Part.
cap stone of the
338
Second Part. The Chorals in
the £leclesiastical Keys.
that
many
chorals belong neither to our major nor minor modes, but
to a
It has already
been stated
chapter
(last part,
I.)
former system of keys, and that they cannot well be treated cording to our different
modern system of modulation.
modulation and harmonization,
do not agree with our
one corresponding to
principles.
treat such chorals properly,
the keys in which they are written
of and select the harmony. the history of music ;
we must ;
first
be familiar with
at least enough so to judge
This study belongs perhaps more to
—but we cannot well comprehend an
subject, without having at least
The
ac-
require a
Their melodies even, independent of harmony,
that old system.
To
i. e.,
They
historical
an outline of its history before us.
familiarization with the ecclesiastical, or antique keys, as
they are sometimes
called, will bring
with
it
another advantage.
These keys have been developed long before our present system of keys and modulation was in existence to the latter. in,
They had
or submit to
more general sible.
it
for in our
;
truth
Considering
and in
;
it
;
they have finally led
to lead into our system and to be lost
from
it
system there
lives
a higher and
only was a progress of music pos-
this point of view, the
former system
does not merely appear deviating from, but preparatory to our present system.
There were then other ways of modulation
and as we analyze the points to which these ways have gain a
new view and
latter gives us for
every general purpose the nearest means.
tells us, for instance, that
a perfect
full
we The It
cadence (with tonic in
the highest and lowest voices, and the final chord cal chief-part)
led,
confirmation of our present system.
upon a rhythmi-
forms the most satisfactory ending of a composi-
But the antique melodies exhibit attempts of not ending Nay, the tonic and its harmony is often not even the basis, the beginning and end of the whole tone-movement. tion.
with the dominant chord, or not upon the tonic harmony.
339 These attempts are the results of an intellectual conception of the tone-element, the births of a truly inspired, songful period,
they are opinions stand firm,
full
of truth,
—though they have They
selves as general laws.
—a
truth which stands and will
been unable to establish them-
are not the arbitrary attempts of a
and experiences brought down to us from one of the most eventful and important epochs in the history of art, and as such, if they otherwise agree with our present prinfew, but they are results
they form an important confirmation of the latter. But this confirmation and agreement is exhibited, not merely in what the ancients did according to our manner, but also in what they deviated from it. Thus they deviate, for instance, in ciples,
had a different object and afterwards they achieve that object exactly according to our present their cadences, wherein they
;
general laws.
The most
essential point of our theory is
follow the old
to
masters in their ideas, to obtain from them the truth therein contained, to conceive their melodies in
them according
in the old chorals it
their
spirit,
to harmonize
Independent of this, there
to their ideas.
which has ceased to be essential
for us,
is
much
because
was not conditioned by the ideas which led the ancients and
To
influenced their works.
the
fact,
among
the latter,
others, belongs
that their system did not contain all the tones which
possess.
At first they had
we
only the scales
c, d, e,
f, g, a, b,
c,
and c, d,
The tone
e,f,ff,a, 6b,
d
c
e
existence at a
^# and
could not serve for
ferent
f
much
came into But the gjjl
c.
chain
g
a
b
c,
later period.
steps and half steps were not of like proportions
from a| and
cij).
time did not permit
it,
d\,,
gb and ab
;
bb
and
«b
;
were
cf dif-
The temperament of the organs of that and though,
upper keys were introduced
at a later period, additional
for these tones,
which led to the even,
temperament, the principles of the old system retained their hold, and reigned until gradually the modern system became predominant.
340 It is
also
known that
the ancients did not
make use of so many-
chords, suspensions, passing tones, &c., that their voices were not
generally carried out so richly and perfectly as those of our time.
But since we
shall see that the
element of their system did not
consist in this, their proceedings will not shall write,
be binding upon us ; we
with due regard to their essential laws, as our object
permits us, or prompts us
We merely add,
that
to.
we have
rhythm, but have adopted
for
not retained their often effective
our theory the melodies, as they
are sung at present in our churches.
341
CHAPTER
I.
THE ECCLESIASTICAL KEYS IN GENERAL. The
keys can be regarded from a two-fold point from a melodic point, as mere scales, and 2nd, from
ecclesiastical
of view
:
1st,
a harmonic point, as scales intended for the basis of harmony (therefore actual keys in our
A.
The
own
sense of the word.)
The Melodic Point.
succession of seven degrees belongs to all
Former theorists attempt
keys.
scale a tonic,
to
make every
ecclesiastical
degree of the
and to build upon it, without depression or Thus they obtained the scales
eleva-
tion of a tone, a scale.
2,) d,e,f,ff,a,
b,c,d;
3)) «)/)5') «> *)«!
4,)/,
i',
«,
«.'
f^)
b,c,d,e,f;
5,)ff,a,b,c,d,e,f,g; 6,)a,b,c,d, e,f,g,a; as the
first
of which, however, they considered the scale of D, They might have added a seventh scale, from
(here the second).
btob: S, c, d,
e,f,g,a, b
:
but this scale not even admitting a tonic triad, it could not become a key. The names of the above six keys were :
1.
Ionian, from
2.
Dorian, from
3.
Phrygian, from e to
4.
Lydian, from / to /;
5.
Mixolydian, from g to g from a to a.
c
to c;
dto d; e ;
;
6. jEolian,
These theorists acknowledged, in melodic respect, two positions for each of their keys.
Their melody
throughout, or principally, from tonic to tonic,
different
moved
— or
either
in other
342 words
:
from the fundamental tone to
its
These melodies they called "aM
moving from
return in another octave.
—even
tonic to tonic, had that name.
the whole scale,
From
such au-
thentic melodies they expected the character of decision, firmness,
transcendant joy, &c.
Or, the melody moved around
the tonic, perhaps from the Such melodies they called "phffalic;" represented in this form, was also called plagalic.
dominant to the scale, if
Fiom
this
its
octave.
melodic form they expected a milder, more animated,
softer character. It is
not our object, however, to invent melodies according to
the ancient system, but merely to learn the treatment of those in
Yet we cannot
existence.
fell
to perceive, that all the melodies
based upon the tonic are in possession of a certain authentic strength, while those which plagalic mildness
and
The Harmonic
B.
Of the
move around the
tonic,
have a certain
flexibility.
Point.
upon the seven degrees of the scale, become keys which admitted of a tonic chord.
tone-chains based
those only could
The tone-chain of ^ admits of neither major nor minor triad, the triad upon its tonic {b-d-f) being diminished ^and consequently could not become a key.
—
Of the remaining
six scales three
the Ionian, the Lydian,
admit of major
^^e-c,
the Mixolydian,
They can three scales
triads, vis:
c-e-ff,
ff-b-d.
compared to our " Major." The other have minor triads upon their Tonic, viz : therefore be
the Dorian,
d-f-a,
the Phrygian,
the jEolian,
e-ff-b,
a-c-e,
and might be compared with our "Minor."' Soon, however,
we
find, that
only the Ionian scale actually
re-
The others deviate
al-
sembles our scales of major or minor.
ready melodically, and consequently cause deviations in the har-
mony
also.
Leaving aside the Lydian key, and attaching our observations
343
key (the Ionian) which really resembles our major, we upon its dominant the Mixolydian key, upon the dominant
to that find
of the gian,
latter, the Dorian, then the iEolian, and finally the Phryalways based upon the dominant of the preceding one.
Thus we see, as in our Quint-circle, a progression of keys ways a fifth distant from each other
C
D
a
al-
E
A
Ionian, Mixolydian, Dorian, iEolian, Phrygian,
which must necessarily end with
because the next tone, B,
jE",
does not admit of a key being built upon
The Ly dian key, if en-
it.
closed in this circle, should find a place before C, Ionian, upon its
subdominant.
But
this progression of ancient
difference
from our own
keys exhibits an important
we always
In the latter
quint-circle.
progress from one key to another similarly constructed one, from
D—in short to all
G to
G*,
same
contents, the
same
major keys, and they
The other
intervals.
ever, leads us every time to
all
have the
progression, how-
a differently constructed key.
The Ionian, exactly like our major, has major triads upon the dominant and subdominant, and upon the former the dominant chord.
Next comes the Mixolydian, mit of a major triad
its
;
Its
tonic
and consequently has no dominant chord. again, this scale admits
and subdominant ad-
dominant, however, has a minor
upon
its
tonic,
On
triad,
the other
side
of a dominant chord,
which however leads to the Ionian tonic (c ). Upon the dominant of the Mixolydian, is based the Dorian key. It is a minor key, for its tonic and dominant ti-iad are minor
;
(as far as
nant triad,
we
can
however,
see, for
is
major.
the present at least)
Upon
The jEolian key, which has minor and the tonic.
its
dominant
triads
its
is
subdomi-
based
:
upon both dominants
Finally follows the Phrygian key, which upon subdominant and tonic has minor triads, while its dominant has neither major nor minor triad, but a diminished one, which, as it were, cripples the whole key. The Lydian key is similarly crippled by its subdominant, which admits of neither major nor minor triad, while tonic and
dominant have major
triads.
344 The Essential Tones of every Key.
C. It is
easy
now to
from another
discover which tones are essential in an eccle^
Those tones are
siastical key.
it is
;
essential
natural that
we
which distinguish one key
begin with those keys which
resemble each other.
Which
tones are
now
stamps the key major;
1, the
minor Seventh,
for it distinguishes it
Which
it
it
from the
stamps the key minor
distinguishes this
In the
Thirds for
;
2, the
Ionian.
are the characteristic tones of the Dorian?
Third, because it
and characteristic of the
essential to,
Mixolydian?
2, the
the
1,
major Sixth,
for
key from the subsequent one, the ^olian.
Mo\\&n we must consider as essential \, the Third, as minor ; 2, the minor Sixth, which distinguishes it :
characteristic of
from the Dorian. The Phrygian is distinguished from the jEolian, and from the other keys
by
The Ionian has
its its
Second, which
it
all
minor.
Third, the sign of major, and
Seventh, which distinguishes
The Lydian has the
is
major
its
from the Mixolydian.
superfluous Fourth to distinguish
it
from
the Ionian.
D.
Admissibility of Foreign Tones.
Thus far the ancient system strictly follows the original scales. But it permits also the use of foreign tones, if they do not destroy Thus the ancients intro the essential characteristics of the key. duced the major seventh in the Dorian and jEoBan keys (cjj and for third and sixth, but not the seventh, are the essential 5'{f), characteristics of those keys.
E.
Transposition and Signature.
These foreign tones permitted also a second application, by means of which each scale could also be represented upon another than the original degree.
the dominant and
How
degrees higher or lower.
We
see
by
a signature ; ly
This was done particularly upon
sometimes one
subdominant, and
was
tliis
the key was a
two 1
the above that none of the ancient keys required
for the foreign tones, if there
accidental.
or
transposition eifected
They had only fifth
lower
;
to
instead of
were any, were mereand J|j, for it],
substitute
C
Ionian
it
was
F Ionian,
345 and the Mixolydian was then upon scales
Dorian upon G; the
C, the
were Ff
ffy
",
C) di
e,
G,
The keys molle, in
a,
called genus
b\,,
c.
d, e, f, g,
c,
5b,
&c.
transposition were called genns
originating in this
contradistinction
d, e, f.
c,
^Ij)
f, g, a,
the original keys, which
to
were
durum.
same manner, the substitution of /| for /H transposed fifth above. The Ionian was thus upon G, the Mixolydian upon D, the Dorian upon A, In the
all
the keys a
The keys designated
G,
a, b,
-0,
e,
A,
b,
d,
c,
/#,
d,
c,
e,
/|, g,
g, a, b, e,
fl
c,
d,
g, a,
&c.
from transposition into the
arising
by adding
to
them the word
:
above were
fifth
"Hypo ;"
for instance
Hypo-Ionian, Hypo-mixolydian, &c.
modern system we have but two keys without signature and A minor. If we meet with melodies, which, without signature, belong to the tone-chain of D, E, or G, we must In our
C major
consider
them
as belonging to the Dorian, Phrygian, or Mixoly-
The signature of one
dian of the ancients.
us the key of jP major, or
which, though having a signature of one G, or A,
the tone-chain of C, lydian,
G
Dorian or
indicates to us the ever, with a
A
in
G
melody under
tone-chain of -Z>, A, or B,
A
we must
( b)
indicates to
major or
this
flat
still
( b)
consider
them
belong to as
mixo-
The signature of one sharp
Phrygian.
key of
flat
D minor, but if we meet with melodies
E
minor.
(|)
Meeting, how-
signature which belongs to the
we must
consider
it
as
D
Mixolydian,
Dorian or B Phrygian. We have thus exhibited the general rule of ancient signature transposed keys. It is immaterial to us that not all keys were
we have only to do with the we find them. It will now be easy to understand the signature of other transTo represent, for instance, the Phrygian key in the positions.
transposed in this manner, as
melodies as
tone-chain of
D or
0,
—
346 «, /i
t
9, «. *.
<^)
«b,
«)
4,
/ e|7,
/,
d,
«.
^, a,
*!?,
ff,
e, c,
a},,
d,
b\,,
e,
—
required in the one case two, in the other case four
melody of the tone-chain flats,
J), therefore,
or of the tone-chain C, with four
flats.
A
with a signature of two to be considered as
flats,, is
a transposed Phrygian.
Thus we see a
series of diiferent
mit foreign tones in
its
keys before us
melodies and harmonies
;
;
each can ad-
each, also, can
be represented by means of foreign tones, in more than one tonechain, and though until now we have only observed the external it is clear that these must also have given them a diiferent internal character, which we shall endeavor, at some future time, to comprehend.
deviations of these keys,
F.
Modulation into other Keyi.
In order to complete our analysis of the ancient system,
must add, finally, that like our own system powerful means of modulation from one key
it
we
possesses the all
into the other, and
the combination of different keys in one composition.
We know of two ways of modulating.
1.
We follow the path
;f the quint-circle, and pass from one major tone to another, or,
ny means of the major key, and
minor
parallel,
we go from
vice versa.
for major, or
major
2.
a minor key to another
We substitute,
on the same
tonic,
for minor.
The ancients, too, modulated according to their quint-succession—and in still different progressions but they always found diiferent keys. Or, by means of tone-transposition, they formed a new key on the same tonic ^modulated without leaving the tonic—but, here too, they had a vastly greater variety than we ;
—
with our major and minor.
On
the other side again, the
more
of their different keys conditioned
it
decided, peculiar character
that certain digressions or
modulations were absolutely inadmissible, whUe we, though generally seizing the nearest related key, are not prevented
from
modulating into every possible key.
Thus much
in general of the ancient
rate consideration of each,
and
its
keys ; and now
treatment.
for a sepa-
347
CHAPTER THE
II.
lONIAIf KEY.
We
know already that the Ionian key is the only one among the ecclesiastical keys resembling one of our modern keys major.
—But
all
our^iajor keys have the same construction, while
the ancients, in their Mixolydian, and,
if
they chose, in their
Lydian key, had two more, differently constructed major keys. Thus the character of each, and consequently that of the Ionian also,
became
peculiarly distinct.
We
can see this at once in the order of the modulation. According to the principles of our modern system the modulation in
major goes almost invariably
for instance
in
C
to
reason also the most
G;
first
this
common,
is
to the
key of the dominant,
the nearest,
—
^but
very reason, in the ancient church-melodies,
for this
was not high-minded, not
liked, it
festal,
could hardly stand for an actual modulation.
do we
find
on the Ionian dominant 1
But
was
least
In
For, what
Either another Ionian tone-
Mixolydian key, which,
be afterwards explained, was as
it
not exalting enough.
fact it
chain, (hypo-Ionian) or the
for that
least exalting modulation.
little sufiicient
for reasons to
to rise from the
Ionian tonic.
we find the modudominant either entirely avoided, by means of ca-
Therefore, in the reign of the ancient system, lation into the
dences in the principal key or the subdominant, or retarded upon the parallel of the subdominant, if not an actual modulation into that
key {A jEolian).
Thus Sebastian Bach,
in three different
treatments of a choral with the following strophe
464.
forms
^=rH=^i=^^
its
and on
:
cadence, the
its
first
time with the subdominant and
recurrence he treats
it
thus
tonic,
348
^pi^iS^P u s^ ^^^^m +-r
465.
349
CHAPTER
III.
THE MIXOLYDIAIf KEY.
We know of
it,
therefore with a
that
it is
minor
a major scale with minor Seventh, and'
triad
on the dominant.
It
lacks therefore
the possibility of a perfect cadence, according to our prmciples.
We have
make our cadence by means we have used occasionally as a half-cadence, and which is generally known under the name of ecclesiastical cadence. This is by no means, however, the only ecclesiastical cadence, and we shall soon arrive at others. Nevernothing
left,
then, but to
of the subdominant ; a cadence which
theless there is in the Mixolydian
key a dominant chord, but it on the tonic and points towards the Ionian scale. For this reason has the Mixolydian key a peculiar inclination to modulate is
into the Ionian.
therefore
it
Mixolydian
Mixolydian (originally Ionian
;
is
in fact Ionian
in
origin,
its
G
takes part in the transpositions of the Ionian. Ionian), like
a modulation which
lies
Q
very far from our
Q-
major.
In order to exhibit the peculiar characteristics of this key give here a Bohemian choral,
F
Ionian goes into
(p cJ,/u^ ^«... ^
,
>
we
X-M
i^3^Ji
"^^m 466.
^i
?i
f
a 1
i
i
f=i=
S«f-,'rrT'rT f-
350
CHAPTER
IV.
THE DORIAK KEY. The Dorian is the first minor key of the ancient system. We know already that it has a major triad upon the subdominant, and that
can change the triad of the dominant into a^ major,
it
by introducing
Thus the major element
(?|.
predominant^ and
is
the minor of the tonic cannot impress us sadly, but merely with
This
a deep earnestness.
and
strict,
but not sad,
it
the character of this key.
is
was the key
Severe
to which the ancients en-
most solemn music, for instance the Oredo, and in most of their ecclesiastical songs. The authentic character and the low region of most of the Dorian melodies corresponds trusted their short
with this character.
The Dorian makes
its
nearest modulation into its dominant,
the ^olian, or represents this key upon
genus molle
(d,
e,
/, g, a,
b\)
,
«, d).
But
its
it is
own
tonic in the
frequently the case
that other modulations precede this one.
The intimate connection with the Mixolydian, with which the Dorian has the subdominant chord and the two characteristic tones
(/and
Mixolydian.
commpn, prompts
b) in
With
with the Ionian
it
the Mixolydian
it
it
to modulate into the
goes into the Ionian, and
goes to the subdominant of the
latter,
F
Lydian.
Again we give here a Dorian choral which exhibits that key its
mosL distant And
467.
rare turns,
i
J
ff.
-^
^
^
in
*mJ
'
351
*^mm^ ^mm
352
CHAPTEE
V,
THE ^OLIANKET. Upon
the dominant of the Dorian rises the jEolian key.
characteristic tones are c and^j the
The
Its
minor Third and minor Sixth.
seventh, however, not being a characteristic tone,
changed into a major seventh, and thus makes
it
is
often
possible to have
the triad of the dominant major, and the cadence of the jEolian
key
decisive.
This key, softer and gentler than
its
predecessors, does not
modulate into the minor or major key of its dominant, for this would require the major triad or septime chord h, rf|, /|; or h, d\, /j(, a.
./Eolian
.(Eolian ct]
is
But the ancient system has no
rfjj,
and
/ being
in the
Nor can the an essential tone, /|t is not permitted. go to I) Dorian, for this would require the tone c\, and
another essential tone.
The
jEolian, instead of
tions, is satisfied
making use of these
with half cadences upon
its
striking
modular
dominant (without
modulation), or turns to the Phiygian (which can hardly be called
a modulation) and through that into the Ionian.
469.
^^^^i#
^^^m^
i^^Si*^*i ur r T'-rr
I
ag^ $
f^^: "Cj
r^r
354
CHAPTER
VI.
THE PHKYGIAN KEY. This
the last of the ecclesiastical keys, and with
is
Third and minor Sixth,
by
its
The
minor Second. d,
had no major seventh
This, however, naturally conditions
even apart from the (rf|)
from
/, 9, a, b, c
rf|,
is characteristic
of all
ecclesiastical scales, that
all
two half steps never succeed each other. to give to the Phrygian scale a d |, two half steps would appear time, would be chromatic.
fact that the ancients
For, it
e.
diatonic scales, and consequently of
«.
minor
latter,/, is therefore its characteristic
lone and cannot be changed. the minor seventh,
its
distinguishes itself from all other keys
it
If therefore,
we were
e,f, &c.
in succession,
and the
scale, for the
From this follows then, that the Phrygian key has no cadence which we should consider perfect ; nor, in fact, can it form any cadence with tones belonging to tones
b,
d
jj,
from which
/jj. it
Thus
it is
originated,
for this
it,
would require the upon the jEolian,
entirely dependent
and can close in no other way but upon
the dominant of the same,
e, g!^, b,
—
i.
e.
with the use of a foreign
tone; the half cadence of the jEolian (from
^
to
^)
serves in
this instance as fuU cadence.
We perceive here in two minor tones, again, the same reversion of the order of modulation which
we
formerly noticed in two
major tones, the Ionian and the Mixolydian ; only that the Phrygian cadence is still less independent than the Mixolydian, because in
its
very
final
chord
it
requires a foreign tone.
This led to the strengthening of either
by
istic tones,
the tonic,
470.
It was effected harmony the characterthem the minor third ol
its cadence.
introducing in this preparatory
—
d and f, or in addition to Thus have we two Phrygian cadences
i*^^ ff.
:
355 which are peculiar to satisfactory as our
this key,
own
but by no means as decisive and
cadences.
In consequence of the relation between the Phrygian and the
Molim. keys the former
likes the
modulation in the
latter, as
well
as the latter inclines towards the former.
Weak
and helpless as the Phrygian stands
there, it is really as-
tonishing that in connection with the Ionian, which can be placed
imder
it
without hesitation.
Ionian.
we
should obtain so significant a result.
We see here a close intimate connection
with the Ionian, the
firmest and clearest major tone, and through
and
its relation
it
we
are led at once
The dependant nature of the Phrygian,
to the Hypo-Ionian &.
to an almost opposite major key, causes that
its
melodies often begin in tones of one of these related keys, so that it is almost impossible to know at once in which key the melody
is^it^en.
^
H,r^.
472,
m
,
.
BE
^^
iUl £
fm^
mw^
1^-4
Uii
^f3g first
I
^PP
r^.rf
the
Ht^ ^^^ ^ A/fe,.^
'^^^^m m Q^ic^^w^
II
m ?3^3F5J^
ii--
r
strophe points distinctly to the Dorian key
;
but the
next strophe having a modulation to the Ionian (7, proves that Only towards the end the former cannot be the reigning key.
we
recognize the Phrygian distinctly.
356
CHAPTER
VII.
THE LTDIAN KEY.
We have reserved One
the analyzation of this key for the
reason for this rather irregular proceeding
is,
last.
even in
that
the ancient system, this key has never been able to acquire an
independent and rich application, and that, since the reformation, it
Only in Bohemian collections do we and in others the Lydian appears
has vanished entirely.
find
Lydian melodies
at
all,
merely passingly in other keys, particularly Its characteristic is
b,
in
Dorian melodies.
the superfluous fourth
This one tone only, distinguishes
it
of the tonic.
from the Ionian and from
all
must not be altered as long as the key is intended to be Lydian. The fact of this tone's making a dominant chord impossible (c-e-g-b\i) would not have mattered much for most of the cadences were prepared, not by the dominant chord, but by the triad of the dominant. Nor would it the other keys
;
b,
therefore,
;
have made much difference that the superfluous fourth (/ b) is an unmelodious proportion ; for it was easy enough to avoid this step wherever
disagreed with the melody.
it
spects this tone
—
b,
thei
But
in other
only characteristic of the key,
—
re-
^was the
cause of the decline of this key. In the first place the
more apt and
Lydian
scales
resembled another much
useful scale (the Ionian in the genus molle /, 9, a,
K
e,
d,
«,
f,)
could not well escape being mixed up
to such a
degree that
with
it.
In the second place the Lydian, in consequence of this
very
b,
lacked the tonic harmony of the subdominant, and conse-
it
quently could not modvdate there, and was thus crippled on one
And,
side.
loss
;
thirdly, there
was nothing to indemnify us
for this b could only lead to a
—a modulation
for this
modulation into the domi-
at once characteristic of nothing and the most Every single key, except the Phrygian, had it, and without demanding a sacrifice. These are the causes of the
nant
commonplace.
357 Lydian's never obtaining any extensive for our separating it
from the other
efficacy,
and the reasons
ecclesiastical keys.
The deep meaning of the ancient system could not be denied, and in many instances we had to accord to it more subtle distinctions
and better
characteristics than our
own.
a misunderstanding and an unartistio roaming,
if
But
it
would be
we were
to en-
deavor, in our labors, to return to the rule of the ancient system.
Every form of expression which the ancient system
oifers to us,
we have in our own system, with the additional advantage that while we can make a free use of them, the ancients were restricted by regulations and rules. These, for the standard of modern
art,
are no longer necessary
;
nay, such oppression would be insupportable to the tone-artist
he wants
liberty.
And
in the
same degree
as this liberty
was
achieved, the directions which the ancient system gave for certain objects had necessarily to
become
inefficient.
358
Third Part. The Secular National Song.*
We need hardly mention that by
"national songs "
those melodies which have really lived
more
those which
strictly,
among
we mean
the people
not
;
should be called patriotic songs, nor
do we speak of those which one composer or another has invented in the
may
manner of the
have
people.
Such manufactured national songs
merit (perhaps more than an actual national
artistical
among
song), but they have not lived
become
its
the people, they have not
property, they have not been attuned to the people's
sense or voices
!
Only where
that has
been done
—where
the
song has ceased to be the work of an individual, a composition,
where
it
has become the property, the organic word, the voice of
the people as such
—only
there
we
And
see the national song before us.
the most vivid characteristic of a nation, one of the
it is
most invaluable vibrations, in which every nation unconsciously exhibits the enigma of its fexistence and of its sensations. This is the deep meaning of the national song, and by it it becomes deeply significant to the musician, who is probably the most capable of taking in and comprehending the simple melody. Whatever the real national song teaches him of his art is true .
and genuine
;
perhaps not for general purposes, but always in the
sense of the nation from which
reason
it
it
originates.
must not be judged by general
But
for
principles,
this
very
but in the
sense of its parents.
We rules
;
have always avoided the abstract application of made if
we do we search for the particular The people who invented them have
a foi-mation does not correspond to general rules,
not pronounce
it
wrong
reasons of the deviation.
for that, but
not known those nales, they have only unconsciously carried them within them.
But present above
all
and nearest to
their heaits
was
* This word does not exactly express the meaning of the author, but as the translator could not find a better one, and as the true meaning of it will become apparent to the reader in the course of his studies, the translator has thought it best to retain this word.
359
moment, of the conditions under which the song Here must we look for the nearest and reasons for the melody of the song, and the deviation from
the feeling of the
became truest
their property.
general law.
Thus much of the interest which the national songs have for They are so important and so instructive that no musician
us.
make himself familiar with them not to imiwould be vain) nor to employ them in his own would be little) but to enter more deeply into the
should neglect to
;
tate them, (that
works, (that soul of art.
This occupation can be limited, as can
every other work, to
the mere performing, or meditating upon the form and' the contents of the song, or i.
e,
it
can consist of an independent treatment,
invention of an accompaniment, or perhaps the representation
of a national song as an independent composition (without words,
upon the Piano, or by a combination of other instniFor the national song, as such, is sung by the people,
for instance
ments).
sometimes unaccompanied and monophonic, sometimes the singers from it by ear, and without regard to rule or principle,
construct,
a duophonic, or triphonie phrase
;
often
it is
accompanied by a pe
culiarly national instrument. If the musician,
now, has to invent an accompaniment, he can
do so, either in the style of the people, in which case his accompaniment will be subordinate or he can accomplish a higher object, i. e., by means of his accompaniment, and by its manner, he can increase the expression of the song, and thus elevate the work ;
itself,
and the hearer, into a higher sphere.
song remains in
its
In the
first
case the
natural sphere, expressive of a popular na-
word or sentiment. In the other case it becomes an independent work of art and can no longer be considered as a mere tional
national song.
To
the latter class belongs the " collection of " cyclus of songs to a distant
Scotch songs," by Beethoven. friend,"
by
the
same
A
author, might also be included here
;
like-
wise the arrangement by Liszt of Schubert's songs.
We
shall
begin with the most simple, and
make
consider the Pianoforte as accompaning instrument.
it
a rule to
360
CHAPTER
I.
GENERAL CONCEPTION OF THE MELODY. Thk
first
task in the treatment of a national song
nation of its key
people a song
;
for it can easily
the desig-
is
he imagined that among the
is
sung in one key or another, just as
1.
CONSIDERATION OF VOICE-REGION.
suits the
it
singer.
In this selection
we must
of tones for the voice.
think above all of a proper position
The national song is intended
d~—f: a tone-chain which lies convenient least in reach of the lower ones.
2.
hy
to he sung
many, and must not exceed the ordinary compass Though it is impossihle to give the exact points to compass might extend, as one nation sings higher or another, it will still he well to confine ourselves to
of voices.
which the lower than the tenth
for high voices
and
is
:
at
CHAKACTBK OF KEYS.
The next important point is the character of the key which we Every musician knows, or ought to know, that every
select.
key, apart from height or depth, and apart from the peculiar character of different instruments, has a character of its own,
warm, now
cool,
character
transmitted to the listener.
is
now
now
sad and gentle,
perceived this difference of character,
it
now
firm,
which
If
we have now
at all
is
hut natural that
clear
and
we
should select, if possible, that key which corresponds best with the character of the song.
361
CHAPTER
II.
