TWE NTIETH-
HARMOI{Y CENTURY
TWENTIETH CET\ïTURY
HARMOÏ{Y Aryto ünãPraçnce Creanue BY VINCENT PERSICHETTI
FABER AND FABER LIMITED 3 Queen Square London
3-*
First Published in England in 1962 by Faber and Faber Limited 3 Queen Square London WCl First published in thìs edition 1978 Printed in the Uni.ted Sutes of Arnerica by Vaitr-BallouPress,lna. dll
rights resertted
ISBN 0 t71 11216 I
CONDITIONS
OF SALE
This book is sold rubject to the condition that it shall not, by any of trade or otherui.se, be lent, re-sold, hired out or otherttsisecirculated without the publisher's prior consent in any f orm of bìnding or cover otber tban tbat in which it ìs published and without a similar condition including this condition being imposeil on the subsequent purchaser
Copyright @ 196l by Vincent Pçrsiçhetti
Contents
FOREÌüORD
9
INTERVALS
I3 r3 r7 r9
CONSTRUCTION INVERSION
AND SPACING
INTERVALS
IN
CHORDS
23 25
OV.ERTONE INFLUENCE MEDIUM
2
SCALE MATERIALS
3l
MODES SYNTI{ETIC
SCALD, FORMÂTIONS
PENTATONIC
ÂND IIEXÂTONIC
CHROMATIC
SCALE
SCÂLES
3r 43 5o 6o
CHORDS BY THIRDS TRIADS SEVENTH
AND NINTH
ELEVENTHS
CHORDS
.AND THIRTEENTHS
)
3**__-
66 66 74 8z
CONTENTS
6) FIFTEENTHS
ÂND SEVENTEENTIIS
TWELVE-NOTE
4
CHORDS
85 87
CHORDS BY FOURTHS THREE-NOTO
CHORDS BY FOURTHS CHORDS BY FOURTHS
FOUR-NOTË
CHORDS BY FOT'RTITS
MULTI-NOTE
93 95 IOI
ro+
ADDED.NOTE CTïORDS
109
SIXTH
CHORDS
r09
OTHEB. âDDED-NOTE
CHORDS
III
AI'GMENTED
T2T
CHORDSBY SECONDS THREE-NOTE
CHORDS BY SECONB
l2l
MULTI-NOTE
CHORDS BY SECONDS
,25 rz6
CLUSTENS
135
POLYCHORDS T\vO
TRIADIC
THREE
UNITS
OR MORE
NON-TRIADIIC
TR,IADIC UNITS
UNITS
r37 r50
r 53 163
COMPOTINDAND MIRROR HARMONY COMPOUND MIRROR
/\ g
CONSTRUCTION
WRITINC
r6j 172
182
HARMOMC DIRECTTON PROC:RESSION CHORD CONNECTION DISSONÂNCE .í I I
Í \
PARÂLLEL
HÁRMoNy
SUCCESSIVE PERFECT FIFTHS CÂDENTTAL
DEVTCES
r8z r89 r94 r98 20r
zo6
1 0 . TIMING AND DYNAMICS
2L2
RITYTHM
2t2
PERCUSSIVE USE OF HARMONY
220
(7
CONTENTS WRITING
PANDIATONIC DYNAMICS
1t
AND RESTS
AND TRANSFORMATION 23O EMBELLISHMENT FIGURÂTION
ORNAMENTAL
EXTENSION ÂND IMITATION CHROMATIC
ALTERATION
PEDAL POINT AND OSTINATO UNISON WRITING
L2
230 235 ')t
2+r 243
KEY CENTERS I9IgL,lIv MODULATION POLYTONALITY ATONALITY SERIAL HARMONY
13
.2J zz6
248 2+8 25r .)) z6r z6z
HAR\{ONIC SYNTHESIS CO\ÍBINI\'G THE}IE
A\D
TEXTURES FORM IDEAS
INDEX OF COMPOSERS SUBJECT r\DEX
271 27r .l)
z8I 285
Foreword
Tne uusrc of the first half of the twentieth century hasproduced a harmonicpracticethat can be defined.During thesesixty years, harmonicideashavebeenin constantflux; composershavecreated new musicaldevicesand techniques.This broad paletteof materials hasfundamentalsignificancefor the presentscene,for amalgamation of the varioussound formationsand techniquesis in Process. Composershaveworked instinctively, with the ear as their guide, and have arrived at someúing of a common usageof thesematerials. Contemporarymusical resourcesinclude a wide range of materialsof the pastand present'and the availabletechniquesyield returns. abundantexpressive Works of high caliber are plentiful in the twentieth century. The rich mixture of materialsand styles is made up of many ingredients:rhythmic energy' vivid harmonic fabric, melodic color, ánd fresh linear writing. There are bold statementsand delicate momentsof fancy, and developmentalforces that embellishments, refuseto be bound by a severeformal plan. There are daringly experimentaland strongly traditional forces which bring divergent materialstogether. 9
r0)
FOREWORD