PIAN OF THE HAEMONY. The
work of the composer begins but now, with the seharmony and the modulation. Though we shall be guided by the same principles which assisted us in our former la^ bors, we shall, in two respects, go farther than in the choral. Firstly, the national songs in general differ more from each actual
lection of the
other than the chorals, for in the one all
we
see a representation of
the various conditions of humaiiity in all their variety
;
the
various sensations are represented in the most peculiar, finest and sharpest features, while in the choral, everything
is
subordinate
to the general form and character of devotion.
we have
Secondly, in the choral,
in addition to the uniformity
of rhythm a uniform distribution of harmony,
—
^generally a chord measural part or syllable,^and in order to avoid under those circumstances monotony and weakness, wa have made our harmonies energetic, and our voices as melodious as possible. But
for each
this is altogether different in our secular
their contents
and
their
predominating
The variety of
songs.
mood has given us
a variety
of rhythm, and has characterized each melody distinctly.
We
no longer speak of a uniform or impartial distribuThe harmony has no longer the obligation to intion of chords. demnify us by variety and vigor for the monotony of the rhythm, can, therefore,
it
intends only to support the melody of the song, and the accom-
panying voices become subordinate to the melody. In the treatment of such melodies
above
all,
1.
we must
decide therefore,
upon
The Measure or
But according
ike
to which law
1
Quantity of the Harmony.
—^According to one already known
to us.
Already in the
first
we have learned many spaces in which the various voices
chapter of the eighth part,
to consider the chords as so
362
move
In going
about.
from one chord to another,
therefore, the
move from one space into another. In the same manner we have considered the various keys through which we pass in the course of a composition as so many voices merely
spaces,
—but
larger
and more important than the former.
It is clear, therefore,
space as an important contents of one space
that we moment
more
consider every step into another
of the whole, which separates the
or less distinctly from that of another.
Consequently
we must keep ic or
together as
much
as possible, in one harmon-
modulatonic space, those tones of the melody which be*
long together.
The rhythmic-melodic
construction of a song decides generally
what tones belong together.
To begin then with our labor, let us take the melody of the well-known, " Qod save the Queen ;" 473,
^^
p^ii^
The whole formation
tells
itat
us at once that the melody consists
of three sections of two measures each.
In order to represent the
progression of this melody in the most clear and simple manner, since
it
would be unnatural to
tion under one chord,
—we
force all the six tones of each sec-
will at least designate the
section with a harmonic point of rest.
companiment
474.
end of each
This would give us an ac-
like the following
^m^^^^^ ^3S3 ±
J-
f£p
But we see already that there can be more than one division of spaces, and that the necessity of supporting the sectional points of the melody
is not always alike pressing. Thus, in the above melody, we might have embraced the first two tones of the first
and third measures, and the three tones of the
fifth
measure, in
363 one chord
and vice versa, we might {ff, b, d, and d, /|, o, c); have given the tones of the second and fourth measures to two or three chords.
The
decision in such case depends
acter of the song, or the object of our treatment
upon the but
;
char-
will al-
it
ways be seen, that, the more changing of chords we permit, the more weighty, and the more tones we comprehend under few chords, the more light and animated will be the song. But returning to our national song we see, that however clear and simple the above treatment, it by no means corresponds to the weight of such a song. The following would be far more suitable
^m^
tT>
m^^^ I
I
475.
The
Italian prayer "
O
sanctissima,"
Andante.
O
,
sano- tis
^=p:
n
-
si
-
m
-
ma
pi
!
-
ta,
-
-
ma Dul
si-
I
a!
--^t'.:^^
iifriz
Ma
In
-
ter a
ra,
had best remain on one chord.
-
ta,
ra pro no
-
should be treated in like manner.
ma
-
teme-
=S^SEli
=F -
is
221
i^i ra
5;££
m^-
bis.
The second and fourth measures The second part would perhaps
begin thus
477.
^PS 4 -iJ-
-J-
P
S=::
f^m-
=?2=
.
-9- -•-
1
-©-
'A
m
364
Number of Accompanying
2.
Voices.*
Next to the chords we must decide upon the number of voices which are to accompany the song. The more tones we combine, the more full and heavy will be the mass of the accompaniment the less voices
we employ,
the
more mobile and
light will
be the
whole.
The above
Two
is
how many
judge
so clear that
it
will
be comparatively easy to
voices are requisite for one song or the other.
voices, three, four, or five voices can
be made
effective if ju-
diciously employed.
Until
now we have only
considered what number of voices is more appropriate for this or the other song we have add two other considerations which were not requisite in
in general
now
to
;
the chorals 1st,
there
We shall soon perceive that
is
in one and the same song sometimes a section which demands a stronger emphasis
sometimes in consequence of the words, sometimes on account of the musical contents of the song itself. The mere change of forte and piano is often insufficient for such purpose ; than another
;
even the peculiar treatment of the hannony will now and then be it. But the alternate use of few and many
unable to accomplish
voices will often produce the desired
song
478.
effect.
Thus the following
:
^^il^gH
^^S^l
3E3EE ^=^ :^m
35 :P5iii=
i^i^^pi might be treated with
full
the shorter tones might
harmony
0 —•-
H *
in the longer
be treated more
lightly,
•—
tones,
M-hile
perhaps thus
:
* As a matter of oourse we have no reference here to the number of singers, nor to the forte and piano of instruments, but merely to the number of voices constituting the harmony.
365
:£3E 479.
OFEF^;
i^-^ H
I I
'J
m
^ 1
i
eE£ -i^-
I
I
==1-f^-
E5
£
But we will remember the advice given on former occasions, (Book I., first part, chapter II.) and effect this change in the num ber of voices only at the beginning of new rhythmical sections. In the chorals such change
even
effective,
as
depends above
it
would be
but as a general thing all,
possible, it is
and occasionally
absolutely unnecessary,
upon the typical character of the choral, number of voices, demands
which, altogether independent from the the
and only consideration.
first
We
—
particularly on instruments incar shall make use pable of forte and piano, or sustaining the tones, like the organ
2nd,
or pianoforte, or for the accomplishment of particular effects the polyphony
for single
with one or two voices.
known
ol
As
illustration
we
give here a well-
military song
^# P^T
5E
480.
—
moments, while otherwise we proceed
g:
a f In such cases the decision depends
M
upon the rhythmical construo words and
tion or accents which the particular character of the
melody demands.
Every other
direction
is
superfluous.
366 Occasionally the
number of voices
is
reduced to
make
the ac-
companiment more practicable. Finally we must consider 3.
Until
The Form of the Harmony.
now we have used
the chords in different positions, &c.,
but always so that the tones belonging to them generally entered
But in this very simultaneous sounding of three more tones there was an unwieldiness and awkwardness which was long a stumbling-block to us, and which we must now try to simultaneously. or
overcome.
The means
for it
were always at our command.
We have
seen already that the tones of a harmony can be introduced not merely simultaneously, but also one after the other first
;
in the
case the haraiony appears in harmonic form, in the latter
case in melodic form. figures in
Between the two stand the well-known
which one or two voices of the harmony anticipate the
others, like
481.
The melodic form of the harmony gives us many ingenious harmonic figurations, and which we
formations, which are called shall
now
consider.
867
CHAPTER
III.
HAEMONIC FIGURATION
Discovery of its Designs,
We we
know
already that with the
name
designate the representation of the
" harmonic figurations"
harmony
in melodic form. are not sounded simultaneously but one afBut in what succession? Here are three tones
The tones of a chord ter the other.
1-
2.
3.
4.
6.
^iig^g^g^ii
482.
which give us already six
different forms.
6.
t-
i
Four tones give us
twenty-four forms, independent of the variations which might be produced by change of rhythm. Even now we see that it is next to impossible to exhaust the foi-ms of harmonic figuration, and that we merely can give an insight into this element. First of all let
us glance at the designs. 1.
In No. arising
Monophonic Designs.
482 we have been made acquainted with the designs
from three tones^ without taking into consideration toneand rhythm. Of course, every other three tones, or
repetition
three differently-situated tones give us six other designs, and
every four tones give us twenty-four designs. its
The nonachord
in
primitive form would give us one hundred and twenty-five de-
signs. tion,
483.:
If
we add
to this the rhythmical variety and tone-repeti-
a single design of No. 482.
Eg
i^^it=
$^^^^^^m.
368 gives us endless numbers of other designs. is
In short this element
absolutely inexhaustible.
Duophonie and Polyphonic Designs.
2.
In the above
we have
resolved a whole chord in melodic form.
But we can retain a part of have here
it,
and
484. Ah
i=i
i tlSWWW
figurate the other
thus
;
we
aSsS-^^i
$
r
figurated four chords in such manner, that at
r
a we retained the
upper voice, at b the lower voice, and at c the upper and lower voices, while the
middle voice
we have made from nic succession
;
in this case
phonic or triphonic
;
is
figurated.
In the former cases
a triphonic or tetraphonic chord a monopho-
we make a
tetraphonic phrase duo-
but in the figural voice there are contained
three or two harmonic voices.
But such duophonie or triphonic phrases can again be made tetraphonic or polyphonic
by the addition of new
voices
:
'^mm^^ HH^P I
485.
ffi
i
^•E
^
li^i^t
$ m^ir^^Sjr^t^^^
^
m ^^m^
r
369 It is clear,
however, from the above, that such phrases,
if re-
duced to the harmonic form, are not triphonic or tetraphonic, but pentaphonic, hexaphonic. &c., and in reality present this appear-
ance
:
=i=S=r= =i=iC=5= =r=«="=?=n^ 486.
^^^m
We leave the
1B=P=
We
have
difficult to find
more.
student to practice such figuration.
here only seized the nearest.
It will
not be
370
CHAPTER
IV.
EXECUTION OF THE HAEMOMC nGURATIOK. It will require
but few observations to guide us merely in the
They
execution of the harmonic figuration.
we
just as
them
consider
fall
into
two
halves,
from, a harinonio or melodic point of
view.
THE HARMONIC POINT OF VIEW.
A.
The harmonic figuration is in reality nothing but an actual har mony, but represented partly or entirely in melodic form. Consequently in our
it
has to submit to
harmony
in general.
all If,
those rules which have guided us
therefore,
we
start
from a previ-
ously fixed harmony, as in No. 482, or imagine at least such a
harmony
as in Nos.
484 and 487, we
proper observance of those rules. to
some
are involuntarily led to a
This will give
rise,
however,
their
harmonic
points worth mentioning, 1.
Retarded Resohition.
Let us reconsider the figurations of No. 484 and basis.
437.,
^i
r
-"-
r
r
r
r
-•-
-»-
-221
-aIn the simple
solved
;
h
goes to
harmony the septime chords c,
/ descends
at A, the seventh goes not to
terwards that is
c follows in
a similar case at
b.
e,
to
e.
are properly re-
In the figuration, however,
but ascends to g.
It is
the same voice, and finally
Are these tones
only
treated wrongly
af-
There
e.
?
No
;
371 the figural voice contains three harmonic voices, the tones of which do not enter simultaneously, but one after the other. This is called
a " retarded resolution."
The same takes place as in the following
suspensions in the harmony,
if there are
:
488.
It is
undeniable that the immediate resolution gives the quick,
est satisfaction,
and
is
therefore the mildest formation.
retarded resolution can exercise
more tones a
many
by
peculiar charm, and
its
is
But the
very retarding of one or
absolutely indispensable, in
cases, to the consistent execution of a figural design.
Octave
2.
The
and Quint- Succession.
attentive reader will already have noticed that in No. 485,
and e, there have occurred octave-successions which No. 486 have been made apparent. Thus we see here. at A, c, D,
489.
^3-^53.
m-
at A, octave-
Are such
No
!
^ "?~T
n
in
i
and quint-successions which appear at b uncovered.
successions
wrong
?
In harmonic respect they are
those of our former harmonic forms
;
by no means
as distinct as
for the figural voice hides
and covers them with melodic bye-tones in such a manner, and is and flowing melody that the suspicious
in itself such a mobile
successions are only the consequences of the doubling of voices.
But even
if
of a figurated phrase
all
the
an actual faulty succession forms the basis ;
for instance, here
372
490.
imm 4M =^ PT T I
I
the melodic form and the intermediate steps (here a sixth between
every two
fifths)
would mitigate the bad
of such succes-
effects
sions considerably.
Passing- Tones.
3.
Though the passing-tones do not belong enter simultaneously with
it,
to the harmony, they and we have often considered them
Therefore
as actual tones of the haiTaony.
it is
evident that they
can be introduced into the harmonic figuration as essential tones of the
lowing
little
harmony.
if
they were
This has been done in the
fol-
phrase
491.
B
-^r4
I
N
\
-d-
=^z
i fipzpipi'^irprp^p; F|
f->-r^^?--r-P=.i
BE
-P
-I
\
i
=?2=
The d measure
in the first is first
measure
is
a passing-tone
;
the c of the second
a suspension and becomes afterwards a passing-
tone to the expected
d.
The same takes place
in the third and
fourth measures.
/
B.- -THE MELODIC POINT OF VIEW.
Each
figural voice represents,
above
all,
a melody, and as far
as its contents and its relations to the other voices permit,
it
373
must follow the laws of melody.
Of these laws
there are
two
in
demand mention.
particular which
1.
— Consistency of Execution.
We have always endeavored to retain
the designs and dii'ecand we have not passed on to others without good ^we will not depart from it now. If we have once seized
tions once seized,
reasoils
—
a design,
we must
shall not depart
let it
from
it
work
to the test of
powers.
its
without good reason, and
we
We
shall per-
haps occasionally return to it. An unnecessary, aimless changing of design would only cause confusion and restlessness.
2.
Each measure
is
Firm
Connection.
a progression, closed in itself
from tone to
tone, in which the relation of each tone to the following is ex-
pressed.
The
closer this relation of tones
does the relation become
;
is,
more apparent
the
therefore have tones which succeed
each other diatonically or chromatically, or which belong to the
same harmony, the
closest relation to each other.
Therefore, in harmonic figuration, the melodic connection will
be the stronger, the closer the tones of a chord
lie
to each other.
Here, for instance, 492..
1^^^
i
M^
spgii
i
be the most firmly, the figure c the least firmly The figure b stands between the two. It is more connected. expansive than a, and less vague than c. These two merits might the figure
easily
a
will
be combined by intermediate tones,
-^^m
^.
as, for
instance
:j=
374
m Thus
I
1
1
1
1
III
^eS far rests the
I
^
melody But the close union
internal connection of the figural
upon the power or formation of the design.
of the isolated tone-groups to a flowing figural voice important. tal
harmony
indicates, or the last tone of the first
brought in diatonic connection with the group.
is equally-
This connection takes place, either as the fundamen-
first tonfi
group can be of
tht^
second
375
CHAPTER
V.
THE EXERCISE OF HAEMONIC FIGUEATION IN PASSAGES AND GIVEN MELODBBS. It is
now
time
to
haps this practice
is
resume the practice of our new means.
Per-
not absolutely necessary for the mere accom-
panying of national songs, but these exercises tend so much to the development of our musical powers, and willi be of so
advantage in later exercises, that Passages reduced
1.
This
is
to
we must
much
not omit them.
Harmonic Figwration.
a comparatively easy task, because the uniformity of
the passage, and the liberty to select, close, and rhythmize ac-
cording to our pleasure, cannot but greatly assist us.
need but few I
illustrations,
and begin with the following
shall
:
I
^:^L^--j--—-g-
.
We
j_j
'_J
I
^=n-r^fff
LU ^»iWipW ^ l^i^ i _
Here
are a few of the
495.
M:
"—•-
F-=F^
^
r
I
most simple beginnings
376
At first
A
visible,
„.
we
melody of the upper voice indicated by the At b and c the melody is still
see the
tones of the figural design.
while here
j^te^iA — rTII t
*
it
if^ i
I
vanishes altogether.
An
extension of our chords would give us an enlarged arena for
Here
our designs and the carrying out of them.
^^^^^^^ ^-^
497.A
M mP
3EEEJ£
Oon
^t=m g:J:
fuoco.
i^^
- -]
r
^
to each chord.
Hen'e
tS" sf-
^^^ s^ we have given a half-measure .
Teneramente.
498.
BES^z fi 1-
we have no duced
X
iz
^-
longer repeated the design slavishly exact, but intro-
at the
same time an
accidental suspension.
377
Accompaniment of Given Melodies.
2.
All our former melodies give us opportunities to practice on them the harmonic figuration. Only the irregular progression of these phrases makes the task somewhat difRcult; we must occasionally relinquish strict adhesion to the design, in order to
keep up with the melody.
In the following fragment
Andante.
499.
we
C the same accompaniment in three different accompaniment threatens to overpower the melody we can easily add an harmonic accompaniment. see at A, B, and
designs.
If this
Lfe^^ 500.
If in it
-t.
^^^^fep|^ the above
we have
with a middle voice.
501.
-*-h#-
i ggj;
figurated the bass,
we
can
now attempt
^ m^^^m^ *=?=
1
t
i
i
378
The
figuratfon
of the upper voice, as might be expected, causes a
greater or lesser deviation from the principal melody. placing of
its
But the
tones on rhythmical chief-parts can soon balance
this slight defect.
502.
1
Sh The
mm 1
=l=f£ '
-J:
further practice of this figuration presents no difficulty,
and we pass on at once,
therefore, to the next chapter.
379
CHAPTER
VI.
PASSIKG-TONE AND BTE-TOITE.
The harmonic mobility, but
figuration developes before us a picture of great
it suffers
from the monotony and emptiness which
are always the companions of the
mere harmonic element, and
which have driven us already to the invention of suspensions and passing-tones (Parts Eighth and Ninth). It lies
near, therefore, to introduce these passing-tones in our
harmonic
figurations.
Thus here.
^=
503.
m
i
LLiLLT J.
^i=±
i^ frTT^T^=t¥ '-^&w-T^:m gS"
at c
^
and d we have enriched the designs of a and b by means of made them more
diatonic and chromatic passing-tones, and have
connected.
But
it
cannot always suit us to introduce the whole series of
diatonic or chromatic intermediate tones, to
or
fill
out every third
fifth
504.
$ ^
a
If
tifi
^
But we must remember that the very step of a third or fifth was nothing but the progression from one degree to the third or fifth,
with omission of the intermediate tones.
Consequently
can omit any or all the intermediate tones in the above.
we
380
iip=ppi&=H=^^E
505.
*-
Instead of the three intermediate tones of a third we need take but two, and the only question arising then would be, which are
The
best omitted'?
the subsequent one,
object of the passing-tone is to lead us into it
must
therefore lean towards the subsequent
tone, join it closely, as it were.
The passing-tones
above.
keep
distant, as it were,
This
is
the case at a in the
at b are less satisfactory, because they
from their actual
The
goal.
passing-
tones at c are in direct contradiction to the supposed key, and
sound strange.
With the same right we can retain but one of the passing-tones, and in that case we shall select the one nearest to the subsequent tone.
506.
The one
P
at
B
ft
a or b
,
.
¥ better than the one at c
is
;
for the c|
does
same in descending. Of the intermediate tones between a tone and its third or fifth, below we can select or omit at pleasure. Of the following diatonic and not lead to
e,
but to
d.
It is
the
chromatic passing-tones, 507. A
,
^
Bill .JJ y,h^^^l=k^:U 1.
I
J
I
-t:-
we
I
t-
can chose these I
"^$
I
I
m^-d=i=R=H=J=iii=:R=fi:^i^
I
m i±:^B^^SEe^pEpf3^ But we must here add a few remarks. The pass is a flowing movement, having in its completeness a softening influence upon the melody, which, without steps.
it,
must
necessarily progress in wide
S81 In incomplete passes the whole influence of the pass ti'ated
is
concen-
upon * ^
^B u 1L
—
_
o_
D _
^
509.
stt: the remaining tone, which; leads smoothly into the next one,
while
it has no connection with the preceding Such isolated tones of a pass are called
one.
HELP TONES.
Embodymg them
in
'
our harmonic figurations
-
'
we gain new tiiriei-
successions, for instance
510.
They
are so sitnple and satisfactory an addition that
we
can even
begin with therd without preparation,
511.
or introduce
them simultaneously with the
^ %^
^ ^^ ^ ii p<«i
512.
chord, without regard
-m-M
i 'm
to its contents,
and without
fearing, even, the effect of false-rela-
tions (Jb against h\ in the above) provided always that the help-
tone leads to a chord^tone,
After this
we need
not hesitate to introduce descending help-
tones in ascending passages, and vice versa, ascending help-tones in descending passages,
513.
i -&-
i
382 or to employ either or both in vague tone-chains of harmonic figuration.
514.
li3Bi i^ffi a^es^
i
One
step farther.
It arises
tion of a harmonic tone
from the above that
we can
give
it
a
fiiL
in the repeti-
a help-tone from above
as well as below (a),
-^^^^fc and consequently we can also introduce the two in immediate succession (b).
the chief-tone.
Each of the passing-tones Consequently
finds its resolution in
we might omit
the latter the
first
time, and unite the help-tones and let their resolution follow
af-
terward.
'''$
Seie^
r^
f
£ as well as d are here resolved in c ; of the
first
tone
is
somewhat
retarded.
only that the resolution
The
attentive student
will here perceive at once that all our musical ornaments, such as
TBILLS, TUlftlS,
DOUBLE TURNS, &C., are in reality nothing but an accumulation of help-tones.
In the form of heIp4ones, too, passing-tones can be introduced in false relations.
some
justification,
reason.
Here
The introduction of them demands, however, and should not be permitted without
sufficient
383
M
^m^^
517.
^ig^^F
1=^
ijtihjt
we see a e| against a cfc|, at b /| against /H. This secure a flowing progression of the different voices. at A,
is
done to
For the
same reason we have here
^^m •hf-
518.
taken g instead of y|.
A similar passage from " Don Giovanni"
519.
can be explained in like manner. Until
now we have merely treated of If we mix, now, the designs
themselves.
we can
— I T 5—-i F^g
^-•-« ^-»-
^
i
by
^
with a pure harmonic figuration ;
520.
the passing-tones
obtained from thein
for instance,
— — s-«-^
^
-f
I-
see the resolution of the passing-tones and help-tones at
once.
But we have already seen
in
No. 516, that help-tones do not
resolve immediately into a harmonic tone.
not hesitate to lead the help-tones
first i ito
We
shall, therefore,
other harmonic tones,
before the tone of the actual resolution appears.
521
P1^^ ^^M
384
Not always, however, will such mixture be good, and least so when the two elements fall confusedly, one into the other. This would be the case manner
we were
m
522.
The design
is clear
S
relate to
Finally
to remodel 520, for instance, in this
iffl.
enough in the
first
and
last quarters
;
but
and third the impression that the two help-tones,
in the second
/I and
if
g and
we must add
d, is
almost entirely
effaced.
that these real and apparent passing-tones
and help-tones can occur simultaneously in two or more voices. This can lead to harmonic formations which were not in the least intended, and which,
by persons fond of
technical terms, are
called
Passing-chords or Transient chords. Their treatment requires no particular directions, as their origin
—
be observed ; each help-tone and therewhole passing-chord consisting of such help-tones ^must
will indicate the rules to fore the
return to the originally-intended
main tone or chord.
—
Thus we
find here
523
Y r at A, within the chord c-e-g
and
a-rfj(-/jj
{b\)-c-e-g)
their
;
at b
we
6b the
groups
£?jt,y|,
6,^t-J,
rfjf,
see actually all the four voices of a chord
proceed to help-tones which seem to form a chord of
own (6-(fj(/j(-a).
however,
and
tells
The
us at once
that case its resolution
resolution of this accidental formation,
tha-t
the chord
would have been
is
not a real one, for in
far different.
385
CHAPTER
YII.
INTRODUCTION OF PASSES AND HELP-TONES INTO FIGURATION.
Thb help-tones have stepped out, as it were, from the diatonic and chromatic passes, and thence have found their way into harmonic figuration. Their practice, therefore, must be attached to the diatonic and chromatic passes. This will have the additional advantage of reminding us of the application of the passes.
The
directions needed are but few,
may serve
524,
and the following phrase
as a basis
m -§-
^i
4&-
SP'^
^-
We begin our task
feE3i
Ei^i '^'
^^
^t
sii
^"f
with the
A,-^FIGCRATiaN OF THE UPPER VOICE. and. at first
with the diatonic passes and help-tones.
'
525.
p
E^E^J
'-J.
t^Sf^fati^iff '
'
!
W
-^ -&2 I
The
first, fifth,
and sixth measures need no explanation, as they
contain nothing new.
The movement
measure, induced us to continue it
became absolutely necessary
it for
in quarter notes of the first
another measure, and
to continue
it
now
throughout the
whole phrase. In the third measure we might have written three times e and then c, but the help-tone made it less monotonous.
S8« Thus we have accidentally arrived
at a figuration of a single
tone, consisting of its repetition and a help-tone.
Following up to
the' idea of figurating
a single tone,
No. 525 a more animated formation
526.
;
we might give
perhaps like this
pgg^EJ^gi^
Let us turn
now
to the
into the upper voice tones
harmonic figuration
;
let
us introduce
from the fundamental harmony.
The
nearest would probably be this
P"^
527.
^E?:
i
z^t^
ES.
ig^^^
^IS^iS
containing harmonic bye-tones and diatonic passes. will proceed to the chromatic passes.
528.
And now we
Here
#^=r^p|?£^c^^ti^
we have
&o.
arrived, for the first time, at a somewhat-varied rhythmi-
Merely passingly do we remember here the rich and powerful means which rhythm oflers us, and which until now were zation.
laying idle.
We might
combine the chromatic passes of No. 520 with the
harmonic bye-tones and the uniform movement of No. 527.
would give us fonnations 529.
$^^^^
i^^gi^ ^^ m^^^m^m
or of greater compass
:
pj
530.
Ths
like this
m
387 or in extended figuration Ten. Dolce.
531
i^^
?-• _^.
E
or in a similar manner, but even
*T&, e.
t' tJ:=.ti
fie-
Ten.
mm
^^ -^^^
t
more animated and marked
:
532.
and a thousand other designs and formations.
B.
FIGURATION OF THE BASS.
except, perhaps, to give
33.
ig= WF ii
The
'-^
find the melodic movement of the we hardly know what to do with it, a more animated ihythmization.
we
Returning to No. 524 bass so meagre, that at
first it
^ g—
introduction of a help-tone instead of a
-^
mere
d-
I
tone-repeti-
388
f f tion (a), or with
upon the
it (b),
(c),
first
-r
ffj
CTT
upon the second part of the
mea&flre, oi
m=a
if show how
rich a
this
us, perhaps, to the following
4-
-sj-
In order to
:7T'
would do away, to a great degree, with
monotony. The design c would lead
535.
I
=P
b34.ffi
J-
5
-M:.
:
*
development a simple design
like
those in No. 534 can furnish,' we merely igive one here,
536.
w ^S
leaving
it
m^Ms'mM
to the student to follow
Were we
up
this exercise.
at all inclined to change the melodic basis in the bass
of No. 525, the harmonic figuration would arriving at a richer foundation. in this
first
us the means of
ofl^er
we might
sketch the bass
manner
537. i5i
1
and by means of the
we would soon It
is
^^
^
J
X
^^^^^ J-
tions.
At
J
different passes, for instatice
arrive at
more
interesting
easily seen that the
;
and extended foraaa
above figuration originated
in
389
No. 537
539.
this case
would have been
:
^^^^!^^
Bi:
much
melodic basis,
not, however, without a change of the
;
which in
nearer to No. 537
b,
would have been a development
like
the following.
640.
FIGURATION OF A MIDDLE VOICE.
C.
The
little
space at our
command
is
here greatly in our
and we must therefore either lay the voices farther
must combine the two middle voices
into one.
The former
ceeding will call into existence formations like this
i
way we ;
apart, or
pro-
:
:^f?=Ji !flic
*jiji~(*~
541.
A:^
e?
LU ^m
Mai^-fIt
the latter would lead from formations like a to such as b and
many _
others.
!''_
1
_i
L-*^
l_l
!_:::
liimpbh mn-!—£j
l_lJ
—v^=^^-
^
542,
These directions
will
be
sufficient to practice all the
different
forms of the pass in connection with the harmonic figuration, and stimulate the inventive faculties of the student.
Yet we would recommend
to the zealous pupil a last exercise,
which in his future polyphonic labors will be of much advantage to him.
We have reference to
390
THE APPLICATION OF HARMONIC FIGURATION, CONNECTION WITH PASSES, HELP-TONES, AND SUSPENSIONS TO HARMONIC PASSAGES. The task
136.^
is
We
ficient.
an easy one, and a few illustrations will be
^^Efed
ff^f r ^
-&-
T-
J. -s-
suf-
Here the bass
return again to the passage 136.
J
^
IN
^^^^^ ^ rr^
descends alternately a fourth, and the third voice, in like manner a third.
The other
voices proceed diatonically.
Let us now
fill
the wider steps with diatonic passes.
::^
—(^
W^:^ 543.
fei-
^
i^^
"M^'r-i'T
^ Why have we,
3 P~
a
at A, introduced suspensions in the
In order to avoid the consecutive fifths
all
three of the upper voices.
At
b
we have
sus-
Let us now attempt the
introduction of passes in the upper voice
they can only be chromatic.
upper voice ?
which the passes would
otherwise have formed with the upper voice.
pended
iS
;
as a matter of course
391
-Ml
^t^
=d=
$
^
ii
644.
at
^^^
J^
zJzz:!^
W=^^
^e=r^T
.
tt^f^
Bi As a
rS
;^^^
last illustration of the rich
and varied developments which
the industrious student can derive from the simplest designs,
we
give the following
W 545.
-±^-^ et:
The
first
r
^lrr=fs^^i four notes of the treble can be considered as the prin-
cipal design, which will
in the tenor, alto,
But- though
be found
in a
more or
less similar form,
and bass.
we have
tration, the pupil
designs.
a«sj
r
given here a somewhat complicated
must not
fail
to begin with the
illus-
most simple
392
CHAPTER Vm. APPLICATION OF THESE
NEW MEANS TO
ARTISTIC
ACCOMPANIMENTS.