accountfor The variousharmonicdevicesdo not, in themselves, creativewriting. Only when theory and techniqueare combined with imaginationand talent do works of imponanceresult.Neverof- twentieth-century harmonic retheless,a practical knowledge_ sourcesis a requiremenìfor both performer and composer.The performeris offeredspecificinformation, and the comPoser'workablematerials Tvrentieth-Century Harrnony is not a speculativeteatise nor one proposing a personalmode of organization.Rather, it is an account of specificharmonic materialscommonly used by twentieth-century composers.Although knowledge of materialsand techniquedoesnot in itself createa personalstyle, precisionin the choice of notes and understandingof harmonic devicesare desirablein perfecting a meansof expressionand in stating a musical idea clearlv and consistentlv. This text aimsto define ihis harmonic activity and make it available to the student and young composer.A detailedstudy of the essentialharmonictechniqueof the twentieth century is presented, accordingto the practiceof contemporarycomposers.The book is for and about creativily; it presentsmusical possibilitiesto stimulate creative musical thought. Specific media are called for, but substitutionsmay. and should be made dependingupon the instrumentalistsand vocalistsavailablein the classroomor to the require originally conceivedmelody and composer.Most exercises harmony in a rhythmic frame; tempo, dynamics,and phrasingare The applicationsdo not in themselves fundamentalconsiderations. for the insupply adequatetraining, but are offered as suggestions from the literature âre not vention of further examples.Passages reproducedout of context; exact pâge locations are listed under the heading "source Material." None of the examplesrePresent râre casesor exceptionalmusicalcoincidences;they do offer rePresentativetwentieth-century harmonic methods. This text may be used in advancedharmony coursesand as a in -collegesand point of departure.in literature of music cgursesconservatones;or 1t may form the harmonic basisof a first-year composition course for both composition and noncomposition majors. The division of musical study into separatesegmentsmelody" counterpoint, harmony, rhphm, and form-is advisable
FOREWORD
(r1
only if the interdependenceof theseforces as found in the literature is maintained.Referenceis madeto contrâpuntal,formal, and orchestraldevices,for harmonic and contrapuntaÌmovementâre affectedby a work's form and medium.The way variouschordal structuresare built, the reasonsthey sound as they do, the connection of the chordsand their suitability for differing conditions, consistencyof texture, and the combining of contrastingtextuÍes mu$ be understood. Following a predeterminedpath of strict axiomsis avoided,for harmonic creativity dependsupon the relation of chord to chord in a particularcontext;any chord may progressto âny other chord, and seeminglyopposingtechniquesmay be combinedunder cerrain formal and dramatic conditions.In theoreticaldeducdonsthe emphasisis pÌacedupon creariveideasand compositionalstimulauon. Composershave,in their music,coordinatedthe variousmusical resourcesof the early part of the century. Significant creators working actively in many mediahavegiven imperusto a flourishing twentieth-century music, have given it pulse and creative health. The embryonic composerhas a technical heritage.Little can stand in his way if he possesses creative talent.
cEÂPrER
|
-
I
oNEI lntervals I
ANv rorve,can succeedany other tone, any tone can soundsimultaneouslywith any other tone or tones,and any group of tones canbe followed by any other group of tones,just asany degreeof tension or nuance can occur in any medium under any kind of stressor duration. Successfulprojection will depend upon the contextualand formal conditionsthat prevail, and upon the skill and the soul of the composer. An understandingof the harmonic processmay begin with an understandingof the melodic and harmonic intervals of sound.
CONSTRUCTION
An interval, like any other musical sound, may have different meaningsfor difrerent composers.While its physical properties âre constant,its usagechangeswith the working context to which it belongs. For centuriestheoristshave, through the scienceof acousticq 13
1 . INTERVALS
14)
observed degreesof interval tension and from this has been evolved a concept of úe relative consonant-dissonantqualities of intervals. Although this consonanr-dissonanrconcept is afiected by countless factors within any given style, and -ay vary consideiably from one âge to another, the notes of an isolated interval-whether sounded simultaneously or successively-do have a basic quality. Thb quality_is determined by the interval's o\Ãrnpanicular physical properties of sound ìr/âvesand overtones. An isolated tone, when sounded, generatesa series of overtones which form intervals that relare to each other by mathematical ratio. Generally, in the tempered scale, intervals are "onrott"rrt considered to be those formed from the lower tones of the overtone series (see Ex. l-2L), the upper overtones producing d.issonant intervals. In practice, these tone-to-tone relationships have been reduced by the use of the chromatic tempered scale from an unlimited number of intervals to twelve intervals which retain the characteristics of their counterpârrs in úe overrone series. Their textural characteristics âre as follows: perfect fifth and octave-open consonances major and minor thirds and sixths+ofr consonances minor seconds and major sevenths-sharp dissonances major seconds and minor sevenths-mild dissonances perfect fourth-consonant or dissonant tritone (augmented fourth or diminished fifth)-ambiguous, be eiúer neutral or restless
Es. 1-1 mild disonancc soÌt consonance
or
consonance dissonance
shqp dissonance
can
(1t
CONSTRUCTION
It is difficult to classify the tritone and the perfect fourth out of musical context. The tritone divides the octave at its halfway point and is the least stable of the intervals. It sounds primarily neutral in chromatic passagesand restlessin diatonic Passages.
Ex. 1-2
t
The perfect fourth soundsconsonantin dissonantsurroundingF and dissonantin consonantsurroundings.
Ex. 1-3 Andante
Intervals can follow each other in any order and may be arranged to form any pattern of tensioninterplay. For example,a seriesof intervalsmay begin with an interval of little tensionand end with an interval of great tension.The qualiry of the perfect fourth and tritone will be determinedsolelyby contexu
I . INTERVALS
16) Ex. 1-4
This is how such a tension ârangement might soundin practice.
Er. 1-Í Anthnte
Next the tension pattern is reversed; intervals of great tension move to those of relative repose. The ambiguous tritone at the end now assumesa neutral character.
Er. 1-6
Intervallic tension may be used to suit any design or function propertiesof intervalsmay of the music.The consonant-dissonant be used to support or oppose,for various expressivepurposes, other forces such as instrumental timbre, dynamics,and tempo. seemconsistentin double reedsplaying loudly. Sharp dissonances However, the sameintervalsasigned the timbre of muted strings createân entfuelydifferent effect. The feeling of one is raucous and of the other, inuospective-one givesthe impressionof intervallic tension disagreementwith other compositionalforces, and the other the impressionof agreemenl
(17
INVERSION AND SPACTNG
Ex. 1-7 Âllegro Obs.ì.
Fls,,Vns.