We are at last fully prepared for every kind
of accompaniment
which the character of our national songs might demand.
now
represent the
endless forms, as
and firm
chords,-
most
we
volatile
We can
and flowing accompaniments
in
formerly constructed accompaniments of full
only occasionally interspersed with hannonic by-
tones &c., &c. (vide Nos. 475, 477, 479.)
Casually
we
learn now,
some of the tones in No. 477, which we could not explain at the time, are nothing but help-tones. Our labor now is but trifling. We have the necessary means in hand we have practised their application, and it only depends now upon our selecting the right means for every particular task, to judge which form of accompaniment or representation is most in keeping with the character that
;
of each song.
The great
similarity of
ferent conceptions of
makes
many of our
which most or
present forms, and the
all
impossible to point to any one
it
right one.
Yet we can be guided by
dif-
of our songs are capable,
form as the only
certain general principles
which will always indicate to us the proper direction, and guard as against aberration. 1.
A
strictly
harmonic accompaniment, like that of No. 475,
produces the most firm, meaning, and heavy 2.
The
richer the change of chords, the
effect.
more interwoven those
chords are, by means of suspensions, passes, &c. &c., the more conspicuous will be the character of this hafinonic
accompaniment, (Nos. 476 and 479.)
The milder and
the change of chords (No. 475,) or the are separated
by
more
rarer
these chords
rests
(No. 480,) the lighter will be the
to the
harmonic accompaniment, we have
accompaniment. 3. In juxtaposition
393 the harmonic figuration, the fundamental character of which is
animation, lightness, grace, and a certain transparent con-
nection of tones. 4.
The
apart these
farther
more
figures, the
will this
tones,
more extended
the
the
movement, the more conspicuous
rapid the
fundamental character become
;
the
more
simul-
taneous voices share in this movement, (No. 485 d and
more do we approach again
the
b,)
to the fullness
and firmness
make
the harmonic
of massive motion. 5.
Passing-tones or help-tones are apt to
more connected,
figuration
full,
melodibally satiated, as
it
were. 6.
The more firmly
the melodic connection of an accompany-
by means of passing-tones, more independent a melody will this voice become, and more attention will it detract from the principal melody. ing voice has been developed
After these observations
we
the
the
accompaniment
will construct our
we will even change the form of accompaniment, if prompted by the deviating tendency of single verses or parts. But in every case we will ensong according to
for each
its
contents
;
deavor to keep in view the general character of the song. It is
necessary, also, to ascertain whether the
melody
is
to
sung, or to be played in connection with the accompaniment.
the former case
accompaniment paniment
so
and contains
it ;
but
it
by
at legist
will itself^
i^
T=l
be well to construct the accomit
affords
a certain satisfaction
no disagreeable passages
quart-successions to which the
546.
;
for
instance,
melody would form the
a^i
:P!=F
sixth,
f-»
§1
Accompanitnent.
\,_4._ S-j_
17*
In
not necessary to place the melody in the
is
that,
be
394 irregular steps in the upper voice, &c. &c.
be treated more
tions will
But these considera-
fully in the chapter
on the accompani-
ment of vocal music.
Here we
to such treatments in
which melody and accompaniment are per-
fo;med on one instrument
—the
shall confine ourselves principally
pianoforte.
Let us begin our labors with the following song
S: ^^47.
^ which, in
its
simple construction, resembles our
As
formations.
This treatment ter.
If
it
is
above,
it
is
first
periodical
sung duophonically by the people.
perfectly in keeping with its object
and charac-
were intended to be accompanied by the pianoforte,
oi
to be played without being sung, a few simple chords, supporting
the rhythm,
548.
would be
sufficient.
answer to the final verse,
The
first
light verses, the
of these accompaniments would
second to the more serious and sad
and the coda might designate
characteristically
this latter
mood more
by moans of a more developed harmony
395
S3
W^^
•-•-*-*»-H-
^
549.
S3Ee!^ *^i ^^
n
1
^:
If this form of accompaniment should be deemed too simple, we were to give an indication of the suppressed emotion of the singer, we might form a more animated middle voice. This has
if
been done here,
in the
most simple manner
Fiu animato.
-sar-t
1
i_J
P
f—
1
•
.
-£«.
1
t=^-M 550.
Ores
d^.
Oi
:?—
L i?=it
Nl_
9J^
I
-T^
R-,
m^^
-^=^-
^e^3^5E
r^^s^^a? biy
I •r
-g-
^
-a-
Sg3s|-
396
The design
consists of the second voice of the national
combined with the
fifth
of the chord.
It is
song,
deserted in the close
is indicated again at the end of the whole. The made itself more independent from the design, and assumes a more complicated foi-m, which might have been differ-
of the thesis, and
antithesis has
ent and simpler
;
for instance
:
.KS-
but which departs altogether from the simple character of a national song.
Let us imagine one of these representations employed second verse, and
we might
excited character, though
448
;)
perliaps ihus
still
give the third one a
resembling our
first
more
for the
anxious,
conception (No.
:
.^
552.
p
_L
„ P
397 But
if
we were
simplicity, if the
to depart
we might surround
it
more from the character of rural by lilce a mere recollection,
still
melody were
to pass
with accompanying reminisceiK'-es,
-«-
-«-
^^= & 553.
Marc.
et^" IS:
c.
espr.
j^J44^ f
*
Fed.- piano.
J^ J ^ '~^"5"I<2>"5" — ^
II I
Maro.
N-«-
-«-/-N-«-:^
r
rt:^^F^>-
espr.
1
I
-'*-'
-*--:8-:r I
1
p
L'-^L -pfp
_dl?l
^
iF:=g:
R--^Fed.
or Other nearer or
more
distant formations.
Franz Liszt has
been peculiarly fortunate in the production of such forms.
554.
^^^^^g^^pgi^ *===*
w^^t
"^^^f^^
=^5Z^ ^ZlSl
-^^m^&-
^n^ii^^
->--N-
--»-#-f -+-—*-
*-:E=K£Et^^S
iM^g
398 Finally, is less
we
will
throw a hasty glance upon the above song.
simple than the former, but admits of
We see in
ceptions.
it
many harmonic
two particularly conspicuous points
:
It
con-
the
pause in the third measure from the end, and the imperfect cadence of the second part, two measures previous is
merely a repetition of the same.
the
same
the song
object, is
—the
for the rest
expression of the longing for her to
whom
We shall have to make use of interrupted
addressed.
and imperfect cadences, gentle, restless desire
;
Both points have one and
;
in a
manner which corresponds
to this
perhaps thus
|^^!S^ 555.
aipi Shall
P
we harmonize
-4^=
the beginning thus
?
5tEJEE&^
^^
f=^
556.
f=r
a
e^-t
m ei
m
S=:
f^-1
-|
-
h
P^N* I
399 It
would appear too unsteady and assuming.
The
latter refers
particularly to the painfully anxious chromatic progression of the bass.
We
should prefer a
full
and gentle figuration of simple
harmonies
^m^jj
" 557.
^'iff^'iVr
^-rjJ^^Tf
E=3^^§^^ggagm T^T
*^
T^ZlTf
1f»-iS»-l7'i
iS-^iS^ and with the following measure we would return the the beginning (as at
a or
p,)
over to the second part, as at
1IE=3
-F-
r
558.
first
c.
m '
~^~rr
^m -•-
d---^J: :fe=F
m^ h=f -
time to
and the second time we would pass
^^tlu:
r
4Q0 Or,
if
we
-conceived
tjiis
song in a more
J^estless
mood,
we
might form a more animated aecompaniment, perhaps thus:
659.
ess ^^
3^
We leave the student to practise and
exercises.
it±i=E=3:
r
m
these and other analyzations
401
APPENDIX.
THE FIGURAL PRELUDE. In the first chapter of the Fourth Part
we have
already men-
tioned the prelude with which a piece of music can be introduced
Our prelude
to the singers or listeners.
at that
tremely meagre, on account of lack of means soon after gained
new
varied harmonic
;
time was ex-
and though we
chords, and were able to construct
passages,
yet
monotony and dryness of our
we
first
could not
attempts, until
more
overcome the
we
arrived at
the harmonic figuration, with or without the passing tones and help-toties.
even
Nor does theory. is
It iS for this
now we have
true
to
that
this subject actually
We
—but
we now
return to the prelude, and
be limited to the most subordinate forms.
consider
it
belong to this branch of musical
merely as an appendix, dispensable
so easy of attainment, that
we
—
it
shall not hesitate
to treat of it.
The prelude
is
intended to prepare us for the key of the subse-
quent composition, either by indicating
it,
or
by actually sounding
the essential harmonies, and in addition to these, perhaps other
near related harmonies. p. 120.
560.
Passages like
Thus much we have leamecTalready
this,
at
402 or these, 4
561
m^ p
BE
4
3
_(2_
yes
-&-
£
bt
6
3
t b
-h^
bs
7
-z^e^:^
b
^ n p -e-
are quite appropriate for purely harmonic preludes.
We have already learned to
develop such passages more firmly
and melodiously, by means of suspensions and might therefore give to the prelude No. 560
P
^
=F=
^P
ai
d
s
We
^=^
W=i^
562.
i
passes.
this
If
W^WS'
i
rx^—^^
T=^^^^
or any other form.
But such formations are
less appropriate for preludes,
the presumptuous development plicity
is
because
not in keeping with the sim-
of the task and the hannonio foundation.
403
Here again we discover in the figural forms the proper means They mitigate the stiffness of the chords, and with all their unas. sumingness give us the possibility of volatile formations, without preventing us from elevating ourselves to more energetic, flowing
and melodious ones ; and as they do away with the monotonous stiffness
of the chords, they permit us at the time to remain
longer with every single chord.
Thus,
by means of harmonic
figuration,
we might form from
one single chord a prelude,
m^^=^^^ 563.
8va.
which, in
its
mobility and variati<3n of form, remunerates us most
amply for its lack of harmonic variety. It would be already a progress if we employed the for the after tial
dominant chord, and closed\ with the tonic
figuration
triad, or
any one 'figurated chord we intrlpduoed the harmonies
to the designation of a key, as
we have done
here
:
if,
essen-
404
S64.
^~—^ •
Legglero.
m
This, too, should
be
practised, first
on paper, and then
at the
pianoforte.
We by
can obtain a richer formation, and one of a higher order,
selecting an harmonic succession, in the
preludes, and afterwards carrying
it
manner of our
first
out according to a fixed
figural design.
The following phrase
u
565.
ffi i p=f=r=rT^^^i^ SfciiEg
may
^m
serve as an illustration of such foundation.
monic
figuration
^ A.
simple har-
405
566.
^pi^^^ls^^l m
^^=f=g=ta^^^ ^
S
^^E^
gives
^%%i
f
ei
it
already mobility and variety, and
steady progression, to obtain from formations, particularly after tones, change of design,
We
requires merely a
and
series
(triplets
we have
fied or divided,
:
new
and rhythmical form.
;
;
a single
and in c we have employed
and eighth-notes.)
In continuing this, how-
seen in a,) our designs would have to be modi-
because the foundation assumes a more rapid
progression after the third measure.
necessary
of
introduced passes, help-
have made but sparing use of these means
two designs
thus
it
series
we have
help-tone has been introduced in b
ever, as
it
we might omit
In
c,
too, this
would be
the second design, and form the
first
406
567.
^m ff
3e#
W^
Thus much of it,
the student
exercise
his
this
may
p^
by no means
diflficult
exercise.
Guided by
venture beyond the limits of the phrase, and
invention in free harmonic formations, either on
paper, or improvising on the pianoforte.
APPENDIX AND NOTES TO
MAEX'S THEORY
MUSICAL COMPOSITION.
BY
E.
GIRAC,
OF THE OONSEETATOET OP PARIS
NEW yOEK: PUBLISHED BY MASON BROTHERS. 23 PARK ROW.
Entered, according to Act of Congress, in the year 1854,
by
MASON BROTHERS, In tbe Clerk's Office of the District Court for the Southern District
of
New
York.
INTEODUCTION. My
object in writing the following Appendixes has been to con-
dense and abridge matters which, in the author, are too prolix, and
mingled with secondary considerations of the subject, which times obscure the practical rules.
ought
be unfolded with as
to
be clear and comprehensive
often-
In instruction books, precepts
much
brevity as possible
definitions
;
the developments strictly cionfined to
;
points immediately connected with the rules or definitions.
will,
no doubt, be
and arguments
satisfied
It is
The
quite a different thing to write for learners, or learned.
latter
with philosophical views, with reasonings
one
skillfully linked
to
another
;
they will follow,
with interest, thoughts developed with a wonderful abundance of expressions,
and sometimes with
brilliant figures of speech.
does very well with readers conversant with the subject.
former
will, after all, derive
but
little
This
But the ,
from those evidences
benefit
of learning, from that fecundity of thought and richness of expres-
man laying down a code you have to practise, that you have to avoid.' He must still do better, he must show the pupil how to observe this, and how to avoid that, by numerous examples So used to do Cherubini, perhaps the subjoined to every precept. sion paraded
by the
writer.
of precepts must say
greatest theorist
man who was early German and the
The
practical
to the pupil,
who ever existed
:
'
this
so did Reicha, the most practical
ever seated on the professor's pulpit. theorists,
So did the
such as Fuchs, Marpurg, Albrechtberger,
Italian padre, Martini,
and many
be too long to give here the names.
others, of
Nothing
is
whom
more
it
would
apt to give an
idea of the soundness of judgment of Beethoven, than the concise-
ness with which he has developed the rules of Counterpoint and
Fugue
in his musical studies.
The
paucity of precepts contrasts
wonderfully with the number of examples.
was influenced by These few been written.
lines serve to I
In
this,
we
think he
his master, Albrechtberger.
show
in
what
spirit the
Appendixes have
have given compressed and short
rules, but sup-
IV
ported and illustrated by numerous exercises, intended both to put the rules in practice,
and
to
serve the student as models of
work
for
himself.
Though
these Appendixes have been composed to be explanatory
commentaries
to the large treatise
of Marx, yet they form a
vi^hole
and from the treatment of the triad down to the passing-notes, where they break off, they form a compendium of the matters contained in them, in which nothing necessary to the instrucin themselves,
tion of the pupil has
been omitted.
They have
another advantage
they offer the teacher of harmony a text-book in which the funda-
mental laws of harmony have been laid down, so that he will have no other task his pupil,
to
perform than to direct and superintend the work of
being thus relieved from giving, himself) but very few
directions.
But how must these Appendixes be used ? In the following manner.
The
student will
first
read attentively, and endeavor to understand
thoroughly the work of xMarx, from page 94
to 113.
put aside the author, and begin the Appendixes
Next, he should
down
to the
When reaching this part of my work,
on the pedal-point.
chapter
he will take
the text of Marx, where the fundamental principles of the pedal are
At the page 219, of the
given (page 215).
author, he
must
resort
again to the Appendixes (page 128), in which the manner of framing
a pedal apd some other developments are given. At this part of his work he will have to finish the Appendixes. I have confined my work to the suspensions, but they are fully developed, and more completely shown in the work of Marx. If the student be aptly possessed of the matters treated in the Appendixes, he will be able to understand and practise the chapter
on passing-notes, and the following of our author.
When reading through the Appendixes for the first time, the pupil will have
to neglect those that are
App. H, App.
I,
mere observations on
and App. K.
When
the text, such as
the Appendixes-v have been
once read through, and studied carefully, the pupil will take the text a second time,
and then read the Appendixes in connection
with the text in the order in which they are referred to by numbers inserted in the book of our author.
addressed to students
These
directions are particularly
left to self-instruction,
or amateurs living in the
country, deprived of any assistance from professional men. pupils enjoying oral teaching, they will use both the text
Appendixes, as directed by their teacher.
As and
to
my
A
few words now on the exercises, especially
students
for the benefit of
left to self-instruction.
After reading the rules and explanations, the pupil should copy the base of the exercises
coming
after
without looking at the upper parts.
This being done, he will
the figuring of the base.
mony
according
to
every rule or explanation,
Particular care must be given fill
up the
to
har-
the figures written carefully under the base.
Before commencing
to
up the harmony, he ought
fill
to read over
and over again the rules on the three musical motions, and watch his
work with utmost
hidden or real.
care, in order to avoid fifths and octaves either
After
it,
he will compare his work with the upper
parts written above the base in the Appendixes.
If he discover
faulty successions, or mistakes in contradiction to the figuring, he
should recommence his task,
he finds no triads,
fault with his
which
I
until,
by comparing
own arrangement.
it
with the exercises,
When
studying the
consider the most difficult labor of the pupil, particu-
lar attention ought to be paid to the connection of chords
most of
;
When
the faulty successions arise from breaking this connection. the student has succeeded in writing his
succeed in
this, it is
work
correctly, (and to
not necessary to arrange the parts just as they
are in the Appendixes,) then he must create a base for himself, and fill
up the harmony.
to the preparation,
In the discords, particular care
when
required
;
These exercises are carefully
is to
be given
next, to the resolution.
figured.
The
figuring
that
is
adopted in the Conservatory, and, generally, by the French school, of which
it is
necessary
to
give the pupil a proper notion and view.
The triad is figured thus, s. The diminished triad, thus, -9-. The augmented triad, thus, fs or
When
^s.
the third of a chord or triad is suddenly altered
cidental, this accidental is placed above the figure
or
|,
showing that the third
The dominant
triad
is
is
affected
The The the
|,
ac-
or
|,
it.
in the
This applies only
doininant seventh, whatever
may
minor key, thus, minor keys.
jf
or
i),
to
be the mode,
is
figured, %.
seventh, arising from the suppression of the fundamental in
dominant seventh,
The
by an
thus,
sometimes designated by the signature
which constitutes the leading note according to the key.
by
s,
is
figured thus,
diminished seventh
is
-?..
figured thus,
-8-.
All the other sevenths, major or minor,
t.
The major dominant ninth, §. The minor dominant ninth,"! "'' ''?• The third is seldom figured, except when
the dominant seventh
resolves incompletely on the third of the tonic.
The perfect fourth is figured «. The augmented, extended, or sharp fourth, +4. The diminished fourth, -t-. The sixth, both major and minor, eBut when the sixth is suddenly altered by signatures ing to the principal key, the accidental or signature the figure, thus,
ijs
The diminished The augmented
or
sixth,
-a-.
sixth is figured
by prefixing the accidental which jje
or
second, both major and minor,
is
figured thus, +2.
The augmented or extended second,
to
!)6.
a.
second, arising from the third inversion of the dominant
seventh, in both modes,
I
prefixed to
be.
affects the sixth to the figure, thus,
The The
not belong-
is
thus, da or
flz.
give this figuring as the one used in a great school, and applied
these Appendixes
;
though,
I
confess, there is
much
that is arbi-
any other method of figurBut the ing which may convey an exact notion of the harmony. trary in this, and I do not disapprove of
who
pupil
exercises, it.
may
I
studies alone, being necessitated to submit it
was incumbent upon me
have now given
all
certain,
if the
to.
that of the
make him acquainted
written, and, I
all
the advantages contemplated
have no doubt, these advantages are
student be a careful
observer of
all
the given
directions.
EM. GIRAC. New-York,
My,
1854.
with
the directions necessary, that the student
derive from these Appendixes
when they were
to
APPENDIX
A.
TREATMENT OF THE TRIADS. The The preparation
much
Triads, to be treated properly, require
of the dissonant chords
and each of their constitutive tones
is
is
skill
and
art.
not a difficult matter,
called to
its
proper place by
the laws of their resolution.
Here the pupil nection which
he must look
mean
exist
—a connection which
between the chords
and the discovery of which depends entirely upon
Besides, there
his care.
every
for,
alone, having no other guide than the con-
is left
may
step,
is
a difficulty which he meets with at
and which must be carefully guarded against
;
we
the faulty successions of real or covered fifths or octaves.
On
pages 101 and 102,
we
have, by our author, been
acquainted with octave and fifth-successions
covered
fifths
again.
Our
We
refer the pupil to
also learned,
on page 100, that the connection of
chords consists in the mutual tones of the chords. Connection cf chords
But
is
is the
In other words.
mutuality of their tones.
there some method to follow in order to obtain this con-
nection without mistake tion of the
?
certainly there
is
;
it
consists in the
mo-
fundamental tone in the base.
The fundamental
tone of a chord
fourth, ffth, or sixth ;
or sixth.
them
care, at present, will be to avoid these obnoxious suc-
We
cessions.
and covered octaves.
made
on page 129, with
;
These
it
may
may
descend a second,
ascend a second,
different motions of the
third,
third, fourth, fifth,
fundamental tone of the
chords are called by theorists, Progressions of the fwndamentod.
They
have, also, admitted two sorts of Progressions
:
the Regular,
and the Irregular.
The
Progression by a third, fourth, a.nd fifth below, and
sion of a sixth, fifth, and yburt/t above, is called the sion.
its
inver-
Regular Progres-
The
Progression of a second below and a second above, and the
corresponding seventh,
The descending
The
is
called Irregular Progression.
progression by a third, gives two mutual tones.
Progression, a fourth down, affords us one mutual tone.
i^ The
Progression by a Jifth gives one mutual tone.
i The same number these progressions sixth, ffth,
As
;
of common tones
that
is,
is
found in the inversion of
in the progressions of the fundamental
and fourth above ; and they are equally good. motion a third above, it cannot be used but under
to the
more than one progression of Such succession by thirds above as this,
certain conditions, and no
admissible.
i is
not very desirable.
is
received,
is this
:
kind
is
&c.
The
condition under which this progression
the fundamental, after skipping a third above,
must be brought downward
may
this
a. fifth,
and the third of the second
be made the leading tone of the third
triad
triad, as,
i Hence,
more
it
would appear
that this progression
by a
third above, is
when leading from a major to a minor triad, which made the dominant of a transient minor key by the
satisfactory
at its turn, is
elevation of
its third.
All the regular progressions afford us some
common
tones.
But
the progression, a third and a fifth below, contains the fifth of the following chord. In such progression, we say that the fifth is
5 •prepared ; and
whenever
we ought
this preparation occurs,
to avail
Hence we will make it a rule, that all the tones which a chord lias in common with the following chord, must be pro. ourselves of
longed into
it.
as,
it,
^~
-^ In our following exercises the chords
by
Previous
to
this sign
we
i mutual tones of
will designate the
-—^ or ^—^ placed over or below them.
our explanations of the irregular progression,
we
feel
obliged to give a full account of the three harmonic motions, which
have only been hinted Theorists
at on pages 90 and 91. acknowledge three kinds of motions
in
harmony
:
the
Direct or Parallel, Oilique, and Contrary.
The Direct or Parallel motion takes place when two or more parts (never
more th^n three) ascend or descend simultaneously,
as,
^^=^b^^^
r-r-r-f-
The
Oblique motion takes place
when one
or more parts or voices
keep on the same tone, whilst one or more ascend or descend.
X
i The
when one
Contrary motion takes place
voices lead in -opposite direction to one or
the
more
or
more
voices,
at
same time
The
first
of these motions
compositions, but
The second
is
when used
is
especially admissable in two part
alone,
affords but
it
far richer than the first
;
few resources.
the contrary motion
most serviceable, on account of the variety of combinations it
parts or
moving
gives
rise.
The power and beauty
of harmony
lie in
to
is
the
which
the proper
6
employment of these motions Combined together ; and
arid skilful
from their motion, the theorists have fixed the following rules
Two
1st.
:
and two octaves, prohibited in the direct motion,
fifths
are allowed in the contrary one.
No more
2d.
when they
Four
3d.
than three parts can move in direct motion
;
and
motion,
fall
thus move, they are liable to give fifths or octaves. parts
moving simultaneously
in parallel
inevitably into faulty successions of fifths or octaves, and most of the time into both of them.
Let us now come have is
not,
to the Irregular progression.
Here the chords
have any common tone, and
consequently there
and cannot
For the
no connection between them.
tones, in
such a progression,
we
distribution of the chord-
are under the necessity of
making
use of the contrary motion in order to avoid the parallel succession
As an example
of fifths or octaves. the two triads/, a,
and g,
c,
b, d,
of that progression,
which
let
us take
in the staff will give us the
following combination of notes
i It suffices to
look at these chords to perceive that no
common
On
between them, and therefore no connection.
exists
tone
the other
hand, if we consider the tones of the chord f, a, c, we discover that to meet the nearest tone of the chord g, h, d,
each of them goes up that
is,
three parts
move up
in direct motion.
Let us see
if,
accord-
ing to the second rule of the motions, there be not here some of the errors mentioned in to d,
In
it.
effect, the treble part
while the base part moves from
fifths in fifths,
parallel motion.
It
is
/
to g,
progresses from c
and thus gives us two
not in our power to avoid these
since the tones are essential to both chords
;
but
we can
avoid
having them progress in parallel motion, by giving the chord-tones of the chord/,
a, c,
another construction, as in the following
i All
now
is right.
We
have obtained the
causing the third of the chord
fundamental tone, /, goes up
/ a,
to g.
c,
to
Jifth
descend
o{ g,
b,
d,
by
to d, whilst the
But as we have adopted the
four part writing in our exercises,
chords in this
way
we
shall construct again
our
:
^
=A=
i
which
is
It is
equally satisfactory.
worth the while
to advise the pupil that, to
avoid faulty suc-
many instances, it does? not suffice to take the contrary much however depends upon the position of the chord-
cessions, in
motion;
Here, for example,
tones. c,
if instead
in the outer regions of the
of placing the third of _/",
harmony, we had placed
^m
tal,
c, is
to the tenor,
and the doubled fundamen-
Both follow a descending motion, and progress
to the treble.
simultaneously in d)
given
fifths,
the one covered
and yet we lead the parts in opposite
;
a,
in the
Thus here
middle ones, another error awaited us.
the third off, a,
it
(a,
the other real {g,
e),
directions.
This we have
avoided above, (at A,) by inverting the intervals.
We
deem
pupil every
much
it
way
proper to enter upon these particulars to show the
how
of keeping from faulty successions, and with
care he must guard against them.
Finally,
we
cannot close our illustrations upon the subject of con-
nection, without laying
down a
last observation,
which
to destroy, by an awkward arrangement of the chord Here, nection which exists between the chords.
i
is
this
:
not
tones, the con-
=i=
an improper use of the contrary motion, has not only destroyed the connection of the chords, but has led us into the very fault of covered fifths and octaves, which we intended to avoid. As both chords
have the tone
c in
common,
would have prompted us /, a,
c,
the proper arrangement of the voices
to tie
thus
i
them, by continuing c in the chord
The
connection being thus observed,
move
all
the other tones,
easily to the nearest intervals of the following chord,
observation
is
of the greatest
moment
in filling
C;
e,
g,
This
up the harmony,
Exercises on the Regulak Progressions.
No.
1.
^ ^ is
No.
2.
55&6&55 5^5 r
-si-
5
In these examples
A
we meet
fifth
with a kind of
of the student.
call the attention
hidden
I
Ty
ite:
which
#:
32:
fifths
They
and octaves,
are called hidden.
or octave is that which takes place between two parts,
one of which proceeds upwards or downwards, one or more degrees, By filling up the skips, while the other skips to the same intervals. the hidden interval appears real to the eye, as.
Real
5th.
Hidden Bra.
Real Sva.
In Nos. 1 and 2 there are several instances of hidden fifths and There are instances of hidden octaves in No. 1, from octaves.
measures 4 5
to 6,
upper
8
5
to 5,
to 9,
parts.
to 6, Y to 8,
and 9
to
10
;
to 10 ; in No. 2, from 2 to 3, between the base and one of the
and 9
in both
Instances of hidden fifths are found from 1 to 2,
between the tenor and treble ; from 6
to 7,
and 7
to 8,
between the
base and one of the upper parts, in No. 2.
But all these successions are permitted whenever the upper part moves to the fifth or octave by a single step, and the lower part skips to the same intervals, as in
Nos.
1
and
2.
second measure of No.
We direct the attention of the pupil to the 2, in
which the connection
is
occasionally
broken in order
to raise the
harmony.
In the present instance, the
raised parts lead in opposite direction to the
and
base
they move
;
their progression is natural according to the rules
on page 130. These conditions ought to be attended to whenever we break the connection of the chords for the sake of raising or depresseasily,
ing the pitch of the voices.
The
irregular progression
regular one
and
;
not so satisfactory to the ear as the
is
that reason,
for
two or three chords, except in the writing. to
We
would say,
be more suited for
it
tain degrees of both
Thus, in the major
and from
cannot
ascending movement seems
which
scales in
from one
scale,
be
it
to two,
There are
also cer-
seems more admissible. from four
to five ;
from
In the minor mode, irom four to five,
six.
and
five to six,
scale
inversion and in three-part-
too, that the
than the descending.
two to three, from five to latter
cannot be carried on beyond
it
first
The
vice versa.
used
in
irregular
The
breaking into the major mode.
other degrees of the progressions
without
following exercises will serve
as illustrations of the foregoing remarks
Major Scale.
No.
^^^ f=r^
3.
j-^--
-^-j-
T=T
E^^l^^
-•— ^e-
jhJTl
rf
-J,-
T
p
ii§f 5
5
5
5
5
5
5
5-5
Minor Scale.
F^Tf ffT 1^ jipgs 555^5
-^
-§Z':3ZL
h
h
55"? 5
5
Ef
10 In both exercises, the irregular progressions produce consecutive fifths
by contrary motion, and, in both scales, go through the aboveAs the minor scales afford but few indigenous
mentioned degrees. chords,
and
it is
always advisable,
here, at the star (*),
of
in their treatment, to get
then, into the triads of the
where the minor
now
them,
So we have done
major mode.
tonic joins the
dominant triad
c.
SEQUEBTCES,
We
call
by
OE PASSAGES OF TRIADS.
term certain motions of the fundamental
this
stepping according to an " adopted model." a certain
number of
tones,
lone,
This model consists of
which regulate the
steps of all the fol-
lowing, as
i Here latter
the
first
tone goes
goes up a fourth
&c.
down
five steps to the second,
to the third,
and so on
to the end.
and the
These
sequences depend entirely on the will or fancy of the composer.
They may occur
in
any
strain of a piece of
music or exercise
;
the
beginning,- middle, end, are equally suited for them.
The one most
commonly found
theorists
is
the above mentioned, which
some
have
styled Seventh-progression, as being thatof the chords of the seventh.
No.
I
5.
i^JJu J
^ ^
'
I
^
gfe * ,-~T"^
rc»
r
^s
^
»
^
d=t
^
^=i
11
=c
j-d_j-.i
--9--»
i
<9-
&Eidg
*
f
-^
^!t"i£:rf: g/ "
—^ F ff T^-
^
=^=^
There are which
is
in
No. 5 three instances of sequences, the model of At a, b, c, too, the by this dotted curve • ' ' *
indicated
harmony is made
to
•
ascend
to
a higher pitch, in order
give the parts
to
a regular position in the uniform steps of the progressions. diminished triad
stars, the
(this is
is
led out of
its
usual
way
always the case in these sequences or passages,
diminished
common
triad, losing its
triads,
damentals
;)
and forced
and
character,
is
in
the ;
which the
assimilated to
into the current of the
the
surrounding fun-
this treatment is quite satifactory.
One example more, and we
No.
own
At
of resolution
shall
have done with the progressions.
Mince Scale.
6.
^
^m^^f^r^ §1
isssi
P
i: m± w p i fTTr ^rr^F
iscziS::
^^p
12
i i^#f^p^
^^==F
= -"g
gj
fg
I=-
Eitas!
i
=Pt
P
*
f f
r
**
»i
^:^
m
In the minor scale the sequences are treated in the same manner as in the
note
is
major
;
with this one but material difference, the leading
disregarded and restored to the major mode.
A, where the measure.
^ reappears
after
it
must be
having been depressed
at
at the sixth
So, at B, the dominant triad is introduced again, after
having been made the
fifth
of the chord
fundamental of the chord g, to
But
can be seen in No. 6 above,
reinstated at the first opportunity, as
I, d, at
e,
g,
h, at
the star;
the two stars.
and the
We come now
the 1.
A
chord
is
Inversion of the Triads.
inverted whenever
any other tone but the funda-
mental
is
in the base
mental
is
placed in the upper parts, and the tone given to the base
is
;
i.
e.
in the inversion
the lowest tone of the chord, but not
of chords the funda-
fundamental, as such a
its
denomination belongs only to that tone which was the lowest in the original construction of the chord
There are
as
many
by
thirds.
inversions as there are tones in the chord,
not counting the fundamental.
According
to this principle, there
are but two inversions in the triads.
The chord
first
is
inversion takes place,
in the base
chord of the
sixth,
;
it
when
the third of the primitive
consists of a third
and figured
In the second inversion, the
and sixth
;
it is
called
e. fifth
of the chord
is
in the base
;
it
13 consists of
a perfect fourth and sixth ;
it
called the chord of the
is
fourth and sixth, and figured I.
First Inversion.
2.
When explaining the irregular progression, we stated (Appendix, page 9) that it cannot be carried beyond two or three chords, at most. Thus, a progression like this :
i ^^ though the
fi,fths
follow the contrary motion, is neither clear nor
satisfactory to the ear
when
tionable,
;
but the same progression becomes unexcep-
the chords are put in the
inversion, as
first
i ^^^ This progression might have been longer and equally good, as in this
example
:
—§--
i The
contrary motion
But
faulty interval.
we must
is
if
even unnecessary, since there
we
desired to have
is
not
more than three
any
parts,
use either the contrary motion, or double one of the upper
parts, thus
:
—isor
i When
used in three-part-writing, the succession of sixths
ject to another condition.
damental tone sixth then
may
is
given
—
is
sub-
^The third being in the base, the fun-
to the
upper
or
The chord
parts.
occur with these two features
:
of the
14 In the
it
changed
case, the primitive fifth is
first
the second,
remains unchanged.
sion of sixths
we
should take the
second, so as not to
fall into
into a fourth
construction,
first
;
in
a succes-
evident, that in
It is
and avoid the
faulty successions of fifths in the upper
parts, vifhich are not less objectionable there
than in
Therefore, such a passage should be written thus
the
base.
:
» ^
^^
I
All
%
1
not in this manner.
these cautions are
required
passages of a certain length require so
much
;
when
when
which the
used in
is it
does not fiflih
is
Thus, in the following:
1
i
which undergoes no other change than
fifth,
a .higher position,
sixth
care, and the position of the primitive
almost indifferent.
in
the
standing alone,
is
that of
as good as this
i which the said
in
interval is
changed
a fourth,
into
The chord
of the sixth needs no further remarks.
Second Inversion.
3.
The second preceding, be
inversion of
made
to
the triads (| chord) can not, as the
form any succession whatever.
So, if
we
are permitted to use such succession as this
i ^^ we
are forbidden to use the
sion.
same chords
in their second
Thus even two consecutives
^
inver-
15 are not admitted, though hidden by the outer parts.
There
is
a
single instance, in
which two consecutive pure or perfect fourths
are allowed
when
it
;
is,
by
the second
perfect fourth is immediately followed
by a sharp
the
fourth
first
is
followed
inversion of the diminished triad.
i the third inversion of the dominant seventh.
or
by
in
which cases the
fourth.
The
six-four chord, even standing alone, cannot be used
except upon certain conditions, viz: Preparation and Resolution; because, although the perfect fourth
yet
it is
considered, and really
denied that this interval Preparation, here, lie
is
is
is,
the inversion of a concord,
is
a sort of discord, and
somewhat
it
cannot be
unsatisfactory.
done as in the discords, by making a tone
over from the preceding chord ; and the sustaining tone becomes
the fourth.
This preparation
may
be effected either by the upper
parts,
^Ei
;
or
by the base
At A, the sustaining a of
itself,
the chord /,
-a, c,
and
g
at
B, the tone
e,
form the preparation of the fourth.
As
to the Resolution of the fourth,
sevenths, in which the resolving chord fifth
it
differs
is,
from that of the
with few exceptions, a
below the fundamental of the seventh. It is not the same with whose resolution is done in the following way if
the perfect fourth,
:
the base resolve the fourth, fourth continues on the
same
it
ascends or descends a step, and the
tone, as
i If the resolution be effected in the the upper parts, the base, fol-
16 lowing a contrary course, keeps on the same tone, and the fourth * resolves by ascending or descending a step
1
i
resolution then, as well as the preparation, can be
The either
by the upper
parts, or
by the
made
base.
necessary only for the perfect fourth ; the sharp from the second inversion of the diminished triad, has no need of preparation; we may strike these chords immePreparation
is
fourth, resulting
diately, thus
i
1
i
^
In the cadences and half-cadences the perfect fourth requires no preparation, as will be seen and exemplified in our further explanations.
'
Finally,
we make an
important observation
:
when
through several chord-tones of the same chord, the
bound
to the
foregoing rules
;
the base runs
\
chord,
is
not
then the following cannot be ob-
jected to
i because in the
a
its
progression the base meets always with, and stops on
same harmony.
new
rf¥ But
if,
after the fourth, the base entered
chord, the preceding example should close thus
upon
:
IS/S-
i f^L^fie
or differently, according to the ending harmony, and conformably to the preceding rules of resolution.
17
A parts,
Notice to the Sttident.— In the construction of the upper we advise him to look carefully at the consecutive fifths or
octaves, either real or covered, vi'hich are most obvious in the inversions, and, in
We now No.
many
come
7.
trf
instances, very difficult to be
guarded against.
the exercises on inversions of the triads.
Unin verted Triads.
1.
^
a
s-
iiS=
*
i F^fT^ »=3— No.
8.
1
^
2.
First Inversion.
^S
^ ife
;^
T= T~"r
^^ r
18
No.
Second Inversion.
3.
9.
J_J=F,
(^
a
i
o :?2iz:rp
!
I
^^
ilr^
J
i ^
I
"-T=f^^Tf gr: -fg
No. 10.
fi.
^
o
.»-
H°
d
P-
i
m^
^ !
5
f
-f^:^
iS~~r7s
:
i
r^
11.
-rr-
^^
6
i^^m
-i.i
^§^
l
6
J
1^
^-
&
©e
i!^ ^=t
No.
jg -
J
I
^f=
*^
i ^^
-
Inversions used promiscuously.
4.
-i-J1
^
id.
fe
t-^
E^
19
-A
I
^
^^a
4
4
f-
?
r
^ We 1st,
have written the above exercises on the same harmony
unin verted chords
4thly,
We
by using both did so, to
;
2dly,
first
inversion
3dly, second inversion;
;
inversions promiscuously.
make
the student understand the different features
harmony can be endowed, and induce him to difference of construction of the upper parts made ne-
with which the same
compare the cessary by each
position of the chords.
advantages from
this
different constructions,
comparison.
we would
derive
many
comparing
these
He may
After
so
induce him
to write
over again
several times these exercises as they are, and then transpose into
different keys,
both with
sharps and
flats.
When
done, he should himself compose other exercises in the i.
e.
by varying the same harmony.
prove
much by
the difficult
We
same way,
warrant that he will im-
so doing, and will be enabled to
work of part-building.
them
all this is
manage dexterously
APPENDIX
B.
The Dominant Seventh, and Dissonant Chords The dominant
in general.
seventh has presented itself to us on page 102,
No. 94, as arising from the sustaining subdominant
tone,
to
which
the dominant has been given to serve as the basis and fundamental
These two tones
tone.
striking together have given rise to an in-
which we are unacquainted, an interval termed discord or dissonance ; and this dissonance, in the present case, is a terval, with
seventh.
Theorists acknowledge two sorts of dissonances improper.
The proper
the seventh, and ninth.
The
improper are
mented
fourth, the diminished
mented
sixth.
five,
and augmented
is
The
the perfect and augfifths,
and the aug-
interval,
the inversion of the other; but, in practice, they are
we
looked upon as different intervals, and so
them.
the proper, and
form but one
Strictly speaking, the seventh and second
since the one
:
dissonances are three in number, the second,
ninth differs from them in this
These dissonances do not form a chord
:
ourselves will consider it
cannot be inverted.
alone, but need the adjunc-
tion of two intermediate tones to the seventh,
and of three
to
the
ninth, as will be perceived
from the explanations which will be given
of the dominant chord and
its
The consonant chord ear,
near-related nona-chord.
or consonance,
is
in itself satisfactory to the
and therefore can be used without preparation.
nance, on the contrary, reason
it
is not satisfactory to the ear;
The and
can be used only under certain conditions, viz
:
disso-
for that
the Pre-
paration and Resolution.
The improper
dissonances,
with the exception of the perfect
fourth, do not require preparation, but only resolution.
The dominant style of to
music ;
be prepa^red,
seventh does not require preparation in the free yet, as there are
it
is
many
incumbent on us
instances in which
to
it
ought
say what preparation
is
81 moreover, besides the dominant seventh, there are several other sev-
law that admits of no exception..
enths, the preparation forvifhich is a
Preparation
which belongs
is
the introduction of a tone into a preceding chord,
to the
succeeding one.
,
This preparatory tone can be either equal in length to
which
serves as a preparation, or longer
it
They of the it is
the seventh
;
chord djf,
prolonged.
B,
at
7
i^
,p
I
which
to the discord
but never shorter.
^fesEE^^^I
i to
;
it is
a, is
I
r
p
the preparatory tone ofg,
At A,
the preparatory tone
C
longer ; at
shorter,
and
this
i,
d,f, in-
equal to
is
causes the
preparation to be objectionable?
The law
of resolution belongs to
dominant triad
ig
subject to
all
it; this
sevenths in general, and the
resolution is five degrees below
the fundamental, or four degrees above.
Inversions of the Dominant Sbventh.
When
a fundamental tone leaves
chord must become the lowest ; but
and not the fundamental
By
tone.
designate only that tone which, in thirds, it
was
the lowest.
its
place, another tone of the
becomes only the lowest tone, the term fundamental tone, we
it
the original
construction
This remains the fundamental
tone,
by
whether
be above, below, or in the middle.
There are
as
many
inversions as there are tones in the chord (be-
sides the fundamental tone)
;
consequently, every seventh has three
inversions.
The dominant sists
seventh, in
of a major third, perfect
its
original construction
fifth,
and afninor seventh.
with this (x) sign below, to distinguish other sevenths, which
is
7 simply.
it
by
thirds, con-
It is
figured
\,
from the figuring of the
22 In the dominant seventh, the fundamental tone tant
;
next to
it,
in importance, is the seventh.
name
position of these tones gives the
Thus, the
first
fifth,
the most impor-
Consequently, the
to the inversions
of the chord.
inversion with the original third in the base,
and sixth. and minor sixth.
the chord of the fifth
minished
is
It consists It is
is
called
of a minor third,
di-
figured |
^^ f In this inversion the
fifth is
in the dominant seventh, being
As
This
diminished.
fifth
occurs only
alvi^ays perfect in the other sevenths.
{he third of the dominant chord (now in the base) invariably
moves upward
to
the tonic,
cannot be doubled in the upper parts,
it
without causing faulty successions of octaves.
The second
inversion (the
fect fourth,
and major
being in the base)
fifth
chord of the third and fourth. sixth.
is
It is
composed of a minor
It is
figured | or |.
i
called the third, per-
^=
Some theorists advise to prepare the fourth in this inversion, and when It cannot be prepared to suppress it. Nevertheless, in practice it occurs very often without preparation. In our exercises, we shall have it prepared, and we counsel the student to do so, in his own, especially when the opportunity presents itself. In the third inversion, in which the seventh
count the intervals from the
latter,
and
call
it
is
in the base,
we
the chord of the se-
composed of a major second, an augmented fourth or
cond.
It is
tritone,
and a major
sixth.
It is
figured
2.
^^m This augmented fourth
is
again the characteristic of the third
inversion of the dominant seventh
other sevenths this fourth
is
;
perfect.
in the third inversion of all the
We
must likewise avoid dou-
23 bling the base in
any of the upper
descend one step in
parts
;
as the second has to
for,
resolution, if doubled,
its
it
would have
to
do
same in the upper parts, and then a faulty succession of octaves would be unavoidable. The names of these inversions are not influenced by any change
the
Both of the
of position in the upper parts.
two chords of the
first
following are called chords of the sixth, and the others are called
chords of the third and fourth.
^m, This addition no new
to
-^
Jm
a
=1
M
pi
our chords, though of great advantage, gives us for all inverted chords
difiiculty,
same
follow the
.we said of the dominant seventh, that
its
third ascends one step, that
seventh descends a half step only, and that
its
ascends one step, the same rules
rules,
Thus, when
which govern the original and fundamental chords. its fifth
descends or
hold good in the different
still
in-
versions.
A
natural consequence of the regular resolution of the dominant
chord fifth.
is that
the chord of the tonic remains incomplete
Theorists have provided for
it.
When
verted, they advise us to double the fundamental
base goes
its
usual
way
(a fifth
down
fifth.
But then there are
only four parts are required,
many
In
instances,
it is
«f the fundamental. the
fifth
is
is
not in-
or a fourth up), the other, in
five parts
allowed
in the to
of which harmony ;
suppress the
unnecessary to have recourse
We
a motion down
it
lacks the
it
so that, while the
;
the upper parts, stretches over to the resolution chord,
forms the
;
the chord
obtain a full resolution,
to the fifth of the tonic, as
to the
it
if
fifth.
doubling
by simply giving :
i In such an event,
we must
give the fundamental tone in the base
a motion contrary to that of the
fifth.
If the fifth cannot be used reg-
24 ularly,
tone
we must
avail ourselves of the doubling of the fundamental
as for the inversions,
;
tion-dhord complete,
it is
always possible
by prolonging
to get the
resolu-
the fundamental tone
to the
chord of the tonic.
Exercise, in which the
of the dominant seventh
fifth
is left out,
and the fundamental doubled.
I
No. 12.
^
r
^
~
r
—[=?=§
1^
4-e
ife
ffl^a
i
^
r f=f=
^
2?I
E^ At
the beginning of the second measure, the fifth of the dominant
seventh' is dropped, to the next chord.
and the doubled fundamental tone stretches over
So
it is
Exercise, in which the or
upward
to
at the ninth fifth is
measure.
preserved, and
moves downward
complete the chord of the tonic.
^
No. 13.
A
~rf
^E 5
- 5-
5
-
^
At N, the fifth moves down to complete the tonic, at P, it moves upward ; in both cases the fundamental traie, in the base, takes the contrary motion.
25
No. 14.
J
J
Exercises on the Invbesions.
^
J
I
i^
1
.# T*!
-iSrI-
r-
f f-f
i^
i ^ No.
m
l_^^
I
^
SEE
-gg-
-S^_ffl.
1
:4=
15.
f
f
i:^ "T2
^-
i f^^ =t t
No.
i z^^
T i
^E
-f-
"
16.
Exercises in the Minor Scale.
j==^j-^—.i
f =t=^
^^
sP--=^
^
26
1
1
No.
w
I
Eg fp—"-« I
I
I
17.
S^ f^m^
^=-U=i
r-^
^E
# « -5-
5-
fc
e^
AM:
-^7^
J
^ At
the third
#•
measure of this exercise, there augmented.
i"
so,
when
the second is
augmented
for the succession of fifths.
should observe that the
mark
that at
A
first
;
Two
a, c,
is
prepared
rather than the
first
latter.
sudden transition from the chord of
g^,
e,
i,
change, from the dominant triad of the minor effect.
not
In the present instance, the student fourth
something more characteristic than the
produces a good
it is
the reverse likewise holds good,
the former is better, preparing a half-cadence,
tonic,
pure or perfect
harmony ; but
;
the 6th tone of the minor scale
mentai of the chord/,
f»
a succession of two
is
fourths, the one perfect, the other
fourths in connection are prohibited in good
trf
he must, is
made
also, re-
the funda-
inversion oi d,f, a;
and
is
possessed of
At B, into
mode
c,
there e,
gs^;
into the
is
a
this
major
APPENDIX Four fifths,
parts, progressing in parallel motion, give necessarily real i
this evident,
we have
base from the fundamental this passage, in this
only
to the
it
is
here, in
suppress the motion of the
fii-st
inversion of the chord, and
-d—^-
\=r^
^^^
No. 175.
to
way
Ii Now,
So
or octaves, and sometimes both.
To render form
C.
&0.
t
the consecutive
E£ fifths
^
^
between the base and the alto part, and and treble, are tangible. Is
the consecutive octavfe between the base this faulty progression avoided
fundamental
by the motion of the base from the
to the first inversion ?
By
no means.
The
funda-
mental tone being struck forcibly in the accented part of the measure, remains unshaken in our ear for the whole measure and the 2d inversion makes but little impression upon it. To get ;
such passage as given in No. 175 correctly written, every second '
note in every measure ought to be the fundamental of a
new
chord,
thus:
i instead of 5, 6, 5, 6,
because
it
&c.
contradicts the
But we cannot adopt such a meaning of the author, which
correction, is
a combi-
28 nation of the fundamental tone with that of the inversions. is
be done, then
to
We
?
What
must keep from such combinations as
give unsatisfactory results.
No. 176 ence
is
where the consecutives take
parts,
the
alto, for
The only
differ-
exist in the
upper
not less faulty than the foregoing.
now
that the errors above mentioned
is,
between the tenor and
placia
and between the same part and the
fifths,
treble, for
the octaves.
Again, No. 177 in
parts
moving
utives.
We
objectionable.
beginning of the second measure
number a succession of hidden
to correct it
have established as a
;
6),
but to succeed in
We
this.
three
to the fourth,
We
fifths.
that
into consec-
in parallel direction, are liable to fall
From the
see in this
is
musical motions (see appendix, page
the
rule,
we
will attempt
are obliged to give up the
three-part writing of our author, and to adopt the four-part writing, in order to
have a
full
hh^
_i_d_
I
harmony.
^E3^
-II-
^pe a
Likewise, in numbers 179 and
m
-^-
5
m-
° +
180, the construction of the
upper parts adopted by the author, has led him into the same
We
consecutives as in No. 177.
correct
No. 179
in the
same
way, but with a closer harmony, thus
4-^
i
s |E3^ W'^^^
3fctg^
^itry-firW^m 5
6
5
6
3 1
The pupil should bear in mind, and never forget, that in three and four-part writing, the hidden fifths and octaves are strictly and
29 absolutely prohibited.
But
in compositions in
which more than
four parts are used, hidden consecutives are allowed. for
such a
liberty,
it
would be almost impossible
Were
to write
it
not
any large
composition, in which grand choruses frequently unite with three or four solo singers, and orchestra. fifths
I
scarcely need to say, that real
and octaves, between the base and the upper
allowed.
parts, are
never
APPENDIX The Diminished Triad Our
author
triad in the
D.
in the
Minor Scale.
us nothing of the employment of the diminished
tells
We
minor mode.
deem
proper to supply this
it
defi-
ciency.
The
diminished triad
major scale, and
is
is
placed on the seventh
degree of the
considered as originating in the dominant chord,
and by Marx himself as an imperfect dominant chord, that dominant chord without chord it
is
altogether correct.
same
gives the
scale
it
position
its
is
result,
fundamental tone.
As
i. e.,
placed on the second degree.
into the tonic,
because
it
it.
From
In the major scale
it.
But
stands on the second degree, and therefore, to
go
to the tonic.
On
the minor
this difference it
of
resolves
stands on the leading tone of the mode, and
for this reason, calls the tonic after
it
the
originating in the dominant chord,
resolves to the tonic.
arises a different use of
is,
Such a view of this
The
in the
minor scale
it
nothing necessitates
qelebrated Reicha, professor of musical
composition in the Conservatory of Paris, without forbidding absolutely the resolution of the chord to the first tone of the minor scale,
very seldom permitted his pupils
to avail
themselves of it, except in
the case of the half-cadences, as will be seen on page 71
According
to the
principles of this great theorist,
forth the following rules
and 72.
we
will set
on the use of the diminished triad in the
minor mode.
A.
The diminished
Treatment of this Chord. triad consists of a
fifth.
i and
is
figured -5-.
minor third and diminished
31
The
diminished
triad,
being a dissonant chord, requires resolu-
This resolution
dominant
tion,
but not preparation.
The
motions of the fundamental tone are the following
i
At A,
the
to the
0T~0
^^Pitg
-?rrHg
of moving
is
fifth
f in
downward
m
the tenor part ascends a step to g^, instead
We
to e.
adopt such an arrangement, because
permits the fundamental in the alto part to
it
of the dominant, which
The It is
Its
first
inversion
figured thus
:
triad.
is
is
always
to
lie
over to the triad
be done, whenever
it
can be.
composed of a minor third and major
sixth.
^
+«.
combinations with the dominant triad are the following
i
B.
^
znsz
sT-o
BAD.
^
elrThe combination
at
B
is
unsatisfactory, and
must be avoided, on
account of the perfect fourth between the treble and base, which not,
TTic second inversion gives a sharp fourth and major sixth. is
is
and can not be prepared.
figured h4, or simply +4.
^
«=:
It
32 This fourth, on account of tion.
It is
used as follows a.
a
being augmented, needs no prepgira-
:
C. BAB.
*-
0T~0
S\'
its
^
33 Resolution on the Diminished Fifth on the Seventh Degree.
B
I
4-
2—
4=:
i^
-^j.^
iS*=«= 1^
Ete
f=^ First IifvKKSioN.
4 < =t==i=
i
1^
r f
J
^
i^ *^
p'rrgg Second Invbesion. 4-
5
i
^ J
Of
f=
same
part
because here
which sounds
be
it.
upper
prefer the
We have
downward
first
sight
of,
that
motion-, to the third of the tonic,
fifth
the
in
always given the dimin-
may
though in the diminished
be
made
to
parts, especially in the first inversion.
lost
(A), for this
immediate resolution, and
this fifth is a true seventh ;
major mode, the
triad of the in the
we
that the fifth meets with its
:
ished fifth (Ex. B.) a
not
*=
the two foregoing' resolutions,
reason the
.4
J
ascend a step
But
must
it
diminished triad of the seventh
degree in the major scale, is by itself a triad, which has an employment and a treatment of its own ; and its resolution is independent of that of the dominant seventh
:
a character which
does not belong to the diminished triad resulting from the suppression of the fundamental chord in the minor mode.
we deem diminished
,
it
better
triad
to
on the
lead
down a
step,
seventh degree of
the fifth
the
minor
Hence, of
the
scale,
'
34
when
combined
with
the
diminished
of
triad
the
second
degree.
B.
We
may
Some Exceptional Resolutions.
consider the above resolutions as the
of the diminished chord in the minor mode. for
common
We
treatment
must now look
some other accidental uses which have been adopted by good
writers, and which,
by the way, are common
to both
ourselves of the opportunity to lay them
avail
they have been omitted by our author,
when
modes.
down
We
here, as
giving the resolution
of this chord in the major scale 1st.
The diminished
triad is
sometimes followed by the chord of
the second degree, major scale, or fourth degree, minor, in instances like these
t
i
=^S^
35 3d. the
We
find again the first inversion of this chord followed
i This
by
inversion of the minor tonic.
first
is,
t
perhaps, the only instance in vi^hich the diminished triad
can be properly followed by the minor tonic chord.
At
least,
we
can say that the other combinations (the half cadences excepted) are very rare.
Finally, there
is
another employment of the diminished triad
very obvious in musical composition. sequences.
by any
We
mean
the passages, or
In such instances, the diminished triad can be followed
triad
whatever of the
scale.
Examples.
*^t:
T \i±-
TT
m i
^t
^=t — * -^
f
$.
:^=tt
-s==^
fE^
3E
T 1
Here each tone of the diminished triad is carried forcibly down, by the current of the harmony, and follows the motion of the parts, such as given by the model. These instances are enough to give a proper notion of the subject.^
APPENDIX
E.
THE KONAOHORD. The Nonachord, whether major nant seventh.
It is
which forms the
or minor, arises from the domi-
the dominant chord, with one superadded third,
These two chords, having the same fundasame resolution ; but although agree-
ninth.
mental, have, of course, the
ing in this point, there
is
between them one characteristic
In the dominant chord, each tone can, at
ence.
the lowest tone in the inversions
;
tlie
turn,
differ-
become
but in the nonachord, the tone
which forms the ninth can never be placed words,
its
in the base.
ninth is not susceptible cf being inverted.
This
damental law of harmony, which admits of no exception. since the ninth cannot b? inverted,
In other is
a fun-
Now,
follows that the nonachord
it
has only three inversions, the very same as the dominant seventh, but somewhat modified in their figuring, on account of the added ninth.
In the construction of the inversions, the fundamental and
ninth must always be
made
to
keep from each other, a distance of
nine degrees.
As name
the position of the fundamental tone and seventh gave the to the inversions of the
dominant seventh, so here, the position
of the fundamental tone, and those of the seventh and ninth, give their
name
to the inversions
A.
The major nonachord
of the nonachord.
Major Nonachord. consists of a
minor seventh, and major ninth.
It is
major
^gured
third, perfect fifth, |.
37
The minor
first
sixth,
inversion consists of a minor third, diminished
and minor seventh, figured
|,
but in
effect,
fifth,
*«*•
^ The second
inversion
fourth, perfect fifth,
.The fourth,
We
third
—
third, perfect
effect,
y.
now
sixth, figured +|-^effect, "^^
give this chord and
The
their respective resolutions.
dominant chord, needs not lution,
third, figured I
inversion gives a major second, major third, sharp
and major
shall
composed of a minor
is
and major
its
be prepared.
to
inversions, together with
ninth, like the seventh in the
The
ninth, in
its
reso-
descends a step.
No. 18.
^m
I
^%fe —e— -»
I*
J.
^^
i
s
§IE
We
have nothing
to
say of the resolutions of the chord tones of
would be merely repeating what has been We have only to state that the fifth said of the dominant seventh. in the nonachord, whether in theinversions or n6t, must always be the nonachord, since
it
38 led
up a
step, in
order to avoid the consecutive
which always descends a
step, thus
m
fifth
with the ninth,
:
and not
m
In this chord, both the seventh and ninth can be resolved at the
same time as above,
No. 18, or one
in
latter case, the ninth first
Example
inverted or not.
In the
after the other.
next, the seventh, whether the chord be
;
:
No. 19. .1
'J-.
P
In four-part writing, the nonachord drops one of
usually the
fifth,
thus
m But there
is
A
r
chord-tones,
i
r T
another form, more generally adopted,
chord of its overburdening tones.
of the fundamental,
its
:
4 s i
this
1
3«=
^^P=t
t
Z^r
J-,
L
^:::>s.
It
to
disencumber
consists in the suppression
as.
i -I-
In this case,
becomes a mere seventh, with a diminished
it
the figuring exhibits lution.
Here
it.
But
it
differs
fifth,
from a seventh, by the
as
reso-
the h is not a fundamental tone, but simply the third
of the nonachord, of which
up a half step
to c, the
it
follows the resolution, and then
moves
fundamental tone of the tonic chord, and
so forth, with the other tones,
which obtain the same resolution as
89 in the nonachord, since, like the latter,
by the chord of the
i We
must always be followed
it
tonic, thus
:^
^
-^z
sr
t
have purposely omitted to give here the third inversion, as it no satisfactory 'result, on account of the consecutive fourth,
affords as,
i Nevertheless, if ever used,
-ipg-
I
we would
induce the student
to
cause
the seventh to descend a step to the dominant, a process which
changes
this
chord into the dominant seventh, thus
i So much
for the
nonachord, like the major, has
consists of the
ninth
We
is
Let us now pass
same
to
The Minor Nonachord.
on the dominant of the minor It
5
major nonachord.
B.