Lento Str. ( sord,)
As composers' attitudes and practices change, the concept of consonance and dissonancemây change. Various degrees of tension may be accepted as consonance. Consonant intervals may sound dissonant in a passage dominated by dissonanr intervals, and in harmony comprised of suongly dissonant intervals these dissonancesoften become the "consonant" norm of the musical organization
INVERSION
'When
AND
SPACING
intervals are inverted, their consonant-dissonant quality changesbecausethe spacingand register have been altered.The extent of changevarieswith the individual interval. Inverting the perfect fifth altersits basicfuncrion, this solid interval becoming an unstableperfect fourth. When sharp disonâncesare inverted, marked changesin intensity occur. The cutting minor second opensinto a widespreadingmajor seventhand thereby losessome of its sting. Inverting the tritone causesa pronounced shift in register even though no changein intervallic distancehas taken place. If intervalsare spacedmore than ân octâve âpârt, the soft consonânces(thirds and sixths) become richer; open consonances (octaves and fifths) and the consonanrperfect fourth become stronger:
1 . INTERVATS
18)
8r. 1-8
(secondsand sevenths)becomelessbiting, yet rÌore Dissonances brillianc Et. l-9
ryp Piano
,{-;
delicao
i
The tritone, neutral in chromatic progressions,becomesmoÍe ambiguousand veiled; restlessin diatonic progressions, it becomes even lessaddicted to resolution-
Ex. 1-10 ( J = s eS1, ^2Vns.= go (vcilcd)
J. fi5
, J=!ì
ë.
-^''l
7_-/ t=>
tf aresc.
.f (ress resüess)
(Ie
INTERVAI^S IN CHORDS
INTERVALS
IN
CHORDS
Two or more intervals occurring simultaneouslyform what b usually felt to be a chord. Chords may be built with equidistant intervals, Er. 1-11
mi. 2nds
ma. mi. 2nds 3rds
ma. 3rds
4úts
p. íús
IÌu. 6ús
ma. 6ths
mr. Tttrs
m& Zús
with different kinds (major, minor, etc.) of the same interval number, Ex. 1-12
ma.&mi. 2nds
ma, & mi. Tths
ma. & mi. 3rds
ma. & mi. óús
p. & aug. 4ús
p. & dnn tús
and wiú mixed intervals. En. 1-13
p.4th mi.3rd
p.4ths ma.3rd
Before a chord is set in harmonic morion the consonant-dish sonântquality of eachinterval containedin the chord should be
I . INTERVALS
N)
noted. It is only by making use of differencesin chordal values as determinedby interval characteristics that harmonictensioncan be controlled. Without this kind of freedom only a limited kind of harmonicprogressioncan be achieved,that which resultsfrom root relationshipswithin a fixed scale and key. Awarenessof intervallic tensionproducesharmonicmovementof a more flexible nature. Good part-writing is, of course,necessaryto achievesuch flexibilitv. A thiee-note chord has three intervals; observe the possible variants in consonant-dissonantcombinations. Et. 1-14
3 cons
2 cons. & I cons.& 1uild diss, 2mild" dis.
2 cons, &
1 cons., 1 mild I mild. &
t úaqpdis. & 1úarpdiss. 2úaqpdiss
A four-note chord contâinssix intervallic factors. and a fivenote chord, ten. Ex. 1-1í
3 com.r2 úarp, I neut,,lì"s.
7 cons.,2 mild, 1 sharpdiss
The quality of chordal tension affects and is affected by dynamics,medium,and spacing,but variesin different musicalcontexts. Handling theseharmonic materialsbecomessimplerif some generalclassificationof the intervallic characteristicsof chords is applied. All chords fall generally into one of two categories, those chords that contain at leastone sharp dissonanceand those Each categorymay be subdivided thar containno sharpdissonance. into those chords containins at least one tritone and those containing no tritone.
(21
INTERVALS IN CHORDS
E*. 1-16
no tritone
flo tntonê
Chords containing a tritone tend to have a restless quality, while those without tritones have stabiüty even when extremely dissonânt. The presence of a perfect fourth in a chord lends ambiguity because of this interval's abiÌity to function either as consonânce or dissonance;other intervals in the chord must determine its character, the chord being classifiableonly in its total interval context. The consonant-dissonant quality of chords containing a perfect fourth is defined by the interval formed by the bass note and the note not involved with the founh. When this interval is a mild or sharp dissonânce, the perfect fourth sounds like an open consonance; when it is a soft consonance the perfect fourth sounds miÌdly dissonant.