The minor
-gyg-
scale.
Like
it. it
its
fundamental tone
resolves to the tonic.
intervals, with the only exception, that the
minor.
find here three inversions, as the ninth cannot be inverted.
The
first
sixth,
and diminished seventh.
is
composed of a minor Its
third,
figuring
diminished is "Z", -5-
but
fifth,
minor
its effect is
'V -55-
40
The second diminished
The fourth,
inversion consists of a minor third, perfect fourth,
fifth,
and major
sixth, figured '|"
—
effect, "*j^.
third inversion gives a major second,
and major
minor
third, sharpi
sixth, figured +|-^effect, nl".
In the following example are given the resolutions of the minor nonachord, and of to the
its
inversions.
The
ninth descends a half step
octave of the dominant.
No. 20.
I
^=g
^
Tsc^: ^
FS
'g
'
#Og -g -'
Tia
ife I
The remarks to
the minor.
'^that
As
it
have been made on the major nonachord apply would be superfluous to repeat thent, we refer
the pupil to the foregoing paragraph,
A, down
to the suppression
the fundamental tone of the major nonachord. characteristic diiferences,
which we
shall note
down
Here
lie
of
some
in the follow-
ing paragraph.
C.
The Diminished Seventh.
The major nonachord, when used without its fundamental, affords us a seventh, which partakes with it of the same resolution to the tonic. Nevertheless, when we look at this seventh, it presents itself to us, at first sight,
with such a character of vagueness, as to
41 leave us in doubt as to the key to which seventh,
h, d,
may
f, a,
the dominant triad of the parallel key,
can give us a clear notion of seventh.
of the key
e,
It is
it.
For instance, the Chord, gi, a, major or minor.
Thus, the
belongs.
it
be followed by the chord, h.
c,
e,
g, or
Its resolution
by
alone
g^, not so with the diminished
i,
d,f, reminds us at once
Again, the seventh,
The
inversion.
h, d, f, a, is not desirable in the third diminished seventh is as commonly employed in
the third inversion, as in the
and second.
first
peculiarities in the use of this inversion.
resolved directly to the tonic, as in the it
would give consecutive
perfect
first
some
and second inversions,
one extended
{/, b),
the
other
In order to keep from the second fourth
(e, a).
First,
fourths,
Biit there are
If the seventh were
we cause
the seventh to descend a half step to the domi-
nant seventh, thus
^ we
Second,
lead
back
it
i
7+
T
to the first inversion.
±^. re
Third,
it
can descend seven degrees,
6
to the leading tone, thus
^^^ 5
Again, the seventh, c,
e,
g.
The
Thus, after g,||
a minor.
b,
d, f, a, resolves
diminished b,
d,f,
we
seventh can
only to the major tonic, be
led
to
are at liberty to go either
either modes. to
a major, or
42
Now
that the diminished seventh is well defined,
improper
to write
it
down, with
it
will not
be
inversions.
its
No. 21. B.
i
i?sz
S^
H-
H-
Efe=
D.
c.
i
m
m
E«=
^
^r
It The seventh (former ninth) The fifth (former
the tonic.
goes
The
third of the resolution chord.
should ascend
may
be seen
;
otherwise,
at B.
it
down
a half step to the
fifth
of
seventh) descends also a step to the
might
third, fall
In the upper parts,
when
may
it
must be taken to place the seventh below the
m
-^
in the base (A),
into consecutive fifths, as
descend
third, thus
;
but care
:
1
With such an arrangement, consecutive fourths are the result, which are not objectionable in the upper parts. As to the third inversion, the
first
way of resolution
(C)
is
by
far the best, the base
there allowing the upper tones of the chord to obtain, without
interchange motion, their respective resolution.
It
two other instances, which, although admitted by are by no means unobjectionable.
is
any
not so in the
strict theorists,
43 Exercises on the Nonachokds.
No. 22.
s
^i^m s^ Isy=fffT"f?"rtf i-ijLJ-
§4 5
5
7
t=^
-B-
^ i =fe^ f
j!
When
;=
I
i^^^^
1
ei
=
=;
^=^^fr=r
moi;e than one of the chord-tones are suppressed in the
nonachord, as here in the
fifth
measure, the third should not be
omitted.
No. 23.
^b
'^
o
=?-f-
rJ-4-r-J-
.S£
7
6 -5-
-5-
— ^-jP^E^^E^
iT
;i
^-
i
,i±
=i=^
.
^
^
^=^
i
^=1t?j=t 5
5
9
5
-^
44
No. 24.
'^
d^ ^^
=i=ra=
F f
JTT
J
^E 5
7 -5-
ESE
«
«
S
1
^f
r
£ No
75
6
5
F
7+5
Exercises on Diminished Sevenths.
25.
^i#tJj^^##4^ rr r TTY ^E^ i^ |~^ ? ^=:^
-*—
3
i|j
8
6
-
5
-5-
+a
I
7+ 5
^^^m
t^=4 i (^^$^^E-f^^^^^^ rr> =t=^=
ir
"ii"
¥
5
is ii
6
il
45 No. 26.
'
I
*
?S
fee
^
I
-0—^-
^^^j^^ T^r-fTT" TT
^^^
^^-
APPENDIX NEW CHORDS
§1.
F.
OF SEVENTHS.
In the harmonization of the major scale,
c,
have been
h,
f, g,
taken as fundamental tones of major and diminished triads ; wards, d,
minor
came
a,
e,
into consideration, as
We will now use d,
triads.
e, a,
after-
fundamental tones of
as fundamentals of the
fol-
lowing seventh
d,f,
a,
c,
g,
h,
d,
e,
a, c, e, g.
They
from the dominant seventh in
differ
tinguish
them from the dominant seventh, and to classify them prowill give them an appellation from the degrees they ocmajor scale.
in the
d,f, a, e,
g,
c,
b, d,
So,
Of these, attention
the
first is
first,
;
we
will call
the seventh of the second degree the seventh of the third degree
a, c, e, g, the
seventh of the sixth degree.
the most conspicuous, and deserves a particular
because, like the dominant seventh,
used without preparation
;
secondly, because
it
a rule
As
to
it,
whenever
it
is
sometimes
We will make
occurs in our exercises.
the dominant seventh resolves into the tonic, the seventh of
the second
tone
prepare
it
serves to prepare the
perfect cadences, and sometimes the half cadences. it
In order to dis-
we
perly,
cupy
that they are
this:
based on minor sevenths and require preparation.
degree resolves into the dominant.
goes to the
dominant,
its
finally, its
fifth
dominant, either
its
third
Its
fundamental
ascends one step to the
ascends or descends one degree, and,
seventh descends one step, and enters upon the domi-
nant harmony.
In
its
original construction
a perfect
fifth,
by
thirds,
and minor seventh.
it
consists of a
minor
third,
47
Like the dominant, and
It is figured 7.
all
the sevenths,
it
has
three inversions.
The
composed of a major
first is
third, perfect fifth,
and major
sixth, figured g,
and
is
called chord of the
The second and minor
fifth
and
sixth.
inversion consists of a minor third, perfect fourth,
sixth,
and
is
called chord of the third and fourth, figured
4 h or I
The
third
inversion
fourth,
and major
figured
2.
is
sixth.
composed of a major second, perfect It
is
called chord of the second, and
P» No.
27.
^^ ate
Exercise.
^1 m
48 This seventh can also resolve directly into the dominant seventh, thus
No.
28.
^
m
zS^
ite
:e^
i
3E
i Its third
can he elevated hy an accidental
transitory dominant seventh,
key,
and forms a
;
then
it
becomes a
slight digression into a
new
as,
No. 29.
ui ^-M
^
i
^^m When
I
used with such an elevation of the
third, the
doubling
of the third must be carefully avoided, because to double the third
would give either consecutive octaves, or a cross base, as appears in the following
example
:
No. 30.
i
^^ -gg-O-
relation with the
49
At A,
tl)e
same motion as the base, At B, the treble gives up the /,
treble necessarily follows the
and. consecutive octaves ensue.
descend
to
f
of the treble.
advisable not to double the part progressing
§ 2.
The
third degree of the
major scale
h, d.
degree, and submits to preparation.
Its
third ascends
one
descends one step,
The
step, to
first
a;
The
to a. is
e,
it is
steps.
chord of the second,
seventh descends to
its
this
and
It
a or
has three
sixth, %
;
the
or | ; and the third a original construction by thirds, it is
and a minor seventh.
seventh with
-^
^r-^
i I
fifth
c.
to
to c,
|,
third, perfect fifth,
—Example of
resolves into the sixth
ascends one step,
a chord of the
In
2.
composed of a minor
It
fundamental goes
its fifth
second a chord of the third and fourth,
No. 31.
by chromatic
the fundamental tone of
is
g,
inversions.
causes a
Consequently,
Sevenths of the Third and Sixth Degrees.
the seventh of the third degree,
its
f toyft,
and the base, progressing irom
to d,
cross-relation with the former
its
inversions.
^
I
§s
'^ 5-5 §:-*§
^
First inversion.
i
J=i
-si'-^-d
^-»
± f=
w-T-tjt 5-6
5-8-5
§ Second Inversion.
=5?Z
i
50
The
seventh of the sixth degree has
degree of the major scale.
minor
third, perfect fifth,
its
its
fundamental on the sixth
original form,
it
consists of
a
and minor seventh.
second degree of the scale, and has the same
It resolves into the
number of
In
inversions as the foregoing, and
is
subject to the
same
laws.
No. 32.
J
$
I
J.
J
r^
^ ^ $ ^=f^ «q-=-
Sometimes, after a modulation
now
i to the
dominant, the two sevenths
before us combine with the seventh of the second degree, to
form a sequence of sevenths, leading
to the primitive tonic, as.
No. 33.
i=at
,i r^
iS=i,
f=^=^P=^r P-
51
The same by the
formula, with the
first
inversion of the one followed
third inversion of the other
No. 34.
i=^
i ^ The same
:f=±
again by changing the order of the inversions.
No. 35.
i
1^=^--
1^ ^
if^ -
5
^z
'^^
a
g
-i
I
Let us now enter upon the development of the
Major Sevenths.
3.
Theorists give that
name
to the
sevenths whose fundamental
the tonic or the subdominant. Let the tonic be
c,
is
and the subdomi-
nant f, and the first of these sevenths will be c, e, g, b, and the second f, a, c, e. As with the sevenths above, we shall style the former the Jirst major seventh, on account of
on the
first
degree of the scale
for being placed
;
its
being placed
the latter the fourth major seventh,
on the fourth degree of the
scale.
They
are the
most discordant of the seventh chords, and of course they ought to
be prepared.
ser, to
and
They
require an exquisite feeling in the compo-
be properly employed
skill, far
;
and when used with discernment
from being harsh and rough, they
strike the ear not
unpleasantly. In their original construction
major
third, a perfect fifth,
i
by
thirds,
they are composed of a
and a major seventh
:
52 Their
inversion consists of a minor third, a perfeet
first
and a minor
and figured
sixth.
t
The second and a major and figured
It
^m m
called the chord of the third and fourth,
It is
or |
fori
The fourth,
third inversion is
and a minor
second, and figured a
The
first
fifth,
called the chord of the fifth and sixth,
inversion consists of a major third, a perfect fourth,
sixth. f,
is
11
composed of a minor second, a perfect
sixth.
It
is
called the chord of the minor
^^ :
major seventh resolves into the subdominant,
as.
No. 36. -ti
—
4-s-
=1:
^ The scale,
1st inversion.
2d inversion.
3d mva-sion,
fourth major seventh leads to the seventh degree of the
i. e.,
No.
to the
harmony of
the diminished triad, as.
37.
i fcp^^^^S 3^
s ^=z±
53
The
seventh,
c,
e,
upon the major
g, b, resolves satisfactorily
triad of the subdorhinant.
But/",
a,
c,
e, is
far
from leading
to
such a repose as might be expected, after so striking a discord as y, a, for
Its
c, e.
something
resolving into the diminished triad leaves us longing fuller, at least for the
cannot be changed
The only way
abruptly. rily as
c,
g, b,
e,
chord, f, a,
c, e,
is
minor
triad, b, d,
/jjl.
Buf/t|
without dragging us to a foreign key too
to fjt,
us
left
to resolve
f, a,
c, e,
as satisfacto-
either to lead the diminished triad after the
to the
dominant
triad of the parallel key.
No. 38.
it or to resolve the seventh, f, a, c, e, into the seventh of the second degree of the minor scale ; and then, by a sequence of sevenths,
we reach
the minor key, as,
No. 39.
^^. 3^
SE^ 5
Let us now pass
7
7
7+
B
to the
3.
Passages of Sevenths.
We- know now how to prepare and resolve every chord of the we are accustomed to the manner of placing them on It remains now to combine them degree of the major scale. every
seventh, and
in passages, or
sequences
;
and
this, in
consequence of our being
practised in their treatment, will not be a hard task.
prepare the
first
of these chords (unless
in this
:
at the
dominant seventh) and
to
to terminate
It consists
we commence
the sequence with the
dominant seventh of some parallel or relative key.
54 But what
A
a parallel or relative key
is
1
major or minor having the same signaThus, the parallel key of g is e, because both have the
key
parallel
ture.
is that
same signature—;fjj. A relative key is that major or minor having an accidental more or less than the principal key. Thus, the relatives of g, of which the signature
is
one sharp
(/it), are, first,
secondly, d, whose signature also the parallel
key of g',
is
and
f^
tones
and
cfa,
and
its
moves a
moving through such a motion,
^
Let each of the following tones
i^
be taken for the fundamental tone of a seventh
first
c,
whose fundamental
will be d.
our preparation chord,
for
:
every chord in
be met with, will serve us for the preparation of the
c will
seventh,
downward, or a
fifth
we meet with a series of we can use them as funda-
S /, a,
a; and
Consequently, whenever
mental tones for sevenths.
which
its parallel,
parallel b,
e minor.
In the sevenths, the fundamental fourth upward.
cjj,
we
If
shall
we
take the triad,
have the following
passage
No. 40.
i
w
Se
=i=
t^is
example, the sustained third of the
m^ As
it
results
^ from
seventh becomes the preparation to to the third,
-^
and soon
to the last,
its
which must be a dominant seventh
Likewise, such passages can take place with the inversions.
No. 41.
i
first
neighbor, that of the second
#:
^
55 Here, there is an alternation of the first and third inversions. following hegins with the third inversion, mingling with the
The first,
alternately
No. 42.
3E
1^
^
1—1
r-^r
f-^
^
In successions of this kind, the second inversion ble
as
the
i is
quently, although regularly prepared and resolved. it
may
poser.
be properly used
The
not so desira-
on account of the fourth returning too
others,
following
is
to
fre-
Nevertheless,
render some particular idea of the com-
an instance of
its
employment
No. 43.
^^m #
i 'ZSZ
«
7
I
7
^
In the minor scale, the passages of sevenths are treated in the
same manner as in garded, by dropping
the major; that
is,
the leading note
is disre-
the accidental from the dominant tone of the
scale, thus
No. 44.
^m
IT
^
:t
At the
star, the
^
g
is
fc iE
made
t
#
w-
1
natural by leaving out the sharp, which
here charactei^es the mode
;
but at
(f), the accidental is restored,
S6 thai the
may
minor key
The same
not be lost sight of.
rule holds
good in the inversions.
When
practising the inversions of such passages,
will
it
be advis-
able for the student to look carefully at the fundamental tones.
As
they should step a
downward, or a fourth upward, he has
fifth
nothing to do but to try every seventh, and examine whether each
fundamental keeps
required step, by placing under each inver-
its
An
sion its respective fundamental.
meaning.
Suppose that we have
example
will
explain our
put the following example to
to
test:
No. 45.
^
i
^
J-=-J-
^ It is
^^
plain that part of these inversions
The
mentals beneath them. necessarily to the
of the
fifth
and
first
to their original construction
if
we
by
in
its
If
thirds,
we
of a seventh leads
which every thing
;
i.
c,
is
to the
we
chords
A, B, C,
immediately find that
which does not agree with
away this foreign we shall have the
take
stead double the fundamental,
succession, in
5
recall the sevenths, at
there is a foreign tone in each seventh,
the fundamentals below.
*
do not agree with the funda-
third inversion
inversion of the next
Now,
sixth.
t ''7
tone,
and
following
correct.
No. 46.
i
f gj o
-
{-s
^
m For, every upper tone answers to
its
* rrpv V
^
41^
^ 7
1
+
respective fundamental.
We
67 urge
this practice
He
upon the student.
will
avoid numberless
We
mistakes by attending to the regularity of the parts.
him, likewise, that
all the sevenths,
be prepared,
beginning of the passages
at the
remind
except the dominant, ought to ;
and that these pas-
sages must close with a dominant seventh, in order to rest upon a tonic of one of the relative keys.
In conclusion,
we propose to him we strongly
the following exercises on the sevenths in general, and
recommend him
to transpose
them
into several
presuming on his industry, we advise him his
keys.
to write
Finally,
some others of
own.
No. 47.
i^^^
o
i
:Jz=rA=J= zscz.
S
9iE^
i
^
T=«-
^ 5
6
5-5-5-5
5
No. 48.
'^S ,^^
-Ma=Sz —
7
7
+
-f?
58
^^1^^^^^ m _^ $ cJ=>\g
^^
§EEE No.
iS-
49.
^t^=i
i^
-^JL
"^^
J
5
6
—
^
L 7
'
T+
No. 50.
ts^^^^^E^
fc-^-
ii*^=f=«HBf^P?=PP^P?
-r-"r
^^
^7+5—
7
7
7
7
7+5
iii ^-u-^T=l^ ^,
f=rii£
^^ 7
7
7+5
k
:i=g=
^=F=^
MT
i
J
r
-^
-e—fH=^
,Sc:z5^
(I
-•
59
No.
r^
jk
51.
#
—
—
%
nzzqr
r
I
5-
7
»
2
5
74.
g
S
g
I
f ?-rf i^e
8
»--—i-
W-
I
I
I
r
I
•—=*-
E^ 5
_c_
e-^
IS*
P-
'^ 6
fe«
6
^| P"r
ii
>
2
g
^g
tt
R
5
8
5
5
No. 53.
'^ ^j—g-
1
#
,HJ°g|J"^sjq^gj
f-f-n:g
^S
5
^^-^^^
..u^
PE^
^
l-V
Passages of Sevenths.
No. 52.
-s
+4
r
j=
!
3iS
5~^
"i
1—=y=|g
~T"o"
T^
r
7+
3
60
J-rJ
^
^
$ I
J-
*
S
i
i
#^
ri
bsl
bJ
I
1
J
d
I
g
The Final Cadence. The
cadence, or simply the cadence,
final
is
the conclusion of a
musical period, on the tonic, either of the principal or relative key, or of
any
other, properly settled.
chords,
which serve
to
The dominant
chord
is
necessary
must be preceded hy some other make the cadence plainer and more solemn.
for the perfect cadence,
hut
it
This run of chords forms what
is
by
called
theorists a
formula of
cadence.
In the beginning of this chapter, the second degree ous, because shall
now
Used
thus,
after the
we
stated that the seventh of
dominant chord, the most conspicu-
serves to prepare the perfect or final cadences.
it
consider
of some of
is,
it
it
often undergoes several tones,
its
We
as leading to such a result.
namely
:
changes in the resolution
the third can either ascend to the
dominant, or descend to the sixth of the second inversion of the tonic chord.
When
to the said sixth,
The
seventh
is
its
fundamental
is
doubled,
and then the third goes upward
it
ascends a step
to the
dominant.
prolonged, and becomes the fourth of the second
inversion of the tonic
;
but finally,
it
must descend a
step to the
61 tiiird
way
of the dominant seventh.
The fundamental
follows
its
usual
of resolution.
No. 54.
^^3^3^^^^^
i
This it
may
is
an exception
to its resolution.
In the perfect cadences,
also resolve immediately into the dominant seventh.
No. 55.
i
^m
-Sr-S
1
-
^.
-P—P-
In the second inversion, not only the seventh must be prepared, it must directly resolve into the dominant
but also the fourth, and seventh, as,
No. 56.
^ i
i
62 Hence, the following too
many
fourths
;
is
not satisfactory, as
and yet the
No. 57. 'jL
e)
e)
first
it is
encumbered with
of the two fourths
is
prepared.
63
i
4
A
J
!
1
j-
J „
i o
I
P-
1
-^ No. 60.
^
:^ g=^-g^ ^g '^o^ i^ P;-e-—i=Hd
!i
St '
—=
r -s^
9^^=^ "r~^
:i
^* 5-
I
6
f^rrTfT -p
g
g
jj
n-Tir
1
T*
I
^^1
r-6
=f
No. 61.
z^
I
J-
E
I ,*^ B
F^
?E2£
^
r
'
P I
I
f
ffi=?
g 5
5
S
I
-r^*-
s)
5
S
5
5
j=j=3JTfc=i:Jzzl »- r.J j a
I
fcE
i
l
5
:
=^::s= 7
+
5
64 No. 62.
^^ ^^
—"-
-s
-^^Ts
r^
>»
iS
7+5
=F
5
5
a*
^
4^^ a^jfe fel J
r
—
^
j ,j
H=
3E -7-
j
-rr—^ &
7
=r=e
In the following example, the seventh of the second degree resolves directly into the dominant seventh, without destroying the fullness of the cadence.
No. 63.
i=ti: ^^ I > r^r
i=Ed=^ ^f=r=F=
^
See
=S=i
-U=f=
f^
1—
65
The Diminished Seventh on the Subdominant,
originating
Seventh of the Second Degree.
IN the
final cadence, the seventh now before us new diminished seventh, of which it is the fundaits minor third is made major, and the chord changes
preparing the
In
gives rise to a
mental tone
;
minor nonachord of the minor key, g. bling a minor nonachord as to its form, it
But although resem-
into a
The fundamental
resolution.
only remain
;
i. e.,
resolution is this
:
is
always
quite unlike
is
left out,
andyjt,
it
in its
a, c, e^,
a diminished seventh on the subdominant, whose the fundamental tone ascends one step to the
dominant, and the third descends one step
;
the
fifth lies
stationary
the seventh does the same, and changes into the major sixth of the
second inversion of the nant seventh,
which
tonic,
finally resolves into the domi-
as.
iw ^ ite:
As can be thirds, this fifth,
Of
seen from the example, in
its
original construction
by
diminished seventh consists of a minor third, diminished
and a diminished seventh. its
dence.
inversions, the It
consists of a
which occasionally
is
i
first
minor
alone third,
is
used to prepare the
diminished
made extended,
fifth,
final ca-
and major
sixth,
as.
%fa^-gr
^==
t-
^ i ?tteJa In order to give the voices a freer and easier motion, this diminished seventh
is
changed often
into
an augmented sixth,
:gto|
i r ^m*^ fe "n
'-^
as.
66 Here,
represents
dji
treble than
e\f,
ejz
and, no doubt,
;
followed by eb.
It
it is
which leads smoothly and unmistakably it
to advise the student
proper
skill in the
to
whom
never
As we cannot
performers.
to
note,
Here we think
etj.
difficulty
of intonation, and
look for great skill in those
performance of choruses
the
for the
give the voices, especially
to
such intervals as require
in choruses,
an easier step
becomes a kind of leading
is
entrusted,
advisable to avoid carefully the following intervals
:
ii
will
be
sharp fourths,
diminished and superfluous sixths, and diminished and superfluous fifths.
All these intervals are nothing but break-neck places for
chorus singers.
There
is, also,
in the
minor
scale, a diminished seventh,
on the
subdominant, originating from the seventh of the second degree,
to
which belong the developments we are now unfolding ; but particular attention
must be given
to the third,
order to avoid the diminished third, construction
by
thirds.
tion of the fourth
which must be elevated, in
when
the chord
is
in its original
This diminished third arises from the eleva-
degree of the minor scale,
This
is
not admitted
;
as,
and
shoiild be avoided thus
Such a caution
is
unnecessary when using the
first
which the sixth can occasionally be made superfluous,
inversion, in as,
No. 64.
^ ^^s^ im i T^T^^fr^ =J=
I 3^^ £ Some
exercises will
now
illustrate the foregoing directions.
67
No. 65.
s id^^hM^^^y^k^^^M^ rr' Tff r? f r ^ §!£ Ef^ I,
1
1
I
=i=FP
7+
?
S
^^Ei
$
5
- -1-
^5=±^-=p=tt
I
I
^ TT
9^=^Ef^=fy=y =^=^ i
The
-'-
S|
seventh of the second degree, in
its
first
inversion, as well
as in cadences, can occasionally resolve into this diminished seventh,
as
it
the
results
same
from
a, in the
The
preceding example.
following gives
inversion, resolving into the diminished seventh, and pre-
paring the end.
No. 66.
^^^m ^ ^
J
j-^
-ir
6
i
:^=3:
^ 5
6
)-
^
5
r—r-7 §ij
—3^H3r:£
J-=fM
^^
r^r 7
+
5
i
68
The
diminished seventh preparing the final cadence in the minor
key.
No.
67.
J-
i:J:
^
p J
I
I
^^^^^^m
J
ate
-
jt
^i^i'm-=^
i
:s_
1 Example on
i^d^d ?^
i»-^'r
'2_
r3 j2
a
5
2
i^
|J
s' tf
6
s—^—s-
-a
tt«i
i5
:
F-e^i
t
I
%
sevenths, in general, and formulas of final ca-
dences.
No. 68.
I
-J-"^eJ-
f—i—•—E3Z
±=1=
t=tsx
S rrrr
i9
ite
i ^
Se -f
^
AjLA^^^A^ S3 F^ f
E^
-f
^^ t
^
:33i
S sg
I
f~ >5
69
:i^*^^
-r^
^
;i
6
6
^S?E3 p—rn^ 'fr^
f
^^^^^5-7
p 7
\^
-I
f=-^
i
:^
g-
=r=F=P
77
ii^EJ --=^f
i
=J=;i^W
— S2
M
^
-i=4=d=
T-r
-I
i
frf-^r %
I
g-
^^ \\~^ I
T
70 Half-Cabences. In the
foregoing chapter,
we have
fully unfolcled
the whole
matter of the final cadences, and pointed out the chords preparing
We now
ihem.
The
come
half-cadence
to the half-cadences.
is
a temporary form of repose of the whole
harmonic body, on the dominant
triad.
This repose
is
in
some
cases limited to a certain length.
^^^
In others,
it is
indefinite, as for .
r
As
example, in the case of the pause,
^^
or organ-point.
in the final
r
cadences there are some chords especially appro-
priate to prepare the end, so also there are particular chords appropriate to prepare the half-cadences.
There are two ways
whan
to
form a half cadence: the one
the chord used to form a half cadence
the dominant triad
;
the other indirect,
when
by
the dominant triad
is
preceded by the second inversion of the tonic case, the fourth does not
We
can go
to the half-cadence, firstly,
Indirectly.
MiNOK. Directly.
-p—g"-
7 7
triad.
In the latter
need any preparation.
both scales. Directly.
direct,
followed directly
is
Indirectly.
from the tonic
triad, in
71 Secondly, from the
first
inversion' of the seventh of the second
degree, and from the uninverted chord
itself,
in both scales.
Major Key.
^=U^^i-
-2=f==i: i ^r-~r
t-J-
J— ^^^ j-
^f-Tf"
--s=^
CiSL-
f Minor Key.
^±d=E^ I
i f—
«
S»-
i
I,
^^
*^3=^
-V—Jf-
f
f
e.
r
Thirdly, from the chord of the second degree, in both scales,
as.
Major Key.
if
m
i r
A a 5
-g— „6
-
i
5
Minor Key.
i;
:v-f-
d=i g=lj=f
1 r
c
^
72 Fourthly, from
ther
chord of the subdominant.
Majoe.
j4 f JMIil^ J s
MiNOK.
¥^^
'^
5-
Fifthly,
-
a
t -<9;r
-
\l
S
from the chord on the sixth degree of the minor scale,
4
as,
ftj
i Sixthly, from the diminished seventh its first
on the subdominant, and
inversion.
A
P^-IB^^^ -7-
The sion,
5
fifth
which
% measure (A) of the foregoing contains a is
fifth
succes-
admitted by some theorists as mitigated by the
superfluous sixth.
B
^
^^
^=^P=
'W
&
^ ^ 1
73
*
!^ Tf"
B
At
there
is
a
t-
I-
fifth
succession, admitted for the
same reason
as
A, above.
in
Besides these, there are two chords, chiefly used half-cadences, viz.
:
and the chord of the augmented
The Chord
§ 1.
This chord
is
prepare the
and superfluous
fourth,
sixth.
of the Fifth and Sttpeefluous Sixth.
composed of a major
It stands
fluous sixth.
to
the chords of the fifth and superfluous sixth,
third, perfect fifth,
and super-
on the sixth degree of both major and minor
scales.
Majok
-m It
seems
to
be the
first
H
inversion of that
placed on the subdominant, with which perfect fifth forbids us to trace
but
its
the
first
it
inversion has a diminished
as standing It
it
fifth.
diminished seventh,
are already acquainted;
to this
seventh, of which
We will,
then, consider
itself.
first,
third
the fundamental descends one step to the dominant.
can either ascend or descend one
scends one step, and forms a this fifth is
by
we
has two ways of resolution.
In the
The
by
S
Minor A.
o.
fifth
step.
The
fifth de-
succession, with the base.
But
generally permitted by the theorist, as being mitigated
the superfluous sixth.
disagreeable to the ear.
In
On
effect, it
has nothing conspicuous or
the other hand,
it
is
very easy
to
74 avoid
it,
should any one consider
objectionable.
it
Finally, the
superfluous sixth leads forcibly up to the dominant.
No. 69.
I
J=d=J=Tl^:
^M^^ ^-[^^'''Tf
SEE
IT In the second, the fiindamental in the foregoing case
and forms with third
it
a perfect fourth,
of the dominant
nant, forming with
chord
;
is
it
and superfluous
sixth
moves
vi^hich
The
triad.
fifth
changes
finally into the
continues to the domi-
a major or minor sixth, according as
used in the major or minor scale.