Ex. 1-17
sharpdis.
mild diss.
soÌt cons.
opencons.
Any kind of chord has, under "normal" conditions, its own natural doubling, such as the doubling of roots in major triads. It is possible,however, to write a chord in numerousother ways" ActuaÌly, any note may be doubled,tripled, or omitted for specific textural purposes.Doubling may be usedto enrich simple chordsn to point up characteristicpart-writing, or to strengthencertain parts of a chord. A doubledmajor third addscolor and a doubled dissonanttone increasesthe bite. Excessivecoupling (all voices doubled) producespercussive-sounding harmony. Chord membersmay be so arrangedthat specific kinds of intçryals monopolizethe musicalpâttern"
1 . INTERVALS
22) Er. 1-18 Ândantino >
#JrJ--
1'/ *::
4ths r---:-1
z--',
>
't a^Lv '/
The choseninterval may forrn sepârateinrervaÌlb strands that move in contra{F motion. E*. 1-19
ú
Spacing is an imeparablepart of the character of a tonal structure. For ordinary balance,the wide intervals are placed at the bottom of úe chord; for tautness,the wide intervalsare placedat úe top. For evenly distributed tension, all instrumenrsor voices are employedin their grateful registersand altered accordingly if specificharmonicstresses or highlightsare desired. spaced harmony Closely crowded with small intervals clears when each chord is broken into a zuccessionof intervalsin cwopart writing.
(23
OVERTONE INFLUENCE
Ex. 1-20
(a)
(b)
(a) ch. e'
But harmony that is clouded may remain so and be eÍfective; both cloudy and clear chordal materialsare essentialingredientsin musical composition.The overtone seriesis useful in measuring the aural difference.
OVERTONE
INFLUENCE
Any tone generatesa seriesof overtonesor partials that reach upward indefinitely, though not all are audible. Ex. 1-21 Overtone series
PâÍtiâls 1
,L - r te-
r
10ut2t3t4lt16 xxx
A tone has both vertical and horizontal implications; its overtones may be used simultaneously in chordal structures or consecutively in melodic lines. Some sounding bodies produce higher overtones than others. A tone produced on ân instrument capable of generating high overtones recognizable by the ear cÍIn have a quality that is resonânt and relatively dissonant becâuse of úe crowding of the upper partials. The samenote played on a medium
1 . INTERVALS
24)
having overtones that stop auraÌly with the lower or middle partiâlswill soundrelatively consonânt,but lack resonance.Such âre someof the differencesthat help give instrumentstheir individual tone qualrry. Basic harmonic materialsmay be traced to the overtone series, but only generalfacts concerningchordal structure and resonance are indicated by the paftials.A triad is formed by partials 1-3-5 (root, fifth, and third), â seventhchord by 1-3-5-7,a ninth chord by L-3-5-7-9,the whole-tonechordsby 7 to 11,chordsby fourths by 6-8-9,and the augmentedfourth chord by 6-8-11.However, deduction concerning harmonic implications of partials beyond the óth is not wholly practicablebecausethe temperedscaledoes not coincide in pitch with the 7th, llth, 13rh, and 14th partials. It is quite posible to relatemulti-note chordsby thirds to the series but the overtonesproduce limited resonance.The major triad (partials1-3-5) is clearly in tune. But the sevenrhparrialis slightly lessthan a minor third from the sixth. and if consideredâs rhe -' seventh (in chords by thirds) misinterprets the narural phenomenon.Our temperedaural thinking can include tones up to the sixth partial but beyond that point the aural perception is merely rational. The acoustician'sobservationsare useful to the composeronly if blendedwith artistic intuition. The fifth (partial 3) is a lower partial than the third (panial 5) and consequendyis more powerful; this is an important factor in understandingrelationshipsof tones, chords, and tonalities.Resonânt harmony is not formed by seekinghigher and higher overtones but by using overtonesof overtones.For example,in a C-E-G-B chord, the seventh(B) is the fifth abovethe third (F.). In this senseboú C and E are accompaniedby their fifths and therefore have strong relationshipswith theseother rones.If we wish to add an additional resonantrone, we should add not a higher, weaker overtone of C (such as Ff) but a lower and stronger overtone of an overtone (such as Gf which is partial No. 5 of E).