No. 70.
I
Major.
Bf^= i f
'
r
as
but the third stretches over to the dominant,
r
f f
f T
&c.
I
'W No. 71.
Minor.
^J=f
1—or—
—
=
^^=
1
«
ill
this
75
As can be
seen from these examples, thus resolved, the pro-
gression causes no consecutive
The Chord
§ 2.
fifths.
of thk Third and Fourth, with the SupERFLiroirs Sixth.
This chord looks like the second inversion of the seventh of second degree with the major third
by
itself.
dominant
Its
but
fundamental moves down
triad
;
dominant triad
;
the
;
its
is
same chord. Finally, the
fundamental of the
same
to the third of the
prolonged, and becomes the
sixth goes forcibly
the fundamental of the dominant, thus
tlie
considered as standing
to the
must descend
third
fourth
its
it is
up
to the
fifth
of
octave of
:
No. 72.
^=&J ^-Mm^
j=:
&c.
^ This fourth, being augmented, has no need of preparation.
Very is,
often these
two chords (#| and +|) combine together
;
that
the fifth of the former resolves into the fourth of the latter,
which afterwards follows combination
also
affords
its
usual
way
of resolution
and
;
fifths.
No. 73.
I gs
^=--jq^i-^:^^
w^
this
another means of avoiding consecutive
^£^ ^E
ti --^
76
B
=t^#
:i =F=P=
zt=^
^
As can be seen at A, the perfect fifth of the fifth and sixth falls on the sharp-fourth of the third and fourth, which resolves into the At B, the
triad of the dominant.
first
inversion of the seventh of
the second degree changes into the diminished seventh, as
been intimated, on page 67.
it
has
'
We
cannot forbear to draw the attention of the student to a formula of half-cadence, which has been employed by Haydn, in his work, " The Seven Words." "We have already said, on page the
diminished seventh of
65,
that
first
inversion, only, are used in the half-cadences.
inversion of this chord
over
is
the
subdominant,
often resolved thus
:
and
its
The second
the base stretches
fundamental of the tonic chord, as
to the
Sometimes the minor third
is
changed
into
an extended second,
thus
1^ In the
last case, the resolution
ceding one
;
of the tonic.
that
is,
remains the same with the pre-
the diminished seventh resolves into the chord
77 Haydn, lution,
in "
The Seven Words," deviating from the above
has made
c
jump down
to the
i
reso-
dominant, thus
:f=
^^^^E making it a formula of half cadence. Before him, no composer had made the second inversion of this seventh deviate from its usual this
way
of resolution;
formula of cadence
however,
it is
No. 74.
very
is
notwithstanding this great
authority,
As employed by Haydn,
seldom used.
effective.
Exercise on the Half-Cadences.
17=?—^ ^
r r
r
T r^
J^i-J—J-
fr *=!;
r
r
t
^
rTrf =t;=t=
78
f
S^^^^^^ ^^=^i^^^==
=*4
BSE^ ^
E
5-
5
5
E^ SP^^ K ^ J
7+5
T^ No. 75.
(I
^-
A
m
J
j::
^
^^ 44 I
=^= /L-^
d==^
^
i
J_r
^7+5 I
s
0_.
i il
E^^
J
W^. i
i
s I
*=j=
^A
.tj-J3 n
=^
^
5
a
-J^-
f=g^r^
f=^ £r+T^ -p ^^
SI
:feES
i
S
'*—-» 2
J j^
V-
^^:
=1=^
i
Melody. J
J
i
-7-
M ^ [j'-^r~r-Y-"j-T-t J
ly
S
*-
:^^=r
Pi
6
^^
1
F^FP
^
.^
^
79
^ =^^ =F^
.J—J_J_
i=i
i
* N. B.
i-
.^i
Jl
i
P^^
l-i
f
i^U
f
— Here, again, we would advise the pupil
to transpose the
foregoing exercises into several keys; and, after looking at each
formula of halfcadence, and practising
whole of the direction,
different instances.
we urge
it
Not
it
separately, to
make
to repeat tediously the
a
same
as a great advantage in point of rapid improve-
ment, whenever every matter has heen seriously thought of and understood.
APPENDIX
e.
MODULATIONS. A
MUSICAL composition
is
grounded on a certain
ascertained by the signature at the beginning.
scale, or key,
This
is
called the
principal scale, or key, in contradistinction to others, which
occasionally be introduced;
ensue, if the
same key were carried out through
from the beginning
to the end.
the whole piece,
Therefore, in order to break this
sameness of scale, new keys are employed, whose for
may
but a troublesome monotony would
effect is to keep,
a while, the principal key out of sight, by placing themselves
in its stead.
The
a modulation. into-another,
Of
introduction of a
Modulating, then,
which
is
is
"
new key to pass
is
technically called
from the original key
foreign to it."
the keys thus resorted
to,
some are
relative to the principal
key, others not, which, for that reason, are called remote keys.
A key is relative to the principal number of accidentals, or one more or A
remote key
is that
or more accidentals.
which
differs
when
one,
it
has the same
less.
from the principal by two
Hence, two kinds of modulations
—Relative
and Remote.
§ 1.
The
relative
Relative Modulations.
modulations are the most obvious in a musical
There are whole quartettes and symphonies by Haydn and Mozart, in which no other modulations are used but
composition.
those in the relative keys.
Rossini
—the
melodious Rossini
—
in
the greater part of his airs, duets, and trios, and in several of his
most effective choruses, confines himself to the relative keys. is one of which he seems particularly fond, and in which he has excelled, which might be styled the Rossinian modulation,
There
namely
:
the modulation from the principal
key up
to the
minor
81
key of the finest
third degree. In this he has concluded numbers of the and most graceful periods. The celebrated Handel has
built
his
with the relative keys;
mightiest effects
occurrence of a remote modulation
is,
so that
in his works,
the
worthy of
remark.
To
Ihodulale into a relative key, the dominant seventh of that
made use
is
We
of,
since
hardly need say that
the
is
it
it is
decisive sign of
immaterial whether
its
it
key
own key.
be inverted or
not.
Let us take an example of a relative key. pal key.
Its relatives
g, with ytt,
and
its
minor,
in the principal key,
we
As we have no
e.
c
be the princi-
we add
l^ to
it,
which
is
key of _/, and
its
;
next,
accident to suppress the
suppressed one sharp, in a scale with sharps.
gives us the
and
Let
are a minor, with the same signature
same thing as
if
This proceeding
minor, d, as relatives to
c,
next to
g
e.
—
Recapitulation. C, principal key ; which three are minor, and two major.
e,
f, d, of
Example of Relative Modulation.
No. 76.
sto-
^StSh-
i
i
relatives, a, g,
W
1
s
fsSL
^— I
As can be
'
perceived from the example, the dominant seventh of
these relatives have sometimes three, sometimes two, or one tone
82 in
common
key,
e,
any tone
common
in
nective tone g,
b,
we
chord It
and
;
as mediator will
is to
for that purpose, at
B we
between the
and
say more, when
tonics, c
we
with
We
it.
have,
which gives us some con-
then, called another chord into action,
e,
The minor
with the tonic chord of the principal key.
alone, has not
have used the chord,
About
e.
this
mediate
develope the remote modulations.
be remarked here, that some of these- keys, although
being nearly related
to the principal
key, are not so to themselves.
above given, the keys, g, e (one sharp), are not relative with the keys, f, d (one flat), as differing from each other by So, in the
list
more than one
accidental.
Thus, when we are
modulate either
to
from g or e to _/" or d, and vice versa, generally an intermediate chord must be placed between the key we intend to leave, and the dominant seventh of that into
which we wish
one most appropriate to such a purpose, principal key, or this
chord thus
+,
is
to pass.
The
the tonic chord of the
some other connected with it. We will mark whenever used as a transition chord between
any key and the dominant seventh of the following
Relative Keys of the Key of C. No. 1.—From
F
No. 2.— From
to G.
i
i
f^
F
to
E
Minor.
^.
-rr^^r^
r nr-^ No. 3.—From
;i
D
Minor to
*
G Major.
No.
4.
—From D to E Minor.
r^
1
83 No. 5.— From
G
Major
to
F
or No.
Major.
a.
^
i
Ei^^3
i^s^ No. 7.— From
G Major to D
^^^ffe^
or No. 7.
Minor.
m
i
m^
a^i No. 9.— E Minor to F.
As we may principal
c,
e,
itself,
different keys.
g, the
first,
to
Minor,
or No.
11.
most of the time, as the mediator
No. 2 has two intermediate chords,
gives no mutual tone to the dominant
seventh of the key, e minor
used
D
see from these examples, the tonic chord of the
key presents
between these because
No. 10.— E Minor to
;
therefore, the chord, g,
secure that mutual tone.
h, d,
has been
In No. 3, the key, d minor,
gives three consecutive tones to the following dominant seventh
major.
we
If
we
consider that d minor
is
a relative key
to
g
perceive that the dominant seventh of the latter key
adapted to modulate from d minor to
g
is
well
major, without any other
mediator, since after every dominant seventh either into the major or minor key.
ofg
minor,
we
are free to pass
84
By from
the
same
reason,
major
g
to
single mediator
In No.
—
we
5,
may
are authorised, in Nos. 7 and 10, to go to
d minor, with a
are justified in passing from the tonic,
the dominant seventh
a tonic
we
d minor, and from e minor the dominant seventh.
of/
(one
flat),
by
Then,
major, to
may
be considered as a dominant seventh, which
into another dominant.
g
the consideration that often
resolve
in the present instance of
No.
5,
we pass from major g to the dominant seventh of the major key,f. The other Nos. require no particular observation and we shall put ;
the preceding remarks in practice.
Exercises on Relative MoBtJLATioNS.
No. 77.
^
:±^=^
^ 9
iJ
J J —*--^ i
-P—
f=
AAA ^ p
m
-i
ife
I
4=^^ -JO
y-fJ-l^l
!
uJ-J-
p^g &
—
r^J-pJ
^""^"^Tfrrrr-rf J
,-i
1^ * ^
J
J
y
-*
s
f=
^^ij-wt^^u=^
i m^rTT'r ^
i
i^
yft
-^-i*-
r
i
»
^¥-^
85
No. 78.
i:e=^
»^
?=^^
E^^
r-r
^i^
-jg^
ite t2
6
^n
i
^^^^P=y=f
ii
^^^
g
i
t
5
No.
^
79.
fo=^-^ m
I
-W=^f^ t-
-t—
^
fc=r=^
ij-ij
^^ -I -^
^-ii
f
——
I-
-i
'«
^
''
»
^ *
--i-
— — t— t— '-I
I-
-^-is-
^i
E^^
^F I
I
EfgE
:ii P!iI^E
i
0-
1—
*
-^ :£
i-i
f
86
^ ^^^ ^^^^^
fe=^
I
J
•,J j(
J
J J
«i
The preceding modulations have been performed by using only but we can obtain the same result by the
the dominant sevenths
;
nonachord and the diminished seventh.
It is
that they are
standing
evident,
endowed with the faculty of modulating. settle
must be with discernment,
i.
when a major key
is
a
new
the
e.,
wanted
;
when
key, and
The
reason to
why
overloaded with tones.
The
to
it
and when we intend
to
touch
to.
the nonachords are less suited than the dominant
perform the modulations
more convenient
used,
major nonachord must be
a minor key, the minor nonachord should be resorted
chord
Notwith-
the dominant seventh, the non-
relationship with
their
achords are seldom used to
used,
both arising from the dominant
triad,
upon considering the origin of these chords,
is,
partly, because of their being
This diminished triad
is,
in this respect,
modulate with.
seventh, derived from the major nonachord, and the dimin-
ished seventh, furnish us with respective modes.
It will
means of modulation, each
in their
be advisable to resolve them into the
dominant chord, before getting the new key,
^^ ^
as.
^
-5-
Occasionaliy, tions
the
;
but
it
we may
use the dominant triad for our modula-
lacks that decision which the dominant seventh and
nonachord possess.
This lack of decision
is
owing
to
its
87
For
adaptability to the the major and minor mode.
instance, in
major, the dominant triad, d,f^, a, reminds us of the keys,
and all
g minor ; and
the tonic chord following
may
it
g g major
alone remove
uncertainty of key.
many
Finally, the minor triads, in
us in modulating. the original
key.
They
triad,
if we we must
But
relative modulations,
which might lead us
to
can likewise
assist
design to confine ourselves to the
take care not to touch any minor
remote keys.
must avoid the minor
triads, c
might lead us into
major,
ej?
instances,
enjoy the peculiarity of effacing entirely
minor, and
JJ?
major, or
Thus, in
/ minor. g minor
;
c major, we The former
the latter into
^ major, or c minor.
But we can change the dominant triad into a minor triad, and pass into a key of which the minor triad is relative. Thus, in the case of c major, by changing g, b, d, into g, V^, d, we are at liberty to modulate into f major and ab major,
d minor, which stand
in near relation both to
g
minor, and to the
principal key, c major, as.
I
^^
^^ i
=£
i& u This minor from one key principal
key
/ major, thus
triad
may
to others ;
for
afford us a proper opportunity of
moving
not related to each other, but related to the
example, in the key of
c,
from
g major
to
88
Na. 90. I
i
El^ &c.
*
Or
to
d minor,
6
I
in
tine
=E
&
ft
same key of
c,
thus
No. 81.
i ^^^=^^^ 4-
J;^
i
=t=ti
now
^^ 5 1^1?
&0.
-*—y-
t=tt=t
6
-5-
We will
--^
»
close the relative modulations,
by two
illustrations
One affords some instances of modulations by the The other is the "Wedding March/'' from the
of the subject. nonachords.
Iphigenia in Aulis, by Gluck.
No. 82.
4:
i
-t_4-
zJz^t
:S^^^ rn^-
^
^
gnrr J^ w=¥ 6
5
^^^^^^m rr
'
5
-
-
5
rfrrfjrrrr^n' 8,85
-
-
5
5
5
57+
5
89
^^
3^
-ei-4-,
--fffmwfy^fffr^' ititt 5
In
this
ta 8
m
i 6
6
=f
5
example, the nonachords resolve
seventh, before touching the
new key except
into
the
dominant
at +.
The Wedding Makoh, from Gluck.
^
iBt
Violin. /
|fa--.=J:a
A «-=-Ht
p o
aznzf;
^
2nd VroLiif.
eS--^
Alto.
^^
^
;>p
Bj^so.
9^^4^##=^#tf:=te g.
i i
i
it
^
=ztl
»
^oco f
1-'='
^
s^Ll
:fc:ffi=Eje
=?s
S*-T5<-
-M-
-m^ 0-^
^m —
pocof
^f^
ri
fs
rp"
90
fe
p
-jg-
-•-^i
I
^iki
Ifefe 1
*^=t=iiz± -
9^
i
=^
1
—
J-J-
—
•-
« pi:
fi-
P ^^^S^^
??q
n^^f^ff^
f^ -f
\
f f —e>
f^^^gi^^ ^
—s —
^
Tsi-r—;:)-
(2
o s
;
H«-»-
^^
E
'
— TS—i- —I
ri
D
4
gj
-
5»-
-(Sl
^^^^J^=J^Jdgi: F?5:
12-
=?=*=?*;
-Ot
^^ ±e ^^ ^^
^^
i=±^r-T
^ r>rf,f 7^^^ tit
\.
-
-
,
P^
^g^
-g
—
z
^
91
^^^^^m i
» d
\ti
PP=F i
—
mmi^^s^^
1-*-*>-*-
-M-
a
a
-P
J>
Pg
^l^
pign^AoL Sg^za
^
(t.
&
This piece
is
admirable
the circumstance in
and remarkably
for its simplicity,
which
it is
performed.
Besides, there
fit
for
is in its
smooth and quiet motion something breathing of early music,
making the listener's mind feel the happiness must have enjoyed upon the occasion.
The
A
and
B
;
harmony moves
after which, at C, the
major, in which the composer concludes the This; affords an instance of what
sition. e.,
first is
part of his
into
d
compo-
called a transition j
a modulation by which the writer ends an important part of
a piece of music in a
At
enamored couple
student should notice the digressions into a minor and d
major, at
i.
the
new
key.
the beginning of the second part (D), Grluck again
makes two
small modulations, one into a minor (E) and the other into d major
(F)
;
and
finally,
(G) a formula of cadence in the principal key is This is a fine to an end.
introduced, and the composition brought
specimen of relative modulations. simplest melodies are
made
It
interesting
may by a
be seen here
skilful blending
how
the
of these
keys.
We
cannot give up this subject without setting forth a
.last
obser-
which should always be kept in view that is, not to multiply modulations, so as "to take away the unity and firmness of the whole structure ;" in other words, we must use modulations moderately, and allow the principal key to be predominant, whatvation,
ever
may
:
be the length of the composition.
92
Remote Modulations.
§ 2.
From it
the
key, as
it
appear,
at
already given
definition
Remote
of
Modulatioiii,,
by
so
much more remote from
disagrees with
it
in its tones.
ensues that a key
the
brought about
;
is
Aremoie modulation may
reading, to imply something difficult to be
first
yet
the principal
it
A remote
not always so.
is
means a great deal harder to be got than a relative lay down here some directions, which will enable
key
one.
by no
is
We
will
the student to
They are many in sum them up here, we could not
bring about the most used of those keys.
number
;
and were we able
to
boast of having given all the possible
many
others
may
still
means of modulating
be discovered by a
man
of genius
;
;
for
the
dominion of the art of music being boundless like the canopy of
Heaven, in which the astronomers, from time some unsuspected star. § 1
.
The same dominant
to time, discover
sevenths which have assisted us in
performing the relative modulations,
may
likewise serve us for the
For
purpose of modulating into the corresponding irrelative ones. instance, in c major
we can reach
the keys,
f
minor and
g
through the very same dominant sevenths which have led us
minor, to their
corresponding major keys.
No. 83. From G Major to F
minor.
^^^^^^
^ b» >
Sla
3
.,
Ug 6
'P
I
&C.
93 No. 84. From C Major to G
U
^^=^^i
Minor.
Sis-
=fe &0.
^=f Moreover, in every scale there are three minor after the principal tonic
we
triads.
Then,
if
use these triads to serve us as connect-
ive chords for the dominant seventh of their respective major ones,
we gain c
a.Te
d
df^ 'i—e
g
b
—a
^ i—a, 4 to
D
c e.
triads in the
key of
Their corresponding major ones are
e-
Example.
No.' 85. From C
'Thiis,
The minor
three remote major keys.
f a—e
From C
Major.
every major scale gives us
five
to
E
Major.
modulations
irito
i.-
keys (three major, and two minor), which are based on the following degrees the major on the second, third, and sixth degrees :
the minor on the fourth and
fifth
degrees.
We
perform these
94 modulations with the same transition chords which have enabled
us
to
modulate into their corresponding relative keys.
The minor
scale gives no
keys
diiferent
from the major.
The alteration which the third of a chord may undergo, § 2. when changed from major to minor, or from minor to major, can more or less distant. This proceeding is frequently Haydn, Mozart, Beethoven, Meyerbeer, and other celebrated composers. For instance, to modulate from g major to e? major, we change the major triad, g, b, d, into g, IP, d, which
lead us to keys followed by
reminds us immediately of
all its relatives
;
and we perform the
said modulation thus
No. 86.
A
^
I
\
4~m
=?=F &c.
iS We might proceed
w still
farther, as,
No. 87.
B ^
i WM The minor
triad, g,
Efe£
Jj>,
d,
through
^=^^ ^
W
its relative, e^,
which we are led by changing this the dominant seventh of the key, a^, major. us of
aj?,
to
g,
triad,
J[?,
e[>,
reminds
g, h^, into
Now, if we intend to return to the key, g major, from the key, we will have to follow the contrary course ; that is, to change
eb,
95
some minor
Here
triad into its major.
c minor, is nearly related to the key, triad,
and change
it
m asE We
must be
Our return following way
into c major.
surely accomplished in the
of a chord,
for instance, the triad,
Let us then choose
eK
to
this
will ^'
g major
'
:
iM4
ii^^
TT f
M rr
=t
when we
careful,
affect
such changes in the third
to place the accidentals in that voice
which can take
them most conveniently ; that is, in that voice which had formerly Thus, in the examples, A and the same tones, without alteration. B,'we have given ib to the alto, which had previously Sb ; and in the example, C, strictly
we have
adhering
given e^
we
to this rule,
In the preceding examples,
and gone direction
with
to those ;
i.
e.,
to the treble,
we have
We
flats.
we
from natural
which'had
By
eb.
shall avoid cross relations.
started
now
are
from natural keys,
to follow
an opposite
intend to go to keys with sharps
and as we changed major thirds
into
change minor
But here the pupil must bear
mind
that in
into
major
thirds.
every scale there are three minor
second, third, and sixth degrees. triads,
into
minor ones, so now we
He must
triads, those
The minor
less
remote keys.
From
c
triad of the second degree
to
modulate
major
may lead
to e
major and a
major, thus
No. 88. -ste-
M
Iee
^fe E
^
in
on the
avail himself on these
which, changed into major, will help him
more or
;
shall
Major.
j^fesEEJ
96
^ ^^
#^^1 A Major.
He iBi= l ^
ite
the third degree to major
The Minor Triad on minor
e,
minor
cj|,
and
/jf.
No. 89.
^^^^^^^ E
P— —
Major.
P-
1
1^
iai 5
I
ss
J
i
p-0ifj^m^^ ^i FB Minor.
C^ Minor.
fe ;
'=31 5
The minor Triad on
^1
i
the sixth degree to b major, a major, and
/ minor. No. 90.
m^^^^^ B1|
T
Major.
m^. "!
9S=y
97
^ s^
r
I
Fj Minor.
4 J
i f^ «i
«PP
m
* We seventh
=r=f
have here introduced such keys as have their dominant connected with some preceding triad. Nevertheless, in
of this connection, such modulations
spite
are
as
require in practice a more extensive development. is
given here,
The
following
a specimen of their treatment
No. 91. Fare-well,
bu
sy
-
world,
r^ i
r
1 Jfcfc
thou
=EE?=
(A)
J
J-
p-T—F=^ Fare--well thou
well, thou
bu - sy
world,
and
+^^
I^ 1 i %H^^^ :li :^:^A :^A
^
J^AJ i ^r T— r-
bu - sy
may we
-vrorld, fate-well,
nev- er
zk
-^ ii J>
^r
fere- well, fare -well,
and
meet a
-
gain,
± -^.
^- Trr^=^
^=
Pare-
may we nev-er
^
A :^A and meet a
-gain,
98 and
may we
i
-.9-' I
(+)
may
-
meet
er
a
=^
r^rT=rT^ we
nev
-
er
meet
may we
nev
-
er
meet
f
-
gam. J
and
i
frT. gam.
fe
:^=^b
Here
nev -I-
rSzzfccd-
^ a
-
gain.
the alto part being stationary on gtt ( A) for several measures,
prepares the ear for the coming key, and the major triad, a, leads
sign
most conveniently
it
the minor triad a, c^,
+,
key of
to the definitive e,
key of c, in which the final But the best course to take, in order
cipal
back again
calls us
cadence
previously to settle the dominant of the
e major.
is
to the prin-
modulations, •
No. 92.
1.
AND
2.
Violins.
I
Ores.
ViOLON.
D.B.
I
g*3
«
e,
the
performed.
make such new key, as
to
cjj;,
At
__J
'
is
99
m :^^^^
^
t^
#
J
^ !
f «!.
aft This fragment
duced
to
two
an extract of an instrumental composition re-
is
violins, violoncello,
so
as
design, the dominant
satisfy
to
and double bass.
the
going
to
remote keys
such
as
sonatas,
exemplifies
It
Before setting forth the new key with a
pretty well our meaning.
new melodic
&c.
is
strongly and firmly decided,(^)
demands of the is
ear.
This method of
very common in instrumental music,
quartettes,
quintettes,
symphonies,
&c.,
&c.
The instrumental compositons of Haydn, Mozart, Beethoven, Hummel, and Mendelssohn, abound with such modulations. The cadences and
§ 3.
half-cadences, also, furnish us with
means of modulations. After every final cadence
make
the tonic, to
By
1st.
third of a
tonic,
third
we
are free to keep on
any tone of
new key. it
the major
are supplied with a modulation into the
downward from
we modulate
No.
we
the preparation for a
keeping on the fundamental, and making
new
key a major c major
it
the preceding one.
Thus, from
into a\f major, thus
93.
li
s^
^^^^^^ m T^ Ft4=F^
fe^^
A
100
-^^ =?=hF
i^ite^ i?^
new
F? / ^
tonic,
r
we modulate
&c.
^1
^^p
keeping on the third and making
By
2nd.
of a
J3
I
into the key,
it
the fundamental
a major third above the
preceding' one, thus
No.
94.
i^^^^^ ^^E^s^ i
^=r4-
Itt*
t-
^
lu
i
3rd.
a
new
By
tonic,
'^ris
^^
ft
keeping on the
we modulate
f
and making
fifth,
into a
it
i
the major third of
new key a minor
third above the
preceding one, thus
No. 95.
^m
f=f-f—^^f=^
^=3 fe
-P
Ei
;
g
:^s^=f=
M^
I f=f^-^=*f=p-t£n^
^^
I
-0~n-»-
&c.
^iSr
101 establish a
new
minor' second above this dominant, thus,:
No. 96.
#^^^
4=^4=^
i
we may
After a fepose on the dominant,
4th.
key on the
^-
^^ ?s
^a=i^u J^
iS
-^-^
-f^-fT-
&6.
=F=i«=
:e^
5th.
^g^
After every major tonic
as the fundamental of a
new minor
we may
get the
fifth
downward
key, thus
No. 97.
=5=t^
i^
i EE f^—
ifc^^^^^ T"
^?-
—
—r5^
f^
-,
-d
ci
T=^=?=
"f— zfzitS
E& p-
.l—
9e-s
—
i=Tl^
»-
mi^=F^^^#^^
^
=fe
-
102
T r r
ptt
E
This modulation eighth measure
we
ivatural,
is
change the preceding chord minor back
to the
6th.
At
and frequently used.
into major, in order to return
keyg' major, in which the final cadence
After every tonic,
we may
start
is
from one of
concluded.
its
tones,
by a melodic design, or octave passage, reach any key we
No.
i=^
\-
fe
f^m ^^i^± frr-r-u^
-^-
Cres.
i
J.
ggP^^ U_l
J
^
k
ji
J.
J.
J.
m ^ ii
and
please,
98.
A
i
the
We
use a proceeding already pointed out.
m^^^-= P^f=^ -^^
J.
A
Ep-p-=TPp=p_^
J.
~-r=T
&c.
103
The chromatic runs
7th.
mote modulations.
may
are frequently used to introduce re-
In such a case every tone of.the tonic
serve as a starting point
to
get the
new
we
l^ave
key, as
No. 99.
I1
fe^Efe^ttteSE^fe
Eg
^.liA ^mi I
S
i
^_i.
i
j-iL-i &c.
m
J.
^e^E£
t
From d major we which
are led,
modulation.
But
this repose
well have taken rest at
el',
on
run would have been
new key part
of
at the it.
It
new
We
might as
same measure, but not before
motion of the musical composition.
may
et';
too short: it is proper to settle the
advisable, moreover,
or five chromatic steps
and complete the
c is quite arbitrary.
beginning of a measure, or at is
steps, into c major, in
tonic,
in the beginning of the third measure,
or at a^, at the middle of the for the
by chromatic
the parts seize upon the
all
ti
In
to
a
least, at the
pay
accented
attention
the
to
slow movement, four
be enough to determine the key
;
on
the contrary, the quicker the motion, the longer ought to be the
chromatic run. 8th.
The
ijiusical
rests
can become means of modulations.
104 withoHt retaining any tone to serve us
doned key and the new one,
as-
as-:
No. 100.
i
I
i
i
^g-
^
a link between the aban-
^
^
^
•-4=F^
Em
t
J
Here we have a
and perfect cadence.
full
The rhythm onfy
leads us to expect a continuation f and immediately we continue, in a foreign key. what right f Because this continuation is a
By
phrase by
a&
itself^
it
were
}
new
a
pfece which takes
up the thread
of the previous phrase at a different place, and perhaps in
a
different sense.
We
ought
parts, after
We have
which they are taken up by the singers or choruses^
may
There
is
preceded by a
finished,
— Since
full
third,
mental tone, third, to
which
it is
tonic triad,
the voices- them-
in
Nos.
1, 2,
and
3, the stationary
tone
cadence, and consetjnently, the musical period' required.
is
and
fifth,
inherent.
we have been
by
not any absolute rule on this point.
no transition
fundamental,
Neverthelessj such
happen, as to be introdniced
Observation. is
with regard to the modulations in this
exemplified them here in this way.
occurrences selves.
to remark,,
they are generally introduced by the accompanying
section, that
The
tone retained can be the
of a tonic
triad,, and the fundaand seventh of any seventh or noneefaordy
fifth
Again, in Nos. 6 and
led, beside
7, the tones to
which
being the fundamental, third, or ffth of a
can be a part of a dominant seventh or nonachord.
Nevertheless, those exemplified in this paragraph are
the
more
usual, and deserve a special practice on the part of the studient.
§ 4.
We can
Passages of Dominant Sevenths.
consider the dominant seventh as a major triad with an
105 additional minor seventh, and change every triad into a dominant
chord, as
^ ^ ^31W
I
\rsr
But, since every dominant seventh already contains within itself a triad,
we
are free to reject the triad
—which
follows the dominant
seventh in the above example-^and to have the dominant sevenths following each other immediately, as
No. 101.
WD r
6
2
*
m3^^Q.
.^
T
r
g
g^
m
I
I7
7
I
I
V
7
L
[!