Ex. 1-22
#=o*
-____-#_ :g!i---------N^
__h=--ti+
No.Íof' < ^Í
rr
MEDIUM
Q'
Chordal structures are most resonantwhen the distancesbetween the membersâre somewhatsimilar to thosein the ovefione series(wide spacingin the lower registerand closespacingin the upper register).The overtoneseriessetsâ norÍn for brilliance.For maximum brilliance, let the lower tones of the chord be accompaniedby their ov/n overtones. The resonantpropenies of an instrument or of objects surrounding the performer creâte additional sonority that underpins the sound. The principle of supporting resonânceby lower sonority is occasionallyapplied to chordal structures.This color device is used primarily when the composerworks with chords in the upper registerand needsto fill in toward the bass.In lower registers,the addition of tonesis limited by the dangerof muddy progressions. Most effectivesupportingtonesare the fifth or ninth below the bottom tone of the chord becausethe fifth is a strong and resonantinterval and the ninth is a fifth below the fifth. Basses plucking the fifth or ninú below the acnral bassline cast a reflectedsheenover the harmony.
Ex. 1-23
D.B. (pizz.)
MEDIUM
The mediumto which a musicalideais given hasa direct bearing upon harmonic writing, as do intervallic texture, spacing, and are built upon the samechordal dynamics.The folÌowing passages
1 . INTERvALS
26)
progression but are conceived in completely different media and this resultsin completelydifferent kinds of harmonic settings. Chordal tension, spacing, and dynamics have changed drasticai-ly in eachversionEt. 1-24 ll'omen's voicc
Seningfor Piano a (J=
r?0)
Awarenessof timbre is essentialto good harmonic craft. eualiry of tone as definedby medium plays a functional role in harmonic movement.Music written for the piano is effective on the piano, but that wrirten for orchestragives an improper impressionwhen played on the piano. Harmonic writing should be èonceivedfor the medium employed. For example,orchesrralcolor may softenthe extremedissonance of thirteenth chords,rob the triad of its soft consonance.or alrer chordal direction. The high register of keyboard insrrumentsor the harmonicsof stringsadd brillianceto parallelharmony.clusters binding secondsmay be loosenedby the-selectionof torre, ".ir"io
(27
MEDIUM
to sound as thirds in separateorchestral choirs. Polychords are made ffansparentwhen each triad or unit within the composite structure is sounded by a separateorchestral section. Pazícato suings define uncertain passingtones in woodwind voices,and a harp may underline obscurerhyúms in lagging sffings.
SourceMaterial (red.) = a reduced score (piano, two pianos, or piano-vocal)
Two-part writing in a two-voice work: Béla Bartók,,14 Violin Duets (Boosey) Arthur Berger, Duo for Oboe and Clarinet (Peters) Pierre Boulez, Le Marteau Sans Maiue, Mvt. III (Universal) Alberto Ginastera, Duo for Flute and Oboe (Mercury) Paul Hindemith, Zwei Kanonische Duette (Schott) Arthur Flonegger, Sonatine for Two Violins (Sirène) Bohuslav 'Walter Martinu, Three Madrigals for Violin and Viola (Boosey) Piston, Duo for Viola and Cello (Associated) Francis Poulenc, Sonata for Two Clarinets (Chester) Serge Prokofiev, Sonata for Two Violins (Russe) Maurice Ravel, Sonate pour Violon et Violoncelle (Durand) Heitor Villa-Lobos, Choros No. 2 for Flute and Clarinet (Eschig)
Two-part writing in a work of more than two voices: Henk Badings, String Quartet No. 2, p. 9 (Schott) Bruno Bettinelli, Sinfonia Breve, p. 1 (Ricordi) Aaron Copland, Piano Sonata,pp.23-24 (Boosey) Hans \Ã/erner Henze, Drei Dithyramben (orchestra), p. 44 (Schott) Paul Hindemith, Organ Sonata No. l, p. 17 (Schott) Vagn Holmboe, Kammerkoncert No. 2, p. 2a (Dania) Benjamin Lees, Fantasia for Piano, p. 4 (Boosey) Peter Mennin, Five Piano Pieces,pp.2-S (C. Fischer) 'Walter Piston, Sonatafor Violin and Piano, p. 20 (Arrow) William Schuman, Symphony No. 4, p. 1 (G. Schirmer) Dmiui Shostakovich,Piano Quintet, p. 39 (Am-Rus) Igor Stravinsky, Threni (red.), pp. 5, 9, 15, 48 (Boosey) KurtWeill, Mahagonny (red.), p. 3 (Universal)
28)
1 . INTERVALS
Two-part coupled writing: Béla Rartók, Mikrokosmos, Vol. lY, p,22 (Boosey) Dmitri Kabalevsky, Piano SonaraNo. 2, p. I (Leeds) Emst Krenek, Jonny Spielt Auf, p. 4 (Universal) Robert Palmer, Piano Quarteg pp. 19-21 (G. Schirmer for S.P.A.M.) Goffredo Petrassi,Salmo IX (rèil.), p. 1 (Ricordi) Hilding Rosenberg,Piano Sonata Nõ. 3, p. ó (Nordiska) Igor Suavinsky, Le Rossignol (red.), p. 3 (Russe)
Passages fearuring specific intervals: Bela Bartók, Concerto for Orchestra, pp. 29-35 (Boosey) _,!ban_perg,Jiinf Orchester-Lieder, O-p. + (red.;, p. 2 (Universal) Niels Viggo Bentzon, Third Piano Sonata,p. 29 (Hansen) Marc Blitzstein, Regina (red.), p. 71 (Chappell) BenjaminBrittgn,-Billy Budd (red.), p. 7 (Boosey) Paul Hindemith, Madrigale, p. 65 (Schott) Arthur Honegger, Judith (rèd.), p. 110 (Salabert) Maurice Ravel, L'Heure Eqpagnole (red.), -19, p. 39 (Durand) Arnold Schoenberg, Six Little Pieces, Op. II (Universal) William Schuman,Voyage (for piano), p. Z 1G. Schirmer) Roger S_ession9, Sr1!e from "The Black Maskers," p. l0 (Marks) Dmitri Shostakovich,Symphony No. 10, pp.66aí (Leeds) Alexandre Tcherepnine, Bãgarèlìesfor Piúo, p. 2 (Heugel) Randall Thompsori, Alleluia, p. tt (E G Schiimer)
Characteristicspacing: êlg-" Coptand, Sonetafor Violin and Piano, p. 33 (Boosey) lVolfgan_g Fg{lgr, Impromptus for Orchestrâ, p. 5 (Schcitt) Alexei Haieff, Piano Concerto (red.), p. a3 (Bóosey) Karl Amadeus Flartrnann, Symphony No. 4, for Suings, p. 38 (Schott) ' Paul Hindemith, Symphonié Mathis'der Maler, p. f ("ScËott) I_gorStravins\y.Symphgny of Psalms,p. ó3 (Boõsey) Gúdo Turchi, Piccolo Concerto Norurno (orchestra), p. 20 (Ricordi)
Examplesof overtones: William Bergsma, Six Sonp, p. 6 (C. Fischer) Elüott Carter, Piano Sonata,p.27 (Music Press) Aaron Copland, Piano Variations, p. 3 (Boosey) David Diamond, Rounds for String Orchestra, p. 20 (Elkan-Vogel) Hans'W'erner Flenze,Sonataper Ãrchi, p. 27 (Schoa) Gustav Holst, The Planets,p. 113 (Boosey) Jean-LouisMartinet, Orphée,p. 19 (Heugel) Olivier Messiaen,Turangalila-Symphonie, p. ó (Durand)
(2e
MEDIUM Àrnold Schoenberg,Piano Pieces,Op. 11, p. 3 (Universal) William Schuman, [Jndertow, p. a0 (G. Schirmer) Roger Sessions,Piano Sonata No. 2, p. 16 (Marks) Igor Stravinsky,Sérénadeen La, p. 9 (Russe) Eernd Alois Zimmermann, Konfigurationen, p. a (Schott)
Applicati.ons A two- or three-line piano reduction may be used in written examples.