I
T
=^
ii^
T
H
^^
LT
1
'I
l^i
>J
^
'^
'%
?
^ir=^=p^j=j==^J2^^=Z^i pti^is
I^ J
feU
~IP^
I
I
y^ H
[7J
k
J
it
m
sJ
6
i
*
-
%
«S
f'
""
This example affords us a specimen of remote modulations, as given by the passages of dominant chords. at the close of the third bar,
and we see in
The it
succession begins
every tone follow the
regular progression, with the exception of the third, which descends
a chromatic step, and becomes the seventh of the following chord.
106
We it
confined the above passage to major
would have led us
avoid this encumbrance,
we now
changes, which
^,
because, if continued,
encumbered with signatures, or to would force us to call on enharmonic
to tonics it
intend to avoid
;
as
it is
our design
to treat
separately the enharmonic modulations.
We will
now
lead these passages in an opposite direction.
foregoing example, by changing the resolution of the third, a
new dominant
seventh and a
new
In the
we
and as the subdominant has been successively changed dominant seventh,
Our
object
now
to elevate the
we have gained
is to
give the third
the
fifth is
a
downward
a
new
its
seventh by a chromatic
instead of progressing
gqf
key, that of the subdominant
flat
at
into
a
every resolution.
usual ascending motion, and the fundamental tone,
step-;
fifth,
has
to
move up
a full step,
retained stationary on the following chord, and the seventh
moves up by a chromatic
step.
At
this time, too,
a dominant seventh to a dominant seventh
second seventh
is
the fundamental of the
inant seventh gives a
new
;
first,,
we proceed from
but the tonic of the
and every
new
Aoxs\,
sharp, as
No. 102.
dEE^E^dfe^: fei =^
i
a
-^
z i f—fcrixiq F-+r^
^
^gi—
§i Lastly,
iE
we
proceed
to
some other modulations, given by the
ipant seventh, deviating from its usual course of resolution, as
dom--
107
No. 103
i_t V* ' » Muting— te=^:
iESa^sEi^SstS i
\Lt
'^'^t-t-
u
pE^gj^^ai ^ ^=^ M^iJ:
i f =^ KE T
I
I
^¥ie^^
rf
I
I
i
^e
P^ At A,
^tJ=^: ?3^
i-±
=i^
?=SS:
-i-y-
the dominant seventh resolves to f, a, c, eV, which is the might as well have to the key of Sfe major.
We
dominant seventh led
it
to
fe?=:.=qh?==iCi«:
a, c, efc
moves up
or to a,
c,
to a, the third
f.
In these resolutions, the fundamental
and the
stretches over to the next chord.
both to
fifth
c,
In the case of a,
and the seventh c,
e^,
it
descends
a step to 67.
At B, the dominant seventh resolves
to
o^
c,
e^.
Here,
all
the
tones follow their usual course, except the fundamental, which goes
up a minor second,
to ak, deviating
from
Properly speaking, the modulations in ing else than interrupted cadences keys,
we had
to place
;
its
downward
this
motion.
paragraph are noth-
but, as they lead to foreign
them under the head of modulations.
108
The Diminished Seventh.
§ 5.
design, here, is to give a full account of the diminished
Our
seventh, as far as
it
helps to carry out remote modulations.
another place, in the
view of
different
We
enharmonic modulations,
we
In
shall give a
it.
have already remarked, on page 41, that this chord may Thus, the diminished
be used both in the major and minor modes.
seventh
Every diminished by a chromatic step, may
belongs to e major, as well as to c minor. seventh, by depressing the leading note
be changed into the dominant seventh of the parallel major key. Then, in c major, if we lower b a chromatic step in the diminished seventh
major
b, d,
f, a^,
it
becomes
Thus, from
et".
c
J]',
major
^^
\
d,f, a^, the dominant seventh of
we may suddenly
Mi^\%
pass to
major
II
But since the diminished seventh can be converted nant seventh, by depressing the leading note,
e|j
it
into
a domi-
by
follows that
ele-
vating the fundamental of the dominant seventh, by a chromatic Thus, in the present step, we convert it into a diminished seventh. instance,
such a change enables us
to
return to c major
;
as,
f^wd^t^i^ Let us now enter
into
some other
interesting combinations of
this chord. 1st.
The
leading tone being unaltered, if
we
step (chromatic or diatonic, according as the case
three other notes of the diminished seventh,
we
elevate a half
may
convert
be,) the it
into
a
109 dominant seventh, whose
tonic
is
a third aibove the preceding one.
Example
^^^^^=% We go from the
fifth
major
ic
The
2d.
to e major.
third being unaltered, if
we
elevate the leading tone,
and seventh, a half step (chromatic or
diatonic),
we
obtain
dominant seventh, whose tonic shall be a fourth below, or a above the preceding one ; as •a.
i From major
c,
The
3d.
fes-
i
^\>sf>-
or major
fifth
we go
eV-,
to
being unaltered,
tonic is a
4th.
te^
to
major
5^.
we
we go
step,
First Alternative. grees
;
we have
regularly three tones
we have two
alternatives.
All the tones ascend, but in different de-
the seventh three times,
ascend, sometimes a whole
diminished third.
tonic
while alternately another remains station-
In the following combination,
ary.
whose
as.
to dl? major.
In the foregoing combinations,
moving up a half
;
^
^^c
elevate the three
obtain a dominant seventh,
shall be a half step above the preceding one
From major
we
seventh being unaltered, if
other tones a half step,
as.
;
^ 1
:#
izs*:
from major c
The
we elevate the leading note, we gain a dominant seventh,
whole step below the former
i We pass
major g.
if
the third and seventh, a half step,
whose
fifth
ft
half step ; while the three others
step, or
a half step, and sometimes a
110
The
list.
seventh ascends a half step, and the three other
tones a whole* step
;
as,
i
-^qS^
f From
c
we go
major or minor
d major.
to
All the parts ascend a half step, and lead from e major or
2d.
minor 'to g major.
i iln this
^
^^ gs^44^
i
example, the diminished seventh
transformed into
is
another diminished seventh, instead of changing into a dominant seventh. eV,
There
is
also a slight blemish in the resolution, in
and d in the tenor
Though
base.
as the
first fifth
much
better to
part, step
by
real fifths with
these consecutives are admitted
a and
by some
which of the
theorists,
comes from a dissonant chord, yet we believe it is avoid it, which is easily done, by causing the dimin-
ished seventh to resglve to the dominant seventh of the
mental, before reaching the tonic
i 3d.
g
;
thus
same funda-
:
i^
S
^^g-
A
The seventh ascends a whole
=F step,
the leading note a
diminished third (or enharmonic step), the third a half ^^Pj and the fifth a whole step ; as,
i ^^^ from major or minor c 4th.
The
to
3
major
W
aV.
seventh ascends a whole step, the leading note a
half step, and the third and
fifth
a whole step
^^^^ from major or minor
c to
f major or minor.
;
as,
Ill
Second Alternative. three
All the
tones descend;
times a half step, and once a whole step
sometimes a whole
the third and
fifth
the seventh
the other tones
step, at other times a half step.
The seventh
1st.
;
a half step, the leading note a whole step,
a half step
as.
;
^^^^^ from major or minor 2d.
note and
seventh a half step, the third a whole step, the leading
fifth
a half step
i from major or minor 3d.
d major.
c to
The
The
step, the fifth
as.
;
E^
i2=?=
c to
=g
f major or minor.
seventh a half step, the leading note and third a half
a whole step
;
as,
^=te^ m i ^^m
m^
-t-
We
go from major or minor 4th.
i from major or minor Lastly,
sequences, to
c to aj? minor.
The seventh a whole
major
Nevertheless,
it
is
flats,
when
it is
all
or
us
the semitones of the
not usual to carry such successions
beyond three or four chromaUc out with
as,
cl'.
we can use the diminished seventh in passages They may enable as we did the dominant seventh.
run upward and downward, through
scale.
ple
the other tones a half step;
^^5fe
J25»=
c to
step,
steps.
These sequences are carried
intended to reach some
:
No. 104. Upward.
^f^^^
flat-tonic.
Exam-
112
No. 105.
^ They may aimed at;
Dovrawatd.
^
\b'
i
fe.^
be carried out with sharps,
if
some sharp-tonic
is
as,
No. 106. Upward
i No. 107. Downward.
^^^^^ we
In No. 104
are led to the
key of/ major or minor;
in
No.
105, to the key of i^ major or minor; in No. 106, to 6 major or
minor; and in No. 107,
a major or minor.
to
ished seventh leads to the tonic, yet the
change the
last
fundamental
changed
;
which
into the
is
easily effected,
example, the
for
part,
is
necessary
have
to
to
all
a.
the parts ascend or descend
by half
are enabled to ascertain the regularity of each at the succession of the semitones.
nothing more to be said on the subject of remote
We
modulations.
to
^m
If
by only glancing
There
is
by lowering the seventh a seventh of No. 107 can be
^
In these sequences,
we
last
dominant of the keys minor or major
^m. steps, so that
practice
diminished seventh into the dominant of the same
Thus,
half step.
Although the dimin-
common
are conscious of having omitted nothing that is
the thorough training of the student.
Finally,
we
remark, that the modulations arising from sequences of
diminished sevenths, belong particularly to the instrumental depart-
ment ; and,
first
of
all, to
piano music.
require, to be tolerably brought about,
demand
the greatest
acumen
in
If adapted to singing, they first
rate singers, as they
the sense of hearing, in order to
113 keep firmly
to the
Of
pitch of the half-step progressing parts.
Qourse, they are but seldom employed in choruses, except in the
high combinations of the stage music of the grand opera, in which the requisites of large performances are found abundantly.
all is
who
It
know
well the ability of those
are to be entrusted with the care of
performing, his compo-
the province of the
composer
to
sitions.
Enharmonic Modulations. Sounds, which are identical in pitch, but placed on different
Thus,
degrees, are called enharmonic. as forming a uniform sound
that
;
placed on two different degrees.
ctt
and
dl?
are considered
equal as to pitch, although
is,
Mathematically, these tones are
somewhat higher than
d\>. But here theorists have followed mathematicians, who, when they find in an operation
not identical
cjj
;
is
a fractional number so small as ence, neglect
Such
result.
it,
is
the case here.
enharmonic sounds garded
;
to
and proceed as
is
and by doing
make
differ-
they had obtained an exact
The
difference in pitch between
so minute, that so, for
but an unimportant
if
it
is,
indeed, to be disre-
a small difference of pitch, which*
is
overlooked, remarkable advantages have been gained, both in the theoretical
monic
which
The word
and practical departments of music.
enhar-
derived from the Greek, enharmonikos, the meaning of
is
is, fitting,
According
in accord, or harmony.
to these notions
of enharmonic sounds, the following
changes take place
The Extended Second.
The Minob Thied,
is
equal to
— ^ry ^^
is
equal to
/U-
Enharmoni- ~%
i
cally
-fe-^
1^
"p-
=5fe®^
The Diminished
The Majob Third,
i -^
-#=s
The Majoe Second,
The DmiNisHED Thibd,
i
1
-
is
equal
-I
Its:
Foiieth.
or 11^
114 The Pebfeot Foceth.
The Extended Thled,
i
is
equal to
-^-
i The Majob Third.
The Diminished Fodbth, is
I
equal to
orHlt^h
The Peefeot
I
The Extended Thied.
t
is
The Diminibhed
i
is
The Diminished
or-
is
equal to
^=
^
ft*
The Diminished
Fifth, is
The Extended
equal
Sixth.
1
Wsi The Minoe
is
Sixth.
to^^
i
or-
The Diminished
The Peefeot
Sixth,
E^
i
equal to
Fifth,
^
I
-
is
equal
Fifth.
"$-
IS*
The Minos
The Extended
Sixth, is
or-
<*
The MijoE
pr
^
^
Fifth.
-bs-
The Diminished Seventh. is
-J^
<*>
equal to
I
Sixth,
The Extended
i
fe
I
Fifth.
The Extended Foueth.
i
i
equal to
Fifth,
^ The Peefeot
i
*
equal to ^Bk-
The Shabp Fodeth,
P
-JT
Fotteth,
i
1
equal
-i
E^ The Minoe Seventh.
Sixth,
i
is
equal to
i
=^s
115
Of
these enharmonic changes, the most used are those of the ex-
tended second, of the major first
sixth,
and of the extended sixth
;
the
being changed into a minor third, in the enharmonic combina-
tions of the diminished seventh
the second,
;
becoming a diminished
seventh, and the third being changed into a minor seventh in the
transformations of the extended sixth.
above
in the
list,
We have liliewise mentioned,
the interval of the diminished third, so pleasing in
melody, and, perhaps, improperly banished from harmonic uses.
had two reasons
doing so:
for
first,
We
because the diminished third
is
sometimes used enharmbnically, and changed into a major second second, because
its
inversion, the extended sixth,
Rossini, notwithstanding the rule
which
Maometto Secondo,
mocked
sufficient, in
in the overture to
The mischievous
several other works.
posely
frequently used
prohibits the use of the dimin-
ished third in harmony, did not scruple to use iu his
is
Moreover, one of the greatest composers of the day,
in practice.
at the prohibition.
our opinion,
to set
it,
and most happily,
La Gazza
Italian
seems
Ladra, and in to
have pur-
So great an authority should be aside, as an antiquated rule, the
exclusion of the diminished third from harmony.
The two streams from which enharmonic changes
flow most
abundantly, are the diminished and dominant sevenths.
The Diminished Seventh.
A.
We
have already, on page 108, given a
treatise
on
laying down the matter of remote modulations.
when now finish up what
The hence,
it
<
this chord,
We
shall
has been partly done there.
diminished seventh consists exclusively of minor thirds follows that every inversion contains an extended second
and by changing alternately this second into a minor third, such inversion forms a new diminished seventh, affording the composer the
means of getting three Let us take,
The
first
for
different keys.
example, the diminished seventh
inversion,
i
w-
116
by
the
change of
^
becomes a new seventh,
into a^,
W^:: and enables us seventh
is
to
modulate into
able to
leading tone a half step, the
minor
c
;
and, as every diminished
become a dominant seventh, by lowering the
we
are subsequently enabled to enter upon
key of elf major.
No. 108. C
Minor.
i?=^^
I
:g= -m:
@fe
—
JS
r
a
r
g~
•
r-^
'i
s— '—•--(a
-I
''
e- ^i
;^
'I
iEE
^
^^
Eb Major.
i^
fet
^
i
I
'^1
I
UMi=^te^-4^ =
The second
5 ^
i
r ?
'si °
g
e
S
l^::
1
I
inversion.
^ by the change of both g^
into
oj?,
diminished seventh.
^
and of i
into
cl*,
we
gain the
117
which
affords us
the modulation to e^ minor or major, and sub-
sequently to the parallel key,
No. 109.
^ major. Eb Minor.
^^ Trrr ige
J:^
^^
1
^
^ G[j
S-l
^
-
I
i
n
Major. I
id=^^=^i^ir^'=T^
I fe
f^
^5
t-F^I i
The
is
third inversion,
enharmonically
by which we get the way open
to
f%
minor or major, or
to the
major parallel key, a| major.
No. 110.
E
i
i%=F
I
m ^^
^m A
Ma]or.
fct
:S--3r^
y=
f
=?==
118 F^ Major.
i^
ite
w
^=
a^i^ ^ *s^
«
A^ ^ jipT^y ss
It
is
- s^
iS
not always necessary to realize the enharmonic change.
The composer very modulation in view
;
often understands
but then
it
is
it,
and reaches directly the
necessary
to
give the seventh a
certain length, especially in the quick motions, that the hearer
comprehend the modulation
No. 111. MOBZEATO.
;
as.
may
119
encumbered with
This
accidentals.
passages, or sequences
;
is
particularly the
case in
as,
No. 112.
i^^^^^fc m^ At
ks-
?
the fourth measure, the dominant triad ought to have been
followed by the chord, gif major, with eight sharps, which would have involved us in an infinity of signatures. Instead of this, we
have cnharmonically changed the above chord, d^ b^,
which has brought us
keys with
into
(at
A)
into
e\>,
g,
less signatures.
Sometimes, however, the enharmonic changes increase the numIn general, the enharmonic
ber of signatures, as in Nos. 109, 110.
modulations must carry a meaning with them.
wishes sharps
to
may
assist
duce an opposite
mony.
If the composer
work a more lively character, the keys with him in carrying out such a design. Flats proeffect, by imparting a gloomy tint to the har-
give his
Let us now pass
to
The Dominant Seventh.
B.
In the synoptical table (previously given) of the enharmonic we have seen that the extended sixth becomes a minor
changes, seventh. that
the
On
the other hand,
extended
—
we have been
sixth carries with
informed, on page 73,
itself
a major third and a
which constitute the dominant perfect fifth dominant seventh into the the change-^of the wherefore, ; seventh Of course, when thus extended sixth, comes in quite naturally. ^just
the
same
intervals
chani^ed, the dominant seventh follows the rules already laid (pp.
73 and 74) concerning
interesting modulations, if
seventh of the principal
this sixth.
we key,
down
This again affords us many
consider that, besides the dominant
we may
ones, and change them enharmonically.
use those of the relative
120 In the following examples, the enharmonic note
is
according to the directions given above, No. Ill, on page 118
No. 113. From C
to
B
Minor.
^?3=^i
^
wI
I
or
From C Major to B
i
ft^
Major.
u
pW%.^=4t
m
1 From G
i^
to
A^ Magor.
#^^3==£
-o-e-
^
^ ^^
mS ?
I
From C
i 9i=f^
i
D
to
E
Miyor.
Vr-h^ I =^P
M^ Ij
J J
I
l
~^
121
At A, d,
e{|,
the dominant seventh represents the extended sixth, which resolves into the perfect cadence of minor h.
At B,
the
same change has taken
g,
h,
place, with this exception only,
that the extended sixth (minor seventh) resolves into the perfect
cadence of h major.
At C,
the
harmony goes
to the relative
key, a minor, of which the
dominant seventh changes enharmonically yfe, aV, ck, d,
which,
at the fourth--
into the extended sixth,
measure, changes into
ek,
all, c,
followed by the dominant seventh of a]? minor.
At D, the harmony turns ically
its
to _/ major, which, changed enharmondominant seventh, closes with the major key, e major, with
four sharps.
Now, sixth,
it
since the dominant seventh can be changed into an extended follows that the latter also is capable of becoming, in
turn, a dominant seventh.
In
this case, the sixth
ceding key becomes the dominant of the following
No. 114.
i:
its
degree of the pre-
122
i4 m I f
^i=i
-fTi"
'T
r
i
E*^
§5tt
i
zoa
the seventh measure, the extended sixth, after being heard in
At
the preceding measure, in
its
regular treatment, changes enharmoni-
oally,
and brings suddenly the harmony into the key of
This,
when
properly done,
is
These few examples are enough
effect.
to
major.
give an exact and
above chords, so far as they
sufficient notion of the
d|?
susceptible of producing a very good
performing enharmonic modulations.
They
may
be used in
are capable of produc-
ing a great variety of effective modulations^ in the hands of an able
musician. shall
We
need not dwell any longer on
now touch what may be
call so
and we
Arbitkary Enharmonic Modulations.
C.
We
this subject,
called
such modulations as are not performed by the two
preceding chords, but merely depend on any other chord, or even
on any sharp or so as to enable
flat
which may present
note
him
to
quently, he takes this note, time,
and then changes
half-cadences
afford
itself to the
it,
the
makes
it
according best
to his
fancy.
opportunities
to
Cadences and
accomplish such
No. 115.
-•—p-
Fre-
stationary a certain length of
modulations.
m^^^^
composer,
carry out an enharmonic change.
-r-r-^
123
^-J^M
$
ffV^TY nff g?=yTr^= -4-
The first
first
period of this example closes with a half-cadence.
part,:of the
at the
same
5
remaining on
time, the whole
ajL finally gives
it
up
for &!?;
mass enters upon the chord,
Sometimes the whole chord enharmonic; as,
transposed into
is
its
J!?,
d,
The and,
f^.
corresponding
No. 116.
pg^fe^^^i^^^i J.
.Jz
1^:
Tr
1^ ^^^- S5 s Efe
§ffi At
£:
#
the end of the second measure, the three tones of the chord,
eK take their corresponding enharmonics that is, the chord, eK becomes g^, J|}, dl^ the dominant triad of cjf after which, the harmony gets into the key of major a. Unisons may, in many instances, afibrd effective means of opera-
fflj?,
c,
ffll',
c,
;
;
ting enharmonic changes.
The
composer, in such occurrences,
concern about harmony, takes hold, of some melodic design, and develops it with the enharmony, in full vocal or orches-
giving up
tral blast.
all
Example
No. 117.
^^^^.^^^M 5^E i ^^^^^ 'CJ
124
^.^^^^j
i^p^^WN^ £MXn ^^^^^^^ #=
ig 1^ We
have
third of a
on any
new
tonic
;
tonic,
that
we can
is,
responding enharmonic, in order tures, or to impart
—
r-t-T-
final
cadence, or even
take this tonic as the major
modulate a major third below the
This modulation
preceding key.
i^—1---^— -
on page 99, that after a
stated,
after a repose
—
more variety
to
may
sometimes require the cor-
avoid an encumbrance of signa-
to the composition.
Example
:
No. 118.
I
^^h^^d
-^-fi I,
»&
=j-r 6
I
'
'^
m 9^M
'
r'
s
I
r"
5
p
±^=^
-rr
^^^ ^ J
:^
E^
± ^^m^ ^^E^^ J
=w
I
:i=i-
ji
i
44i:^^J-i •g
§i 5
5
L
C
1
(
E
ig~
^I
I
I
I
125
As
it
results from this example,
to the preceding tonic again.
(ninth and tenth measures)
^,
This
of the tonic,
happens very often that a ered, and mentally changed into It
enharmony may lead us back is effected here by changing
flat-tonic is
e,
into
aK
enharmonically consid-
its corresponding sharp one, which becomes the leading tone of the tonic, a half step higher. For instance, from a{» tonic (being mentally changed into gji) we can immediately go into major aj^ (three sharps), from dl? major to
really
tit]
(two sharps), and-so-forth.
An
example
will illustrate the sub-
ject.
This does very well in instrumental compositions. piece
it
would be proper
to
monically, becomes a sort of leading note
No. 120.
^
^s
J..
:l
In a vocal
keep the tonic stationary, which, enhar-
d.
±
A
;
thus
126
m
fc=d:
mm
4t"
_
2
6
Here, the three tones,
h^,
next
singer
never
who has
to perform'
h.
In such occurrences, the
such a part as that of the treble here, ajt ; and then the partners up the chord, counting the tone of the
sing these three tones, as
fails to
of the treble mentally
fill
treble as the third of the
party doing so, that they
dominant triad of hh major
may
realize in their singing the tone intended
The same modulation can
the whole
First, the flat tonic
by the composer.
be carried out in two other different
may
be made the third of a dominant
second, the fundamental of a diminished seventh.
we
;
not mistake the pitch of their respec-
In the execution of enharmonic passages, good singers
tive parts.
ways.
measure, are really the
to the third
leading tone of the following key,
obtain the
same
tonic as in the
But
;
in both cases
The
two foregoing examples.
following will give an illustration of both cases
No. 121. God's word will
In
I¥W^
S3 Eg
i
re
- joice,
In
the
=#^
r -^^ .
word will
God's
word
—
will
I
re
-
fti^
sa jgpg^E^E^^f fe
word will
joioe.
'f
In the Lord's word will
I f==F=pr±^T=^PT .i_i^_
^
I""
comfort me,
I
ft.t
the Lord's
Lord's
^=r^=;h=hf^i
i^
In
m
I
lA^ ? comfort me.
S^i =F^ -d-
-d-
-^z~f~w In the Lord's
127 comfort me,
In
God's word will
m
-J-^^r-4 Si^i^ ^w ^^^^ —r^
1
i.fe^^J
|i
e^
Jw
J'
_i
^^^^S^ •-^ J
J^
^v
word
will I
I
re
-
comfort me, In
In
joice,
word
God's
the Lord's word
re
s
me,
-
In
joice,
the Lord's word
In the Lord's word
will
s
Ji i
J
—
J
=e^
In the Lord's word will I
me,
At
the fourth
third of
the
passes from
el'
from which
it
into
g:}f,
measure of
dominant to
et|.
this
triad,
example, the 6t[,
The current
turns to aV.
d|,
4: com- fort
me.
com-fort
I
^^m. S s^ J
will I
J_J. ^^
-JU-.
will
com- fort
will I
M^^^^ii I
[|j
tonic,
/j|,
^
^s-
J
J
i^E com -fort me.
e{',
becomes the
and the harmony
of chords leads "back again to
et",
This tonic (thirteenth measure) changes
the fundamental of the diminished seventh,
gj^,
b^, d, f,
which brings the harmony from a^ to a minor. Finally, all the parts verge to e^and get the final cadence in the principal key.
The foregoing remarks, with the examples, have unfolded the whole matter of enharmonic modulations. For the practical use of them, we refer the student to the works of the great writers.
128
They
will give
him more information on the
tions in general, than
heaped
The
On
piles of volumes
subject, and modulaon harmony'
Pkdal-Point.
pages 217 and 218 of our author, the origin and object of the
Pedal-point have been fully unfolded.
what proceeding we can procure a
It
remains now
The
pedal-point.
to
say by
proceeding
harmony above the sustained tonp should be considered Viewed thus, it must have a regular base as if it were to be performed without the assisting pedal. This is required, because the parts above contrast by their motion to the stillness of the immovable tone below. is this
the
:
as an independent whole.
Now, from what source
shall the chords be
drawn ?
From
those
keys that are nearest related to the pedal, avoiding those in which, if used, the
common
tion or depression.
of the
first
and
last
tone would have to be altered, either
Usually, the sustained tone
chord of the harmony.
is
by
eleva-
the fundamental
The
following
is
sample of a pedal-construction
No. 122.
^A^^ -^Ai^^ ^ r^TTfTf^ ^=^-
Ti
g£E 4
5
'.
5
5
-
E^
irh^
i t
-
F5b=t
a
129
;
I
^
i
-o 1
^ TTa 1-
U
6
i
f= I
—g=aP=f
f-
r
^:
We
find here all the requisites of a correct
fulfilling
the part of the base.
the voice building a
still
Now,
harmony, the tenor
the pedal-point will add to
stronger link and support.
No. 123.
j=j^^d=j=d^.i=M^=j=^ i ^f=n=ffTTfv^r^~r~r--
130
*
i a
)i
^
i
The
pedal
I
I
may
s
:^
Enough has been
said
just laid
on
down
^
z
s
also be properly placed on the tonic,
same rules which have been
dominant.
„9
8
i^
=«i==»
»l
to the
„9
»5
»i
and submits
for that of the
this subject to require
no
further explanation.
Let us now come
to
another kind of sustained tone, which
called the inward or middle pedal. tions,
It
an essential part of the chords, which
outer pedal.
The
reason of this
is
is
ought to be, with few excepis
not the case with the
obvious.
In the latter, the
remoteness of the sustained tone mitigates the harshness of the tones foreign to the pedal closely against each other,
unpleasant intervals ;
so,
;
but in the former, the discords dash
and nothing indemnifies us
intended to express a design of the composer case, they tone,
must be removed as
and buried
The inward
for these
they must be avoided, unless they are ;
far as possible
and even in such a from the sustaining
in the centre of the parts.
pedal
commonly
stands upon the dominant
;
as,
131
No. 124.
-/-.-^-^i
I
»
ih
^=±
In the following,
we make
from the very beginning
the inward pedal partake of the chords
to the
conclusion,
afforded to the pupil an instance of
which
—»
is
laid
what
is
by which we have
called a plagal cadence,
on the subdominant, while the perfect cadence
placed on the dominant.
i
^
~©
—
7
r
»
•—r-3^
--^-^ PLAQAL CADENUB.
is
132
to the tonic,
conclusion
tlie
harmony
the seventh measure of No. 125, the
At
suhdominant
is
from the dominant
is
We
to the tonic.
attention of the student to this kind of cadence,
the most able writers, and
leads from the
contrary to the perfect cadence, of which
which
is
call the
used by
sometimes most successful and
effec-
tive.
Sometimes, the pedal point consists of a single note.
an occurrence, every step of the base leads nant,
which becomes the basis of a pedal a harmonic design
to develop
;
to
point.
a
new It
In such
tonic or domi-
may serve, then,
as.
No. 126.
f ^ m^^w rwn ^E^=?^ ?
i
^S44^^44m ^3
f We have said that
the inward pedal
1—1 is
placed on the dominant.
Nos. 306 and 308 of our author, in consequence of the signature, seem to have the sustained tone upon the tonic. But the ib in No. 316, and
f^
spite of their
There
is
in 318,
change these tonics
into real dominants, in
ending upon the tonio.
a conclusion of the final cadence very
common among
composers, which must be referred to the pedal-point on the tonio.
Here
it is
(at
A)
133
No. 172.
^
JAIN T e:*
.snj gi
g*
fli
This
is
nothing else than the dominant seventh stretching over
to the tonic.
Such a cadence
is
comntionly
Andante and Andantino, but seldom motions.
T
J
^s
^n.^:
made use of
in the Allegro,
in the
and the
like
APPENDIX
H.
This treatment of the diminished seventh
The
f
below.
but
is too loose, altogether.
(former seventh in the nonachord) should meet e a step
In the middle parts,
when
in the base,
it
it is
sometimes made
ascend a step
to
must be resolved regularly.
May
be, that
such a resolution as given here by the author, occurs in the works of good composers
;
but this
from books calculated to
be taught according
for
he must never be allowed
c, d, e,
a negligence which must be removed
to the rules
have mastered the highest 292, at
is
musical instruction.
we would
to break, before difficulties
i
student ought
he
is
acknowledged
of the counterpoint.
prefer to read thus
JO.
z^sz
The
of the severest discipline, which
-2:
i
to
No.
APPENDIX Suspension First.
—h
is
I.
subject to the following conditions
must be prepared;
exist in the preceding chord,
e.,
i.
must same voice
the dissonant tone
and must be given
to the
or instrument which forms the suspension.
Second.
—
must be resolved
It
and the chord
to
which
it
i.
;
stretches
the discrepancy between
e.,
must
it
and the suspending
cease,
voice or instrument finally enter upon the proper tone of the chord.
Thieik
—The preparatory tone can be
than the suspension tone.
sometimes
may
It
the whole measure.
fills
suspensions are equally good
longer, but never shorter
be, too, equal to
it.
The
latter
Accordingly, the following
:
No. 128.
i
f
At D, is
1 r
3
s^=f=
r
the preparatory tone
equal
right.
TS-
%^
^.
i it is
?=E= i
;
at
But
f is
F, the suspension
r at
E,
the whole measure, and
all
longer than the suspension fills
here.
^
No. 129.
i
^-S-
=j
-J4^i-^
*
f
I
;
136 there
The
no suspension.
is
tones,
d, e, (at the signs +)
c,
being
shorter than the tones following them, the minims are merely appog;
which are quite equivalent
giatures,
to this,
^
No. 130.
EE Fourth.
—The
-^
^^^ may
preparatory tone
be placed either on the
accented or unapcented part of the measure
must
tone
fall
;
but the suspension
on the accented one, and the resolution on the unac-
This
cented part.
&c.
is
peculiar to suspensions.
In
this; also,
they
disagree with the chords of the seventh, in which the dissonant tone
can be placed anywhere
in the
measure.
Hence, the following sus-
pension, and the like, is wrong,
P^^ W r
4-
i
in
which the preparatory tone
suspension In the
falls
on the accented
lies
part,
and the
on the second beat, and so escapes the accent.
common
2> and .2., the first beat is In the quadruple time, the first and
double time, J^,
accented, the second
is not.
and fourth not. In triple time, and second beats are often accented, the third is not. In
third beats are accented, the second
the
first
the
compound measures, the accents are
distributed in the
same way
but in slow movements,
with the simple ones, in quick motions;
such as Andante, Andantino, Grave, Adagio, &c., the suspension
When there are four of them in a measure, as in 2 ^ the accents are divided, as they are in the comcan be placed on quavers.
mon quadruple
time
;
i.
e.,
second and fourth are not.
the
and third are accented, the compound, A, A., -g-, 1 2^ jn
first
In
which the ternary
division of quavers takes place,
are
in
distributed
as
triple
time;
quavers are accented, the third quavers applies, of course, as
-6.
and
-S.
;
i.
e.,
is not.
the
first
What
to the crotchets in the
is
the accents
and second said
of the
compounds, such
but they are less used than the former.
Examples
137 of suspension in compound time will be given on
pages,
150,
161, 162, 163.
Fifth.—The suspension
tone must form a dissonance with one
of the tones of the suspension-chord.
This
is
the sequel of the preparation and resolution, which imply
necessarily a dissonance
and
pension.
;
for dissonances alone
Then, when there
need preparation
not discord, there
is
not sus-
Hence, the following passage, in which there
is
not
resolution.
discord, does not contain
Na
is
any
any suspension.
131.
^
•+^=^
1
But the next
No. 132.
i ^^^^^^fe is
an example of regular suspensions, and agrees with our direc-
tions
for
;
suspension does not
lie
chord stretches over into another, but in the discord
The
itself.
in the fact that
to
which
it
is
a tone of a
not indigenous,
*
rigorous application of the principle of resolution, which is
peculiar
to
dissonances, excludes forcibly
by an ascending
resolve
step;
i.
e.,
such suspensions as
suspension from below.
It
may
be replied, that there are instances of suspehsion resolving from below. There are indeed passages which, at t"he first sight,
seem
to
notions
contain,
now
suspensions.
such suspensions
familiar to us,
The
following
but "by referring them
;
will be
it
is
;p'lain
an instance of the kind
• Reicha's Treatise
to the
that they exclude
on Harmony.
i
real
138 No. 133.
=w=
1
ii
^
ia;
^ ¥
There
is
?
1 1
i
no suspension in
this.
7
!
?
I
¥
At the beginning of the
second, third, and fourth measures,
we have
first,
a short tonic pedal
formed by the dominant seventh and uonachord major and minor, following
usual
their
way
of resolutions above
the
sustaining
Here, again.
tonic in the base.
No. 134.
fci
m
i
LJI
I
^m
fesHg at the
beginning of the
first
h forms an appoggiature
;
of the second measure, of
measure, no suspension can be found.
so does the
the
same tone
alto-part.
As
at the
beginning
to the last, there is
again a short tonic-pedal, with dominant triad.
The above exam-
ple could be changed, as follows
'
No. 135.
i ^ i ^f r
which represents exactly No. 134.
When
^ passages of ascending
dissonances cannot be traced either to the pedal or to the appoggiatures, they are inexplicable.
We
should remark here, that the
great masters, in the treatment of voices, have seldom indulged in
139 discords resolving from below.
Handel has not a single example
of suspension resolving from below. few, if any.
is
It
Mozart and Haydn have very
true, that in their quartets, quintets,
phonies, such dissonances are found
now and
then
;
and sym-
but
all
these
instances can be referred either to the pedal-point, or to grace-notes.
Moreover, instrumental music
is
a free kind of style, which admits
of more liberty than the severe one which must now be the main object of the student.
Sixth.
—"When a tone
of a chord
is
suspended,
it
can never be
introduced simultaneously with the suspension tone, except when it
forms a ninth with
as
it,
when
the fundamental is suspended in
And, even when the retarded interval should
the upper parts.
have a necessary and determined stepping upwards or downwards, (such as the leading note in the dominant seventh, or the diminished triad and the seventh in
never allowed
to
the chords of the seventh),
all
it
is
any part whatever, the retarded
introduce, in
interval simultaneously with the suspension tone.
No. 136.
A
-^
I
I At A,
s
6
g
J -
I
8
the alto part (second measure) introduces the
suspended
tone simultaneously with the suspension-tone, so as to form an irregular and harsh interval.
But
at B, the
suspended tone, though
introduced simultaneously with the suspension, gives a
regular
interval of a ninth.
Seventh.
—Suspensions
successions of
fifths
gate such successions. able
are
wrong when they
and octaves,
fall
on a faulty
for they neither correct nor miti-
Hence, the following harmony
is objection-
:
No. 137.
^
^ r
for there exists a succession of fifths
r
between the tenor part and the
140
which
treble,
middle part
apparently disguised
is
at
C
;
but if
we
by the suspension of the
leave out the suspensions, as in D, this
The harmony
succession of fifths shows itself naked to the eye. not
more admissible
have
is
We will
in the former case than in the latter.
correct in the following
it
No. 138.
^U—^
i Here
also
No. 139.
m there
kh-«
Jf J
,1
JtJ-J
rff "W
ff
an example of wrong suspensions, as they arise from a
is
succession of octaves, as
it
can be seen
We
with the suspensions at F.
E, which are
at
still
these preliminary directions, which, if observed, will enable
many mistakes We now pass to
avoid a great portance.
which
in a matter
The Employment of the Suspensions
1.
Thus
far
we know
only what suspension
depends, having postponed
tions
it
with
its
nature.
Now we
have
is,
is
to
in the Triads.
and on what condi-
we became
use
to
proceed farther, and
till
him
of ma,terial im-
its
methodically, we shall use the suspension,
§1.
worse
call the attention of the student to
first in
acquainted to
do so
the
Uninveeted Triad.
Every tone of a triad can be retarded by suspensions. With regard which when retarded gives no dissonance, but simply a
to the fifth,
chord of the sixth,
we
advise the pupil not to suspend
the suspension tone be introduced simultaneously with
pended
at
a distance of a ninth, thus
:
No. 140.
i
4^ *T
ST g
it,
unless
that
sus-
141
When
the third
perfect fourth and
suspended,
is
fifth,
it
gives a chord consisting of a
called i i:
No. 141,
I
5
The fundamental can be suspended parts, the base introducing the
in
two ways
by the upper
:
suspended fundamental simultane-
ously with the suspension tone, or by the base itself. In the first case it forms a chord consisting of a third, fifth, and ninth, called
^
No. 142
I In the second case,
and perfect
it
1
forms a chord consisting of a major second
fourth, called f z i, as
No. 143.
i When is
t
the fundamental
r 7 is
suspended in one of
the,
upper parts,
it
rarely allowed to omit the third of the suspension chord.
§ 2.
The third
suspension
First Inversion of the Triad. of the sixth gives a chord composed of the | - •, as
and seventh, called
No. 144.
i
7^6
142
The
third is not suspended in this inversdon
would introduce a hase
may
itself,
;
for the suspension
| chord instead of a real suspension.
The
tone-
be suspended, either by the upper parts, or by the base
when
upper
in the
parts,
gives a chord composed of a
it
*
ninth and sixth, called § *
No. J45.
^ When
the base-tone
is
retarded
chord composed of a second and
by
fifth,
the base
called | S
itself, it
forms a
:
No. 146.
&
TSP
§ 3.
The
1
Second Inversion of the Teiad.
suspension of the sixth in this inversion gives us a chord
composed of a fourth and seventh, called
2 5
No. 147.
mi:^^^^ r — f f
The fifth
suspension of the fourth forms a chord composed of a
and sixth called
§ 4
:
No. 148.
143 This suspension can take place only
in cadences or half-ca-
dences, in which the fourth does not need
preparation. In the other cases the preparation of the fourth excludes any suspension
whatever.
The base-tone here is retarded only in the upper parts. forms a chord composed of a fourth, sixth, and ninth. It
It is
called g *:
^^^ No. 149.
•
Ff
We
shall
now
give some
r r
V
exercises on the
employment of the
suspensions in the triads and their inversions, that the student may, after them, exert his
own
industry.
^^
No. 150.
I
_J_j
i
—
J^—Vi
^^
i ite
J
i
J
I
-
M
4-^^
-?^-+
(I
i-—-i
f
r
-i.-^ I
4-
mr r
r
ifcrp: I
"•
-
%
144
^^^^^^ ff
f
^ 6
'
6
7
Q
9~P
^
if
jT^=bJ
J
J
^^^ 5
-
i
r-
-r
=i=^
r
rr
^^^
£
p
- e
n
-7-
EiE
i""
fii
^ I
I
J?
-^T
I5t=i£:
^ffT
•
^^ ^^^M rtf^ «t
r
I
|
r
g
»-
i=
^S I
—
--f=^
r r
5
6
J
I
-r
r f
f
-^
A J—r^ i^
J
r
7
~^
I
^ i_
~Lrf
f
f
E^^
is
I
f
r
i
^^*
%
r^ s ?
I
E^ f^^
sj
i
145
No. 151.
^^
^ §
7
e
f
+ 5 4
^^^
3
^^d ^r
rrrp_i.
J
1
i:^r
*
-
££ g
>l^ij ^^ d^ fTrf==trn^^=^ iE i
g
-
?-
e
a
- 5-
u^^^^^ ^ i
T^=rr=^
f
^
^r
When
5-
6
5-^j,|
I
reading over these exercises on suspensions, the student
should trace every case of suspension to the directions given, and sion belongs.
ascertain
He
to
what particular
direction
already-
each suspen-
should also be certain, before ending his examina-
(7)
146 tion
whether the suspension
And what
an inversion.
He must
point.
used on the uninverted chord, or on
is
inversion
In No. 150 there
?
is
a pedal-
know
look back at the rules of the pedal, and
whether these be rightly applied, and why? are there suspensions and where are they
in this pedal ? will
make
?
All these previous searches
his task of writing other exercises easier
and more
profit-
able for him.
2.
Suspensions in the Dissonant Chords.
The chord of
class, in
this
usuall)' used, is the
which the suspensions are most
dominant seventh.
The fundamental
never retarded in the parts above the base that
such a suspension
tone
and the reason of
;
it
is is,
nothing but the former nonachord
is
±
i But
resolved to the seventh. the dominant seventh
f-
l is
the suspension of the fundamental in
sometimes used in the base
itself,
and
this is a
real suspension.
The sixth,
suspension of the
and seventh.
It is
i
fifth
gives a chord composed of a third,
called a \ chord.
^ t
j-
^ ^
In the construction of this suspension,
it
is
proper to remove the
suspension tone from the seventh in order to avoid the close dis-
sonances of e, f, g, as in the above example.
The fifth,
suspension of the third gives a chord consisting of a fourth,
and seventh, called
i This suspension nant seventh.
is
Z
chord
^^ * the one most usually
employed
in the domi-
147
The
suspension of the fundamental by the the base gives a chord
composed of a second,
fourth,
and
sixth, called 2
P
t First Inveksion.
§ 1.
The the
inversion of the dominant seventh consists of a third,
first
diminished first
:
fifth,
and
Only two suspensions are
sixth.
possible in
inversion of the dominant seventh, as the fundamental can
not be suspended in the upper parts, for the reason assigned in the
The
previous directions.
but seldom.
The
cautions.
suspension of
Nevertheless,
close dissonances
i should be avoided
^ for,
;
i becomes
The
if
here, this suspension
is
it
we remove
M
the suspension tone
m.
I 4
5-
3
and even
efiective.
supension of the fundamental tone, (the primitive third of
the chord)
and
f, g,
ss-
T
satisfactory,
takes place here
Tgg-
But
-S
^= 5
it
e,
constructed as
would be hardly bearable. to the upper parts,
.the third
can occur, but with the following
it
fifth,
by the
base, gives a chord
composed of a second,
fourth,
called |:
s 1= i )
i This suspension satisfactory to
the
is
-r
f
I
more common than the
ear.
It
foregoing, and
more
does not require the same cautions
148 fof the aWaflgemetlt of its tones, as the dissonances lie at
a distance
from each other.
Second iNtfiRSiON.
§ 2.
This inversion of the sixth
is
is
The
a f chord with a major sixth.
of very frequent use, and effective.
suspension It
forms a
chord consisting of a third, perfect fourth, and seventh, called 2
i—^ It is practicable,
The
a^
I
whatever
may
be the arrangement oLthe parts.,
suspension of the basS'tone can only be done by the upper
parts.
It
forms a chord of a
third, perfect fourth, sixth,
and ninth,
called S
j^—
i
For the arrangement of the be attended
The
^^-
^-.
parts, the directions
given in § 1 must
to.
suspension of the
seldom, if ever, used.
P
It
J=
base' tone
by the base
itself,
is
very
would be thus:
=t: I* 5
§ 3.
Third Inversion.
This inversion consists of a second, augmented sixth.
Two
effective suspensions
can be Used in
the suspension of the sixth and of the
augmented
fourth,
and major
this inversion-"
fourth.
149
The suspension of the sixth gives a chord consisting of a major second, augmented fourth, and seventh, called 2
i^ The fifth,
?
suspension of the fourth gives a chord consisting of a second,
and
sixth, called S
:
da^E^
r
All the suspensions which can be formed in the dominant seventh can likewise be used in the other sevenths, with only this difference, in the latter the fundamental can be retarded, both by the upper parts and by the base itself. So, we do not think it necessary to enter upon any particular explanation concerning these that
sevenths. the
student
All
the
foregoing
to
use
the
seventh whatever.
We
directions
same will
enough
are
to
suspensions (as above)
now
No. 152.
J^J
\-
ft
I
ga m
J
I
ist
'f^^' =iJ=x^
i
i
^
J.
I
^ H
'i
f-T S6
any
give some exercises of the sus-
pensions in the sevenths in general.
-^^-^-^
enable in
150
AJ-ii
^
^
-r^-
d= I
Is
*
No. 153 ANOANTS.
^5
i •?•?
^
urn-
a^^ ^ss; ni
T
Tt
m
^'
^m
T^-
il5-
^M'^^-
^^-^ atitf
^
^=Srzi!i
-S-T*
^=^
2^
No. 154.
^
^F??c
£=5
-J^^
E^
-Jc:i
iE !!
^m
^ ^^^^
^^
151
J~j_4-J^-^-j_J-j-,^-
J—
iT
—
J
,
,
J ^
iJ ^
!
^U-^
-SF—
i
i<
r-T r-r-r-r-
p^^^^ S
We him
refer the pupil to the
to ascertain
their inversions.
ii
If
remarks under No. 151, and exhort
here the suspensions made in the sevenths and
We
would induce him,
also, before
he reads the
exercise No. 153, to look at the previous direction, No. 4th, on the
compound
time, (page 136.)
Suspensions in the diminished seventh are not very common, save that of the leading tone, the third of the dominant seventh, from
which
it is
There
derived.
inversions.
Next
is
an instance of it in the ninth measure
This suspension can be used through
of No. 154, above. to
the
it,
fifth
may
all
the
be successfully suspended,
if
done with discernment. In the extended sixth,the sixth only
i
^^ J—
This suspension it is
t is
even more elegant
is
apt to be suspended
:
*: !|*
*-
t
Y
Very commonly found, and satisfactory; to use that
chord with the suspension.
152
Double Suspensions,
3.
Thus
we have used our
suspensions in only one part of our have them in two parts simultaneously, in other words, instead of one we will have two suspensions meeting together; but no more than two can be used at the same far
Now we
exercises.
Of course,
time.
will
all
when
the conditions required
a single suspen.
must be attended to, when two occur simultaneously. (Directions 1, 2, 3, 4, 5, 6,) Pages 135, 137, 138, ISff. sion is used
As
to the resolution,
we must
observe that the resolution of both
suspensions ought not to be simultaneous
;
that
that suspension
which introduces a new dissonance. the opinion of Reicha, in his treatise on harmony. must resolve
first
^
This suspension presents
we
itself to
i us with two different features.
discover two discords, g, a, a ninth, and
The second
is
J
'A
First,
Such
c,
d, a second.
feature gives us likewise two discords, the
same
ninth,
g, a ; but the chord of the second vanishing gives us a new sonance, viz a seventh, J, a, with a in the treble.
dis-
:
The to
ninth alone, combined with another discord, can give room
double suspensions in the
triads.
In
all
the other instances there
can be no double suspensions, because only one dissonance can be had.
Hercf
^ )
i we have two
I
tones stretching over from one chord to another.
But
the tone a, of the chord f, a, c, prolonged to the following e, g, c, continues only the whole chord f, a, c, on to the beginning of the second chord ; and g, next to a, the intended suspension, instead of
introducing a
new chord by
resolving a,
is,
by
its
shortness, rather
an anticipation of the following sixth chord than a suspension tone
153 over the base.
Nay,
the stretching a, of the triad /, a,
from giving anything striking or new
to the
second
suspension of the sixth chord by the base.
c,
far
triad, spoils the
This shows that real
suspensions are based on dissonances.
Double suspensions are more properly used three tones, than in those of four, that
With one
sevenths.
is,
in the chords of
in the triads than in the
suspension, a seventh has two dissonances,
with a double suspension,
it
contains three dissonances.
almost an over-burden of discords to the ear.
For
This
is
this reason,
double suspensions must be used moderately.
No. 155.
EEEfc
Exercises
on.
Double Suspensions.
.1—i-A. J
1^=^
I
J-
~J
J
I
^^tSz^:
^
-i^-j-
^
^TT—r—
m
!
^
^m
i
-J
^-
p V:^r^ i»
i
i
f
m
i2=5= 6
I
(7*)
i
^
154
No. 156.
^ §fe^ _ 8
ll!
3
4-h4
^=J=4
^
^.Z^ % "^TTT
.
1
S
I
^^ rrTF^
f^^^^^^g
5 6
II
5
_
1^
5-
8
5_
5
3
r F
r
f
* li 3.
6
A New
-7-
Feature of Resolution
In our preceding talces place is still
on a
8 »-
in
the StrsPENSioNS.
exereises, the resolation of the suspensions
while the chord into which the suspension finds
in existence.
diflferent
chord.
Now, we
will
its
way
have the resolution take place
Thus, in the following
No. 157. \k
i the/ (at A) of the
].
.
B
J==^
treble ot^ht to resolre into e of the chord
c, e,
g;
155 and in the
like
chord g,
d.
b,
manner should
meantime the chords c, e, and h, d, f; for it
the a,
the e (at B) resolve into d of the
Both tones pursue
in the proper tone.
their prescribed course
;
but in
g, and d, f, a, have changed into is sufficient that the resolution is effected c,
e,
The chords do
not influence
Here, again,
it.
J
i
f 'r °c-^i I
in the |, in
which the
suspension had
third is retarded
to resolve
by
the perfect fourth; the
on the dominant
under the very same resolution-tone, changes
The same
sion of the dominant seventh.
i had
to
;
but the base,
into the third inver-
suspension
(|),
;i=4 *f=^
afTords us a modulation into the parallel tion
triad
take place on g,
from the dominant triad of
c,
minor key.
The
But the base changes
b, d.
its
resolu-
course
into the first inversion of the
dom-
inant triad of a minor.
This resolution of the suspension gives room
to successions of
ninths which are not practicable with the usual nonachords, on
account of the number of their tones, which prevents us from using
such passages as these
No. 158.
=i5
f
f—
&e.
i-
But with the supensions we can use the same succession, in which the ninth occurs stripped of the sevenths, and steps more freely.
156
^5
^r-A
S=-st
r
f
i •
'.
* °
f
'.
F
or
—
&e.
1
5-9
6
or
-^- -i &a.
f5
Here the
9
5
5
9
resolution of the suspension
was expected
to
take place
on the sustaining-tone of the base, which introduces every measure. But by the progressing of the base, a fifth below at A, a third below B, and again a third below, but with a different harmony,
at
at C,
the resolution is performed on different chords throughout.
By
we can
obtain
resolution of the sevenths can also progress from major to
minor
resolving the suspensions on a different chord,
the following succession of sevenths
-«=?=»•
'h-J
i The
J-tJ
j^k
rf
or extended sixths
;
and from minor
to
major
sixths,
and
vice versa,
as:
i From
1^^ i^ r the above examples,
s !*
it
^
i-=d
¥=¥
results that the base
can take
its
157
way
through every succession in which the resolution of the sus-
pension meets with
There are
still
proper tone.
its
some
peculiarities
which regard the
resolution,
and which should be noticed here. Firstly, the suspension-tone
can be permitted
or more chord-tones before obtaining
its
to pass
due, that
is,
through one
the resolution
can be postponed by placing, between the suspension and one or more chord-tones.
Thus
resolution,
here
^^^^^^^ A
B
r r-
"
I
At A,
new chord
At B, we
resolution. its
«
3
the suspended e resolves correctly into d, but not before
the third of the
and
5
%
find
finds its
way between
suspension and
even three tones between the suspension
resolution.
Secondly, by a cpntrary course, the voice or part which contains the
suspension can, immediately after the
through several tones of the chord.
resolution, pass
Here, for instance.
^^
^^^^ -'p-^t
ite
'^
i?
m
^^
i
m.
m^
1=
i
^
158
The dtnple
suspension of the treble at A, B, C, D, of the preceding exis
correctly resolved into the next tone, but immediately after
the resolution the voice passes through several tones of the chord.
may be proper sometimes some othe/ intermediate one, It
to
suppress the resolution-tone, and
to avoid confusion arising
from an
encui^brance of chord-tones, as here
No. 159.
^^^^^
I
-fT
^^=^
But, as a general thing,
it
is
as
we
is
as possible.
base, also, is allowed to step from one
many
As
to
of them
tone to another.
oflen necessary in order to preserve the certainty of time,
which must never be sion.
much
are always allowed to cancel as
think proper.
The This
we
t-:^
not correct to suppress the resolution,
and we ought to avoid doing this as the chord-tones,
&e.
^m
1s>-^=
But
left
in doing so,
uncertain, especially in every
we
should take care lest
character of the suspension, and even destroy
suspen-
we change
the
it.
No. 160.
^^ ^ ^i^Ti
^
r^ '
s
'
"li
"
i
159
We and
have here a
slurs
movement;
•strongly the
suspension,
The upper
g.
which
is
| at
it
move with suspensions decided motion, marks
parts
meantime, the base, by
in the
:
its
preserves, too, the
A, and I
character of the
At A,
6 at B.
the base, before
passing through the chord-tones d, g, b, strikes g, the fundamental of I ; at B, it strikes c, the fundamental of I 1, before moving
through the chord-tones,
But now
c, e, c.
No. 161.
i
^
iy^^
f
I
the character of the suspension t
the l 5 and (at
-, into
rule
the
D)
is
changed
the suspension
(at is
C) from the primitive
destroyed, according to
previously given, that the suspension consists in
the
dissonance.
The for
slur,
—
-
•
is
In the above,
not essential to the suspension.
example, the slurred minims might be changed into quavers,
thus
No. 162.
i
^_
^F^
IP
-S)~TSr
g-
•
m
3
without destroying the suspension. so as to receive words,
as here
I
-
It
and yet preserve
&e.
m^
mpE^^i^i^-r^t^ -
u
i
might likewise be modified its
character of suspension,
160
No. 163.
M sf^gr^l^=^=^= ^^^
I
^ ^tg
-"^
sr^^~^^^
&0.
^^ But in the
last case, if there
were an orchestra, some of the wind
instrument parts would have to restore the suspension with the slur.
This has a good
effect.
However
different
the
No. 163 may
be from No. 162, and \he latter from No. 160, in
all,
the sus-
pensions are equally maintained entire; and though, in the No. 163, the
measure
is
changed, though the accompanying parts the suspension
as genuine in
differ
as in the preced-
materially,
still
ing ones.
This serves to show the student that a musical idea can
be developed and varied in the
harmony.
its
is
it
form, and yet remain the same, as to
161
Exercises on Suspensions in General.
No. 164.
I
F ^— -f-
iilz
^
i=3z
nr^P^
I
£^H' J^.T?f
1^
l
i
J=^^=S5g^i=rf^
.i^^^
itE
tz
i
*r&fc—1-
^ ^Se^
-rmjr 6
^^^^iii lyJi 1
T
^
9
-*T-'
6
9
5
jS-'Q
G a
s^m 5
5 7
4 +
feEE^;^; 5
162
^m No. 165.
J-rJ
-J-i^J
I
Ie
g
I
-<=-
3^
J-i-^
-•=4-12-
,
^-y-^-
I
fTFT^^ -^1
§5 i;iLL
^
J
"
I
=^^-
j_i j f-r^rrr,^rTTr^ ,
^ 1-^3 T &5 i
7
i -
l±
I
No. 166.
|«
s P-^^-f^^^ ^^S^^"^^ iS^^^i^^^^^ -I—I-
^^-s^i
f^
1=
r
E5=i:
t-
-I-
163
k4^
P
^^^^^
-^
^r^rfx^^' iS^^ 2^3 3^S^^=§ ^E±
In the foregoing exercises on suspensions, particular attention has been paid, especially in compound measure, that each beat should be carefully marked and distinct; that when one or two parts stretch
over from one beat to another, one or even two of the move up or down to the sustaining tones. This pro
other parts
ceeding renders the whole composition easier for the performers,
and more because
intelligible to the hearers.
it is
of the highest moment.
We
insist
upon
this point,
APPENDIX No tone
Suspension can be found in
cjf,
at the begijining
this
J.
Beethoven's fragment.
of the second measure, and
dji,
The
at the be-
ginning of the third, do not form any suspension whatever.
If a
melody adorned with appoggiatures or grace-notes be reversed and sent to the base, the same ornaments still remain in the base, and preserve the same character. To make it plain, we will restore this melodic design to the treble part, from which it has been detached by Beethoven.
tt s
F?=
For the eye, as well as any suspension.
The tones itt,
cjf
the other on
and cj{.
djf
--ft
m
l,_p±,,-^
for the ear,
it
is
impossible to discover
form evidently an appoggiature, the one on
The
figuring of this melody being the equiva-
lent to this
p^^^f^^m^ since the appoggiature takes diately succeeds tion
it.
Now
its
time from the note which imme-
the melody does not undergo any altera-
by being reversed, and being transposed from the
treble to
the base.
To show
the difference which exists between a real suspension
165 in the base, and the fragment of Beethoven, above quoted,
we
avail ourselves of a quotation from Mozart, in his opera, the
di Figaro. in this
will
Nozze
Mozart introduces a duet between Suzanna and Figaro,
manner
fe -
'^^^f^^'^i
^ &c.
9^~J What It
is
r
=^
a diiference between Beethoven's and Mozart's passage
impossible to mistake the suspension in the melodic design
entrusted
by Mozart
to the part
requisites of a suspension
of the base.
We
iind in
—
preparation, resolution, &c.,
it
all
the
—whereas,
nothing such can be found in Beethoven's example quoted by our author. If the student wish to study a beautiful specimen of suspensions in the base, arising
from melodic designs,
we
refer
him
to the
An-
dante introduction of Grluck's admirable overture to IpJiigenie en Aulide, in which the great German master indulges in suspensions,
passing from one part into another in a masterly manner.
APPENDIX
K.
In his attempt to give an explanation of this quotation from Beethoven, our author ing e
The
an evident mistake.
falls into
simply a ped'al-point on the dominant of the tonic
is
part immediately above the pedal
is,
upper
parts.
The
now and
The
according to the principles of
the pedal-framing, the regular base of the parts oVer
sustaining tone discharges
sustain-
a.
it,
though the
then the same office towards the
tones of a, f^, h, (beginning of the second to the seventh of the second degree of major
measure) belong, here, a,
whose fundamental,
h, is
placed on the tenor.
solves into the dominant triad,
e,
gj(^,
b.
This seventh
re-
Accordingly, the tone
a,
which begins the second measure, and arising from the retained a of the preceding chords, does not form here any suspension it ;
is
the seventh of the mentioned
tone,
if
fragment,
any suspension is
a
to
be
found
the e of the treble part.
suspension, since is
is
seventh.
it
But
The only suspended in
this
this
Beethoven's cannot be a
comes in suddenly without preparation, which
fundamental law in matters of suspension.
mere grace-note.
e
This
e
is
a