1. Write a phrasefor two flutes that containsseveraldissonantperfect fourths. Folìow this phrase with one that contains severalconsonant perfect fourths. 2. Write a fast and tempesflrouspassagefor two oboesemploying no sharpdissonantintervals. 3. Write a soft, lyric passageconsistingmostly of dissonantintervals. Score for two muted violins. 4. Extend the following oboe and English horn opening:
Ex. 1-25
5. Write for violin and cello a preludethat containsboth a crescendo and diminuendo of interval tension.Do not allow the dvnamic level to coincide with the intervallic tensionlevel. 6. Add a secondtrumpet part to the following trumpet line, employing a crescendoof interval tension:
30)
1 . INTERVALS
Er. 1-26
7. Construct a declamatoryphrasefor three horns using chords built by eqúdistant intervais. 8. Write a passage for three clarinetsusing only chordswith one consonant, one mild dissonant,and one sharp dissonantinteÍval. Employ a vafiety of spacings. 9. Write a passagefor string quartet using only chords of mixed intervals. 10. Write a percussive passagefor string orchestra using excessive doubling and coupling. 11. Write a scherzandopassagefor piano using similar intervals in both hands,moving in conrary motion. 12. Move three bassoonsqúckly through widely spacedconsonant chords
CEÀPTER
Tlvo
ScaleMaterials
MODES A cBxrner, ToNE to which other tones are related can establish tonality, and the manner in which these other tones are placed around the central tone produces modality. A great number of scale patterns have been used by twentieth-century composers,but seven stand apart from the others becauseof their whole-half-step order. Each has its special character, and any tone may be used as the tonic starting point.
Ex. 2-I
ionian (rnajor) Transposed to úe same tonic center for comgarisoo
2 . SCALE MATERIALS
aeolian (nat. mL)
Most of thesetwentieth-century modesbear the namesgiven them during the Middle Ages but the resemblanceis one of construcrion,trãt or"g". Ionian-isthe familiar mafor scaleand aeolian, the natural minorl locrian (infrequently used) is unmistakablebecauseof its diminishedtonic uiad. of the four remainingmodes, rwo have maior tonic and two have minor tonic triads. Lydian consistsof the major scale with the fourth scale step raised; mixolydian of the ma]or scale with the leading-tone lowered. Dorian is úe naturalminor with its sixth stepraised;and phrygian, the natural minor with the secondscalesteplowered. The distinctive flavor of theselast four modesis exploited by in which the characteristicscale employing harmonicprogressions -tone keeps the mode from becoming a *.i ú",í* often. Tiús -rlot or natural minor scale.For example,a lydian passageon D sháuld contâin a high percentageof chords that include the ton€ Gf (raisedfourth .t.p); otherwisethe lydian flavor will be lost. e s"t of chordsmay be found within the diatonic limits of each mode. As in major and minor modes,there is a definite r'elation between primary and secondaryúordal materials'1.h" pï*"ty chordsarËthe tánic, plus two dominantequivalents.Thesedouble dominantsare those maior or minpr uiads that include the char-
(33
MODES
acteristic scâle step which producesthe principal flavor of the mode.In eachmodethere lurks a diminishedtriad; this is a dificult chord becauseits diminishedfifth tends to suggestthe dominant seventhof the maior key with the samenumber of sharpsor flats asthe modein question. In the lydian mode with its characteristicfourth step (major scalewith the raisedfourth), the primary chordsare I, II, and VII and the secondaryare III, V, and VI. The diminishedtriad is IV. With the lydian on D, for example,this works out âsfollows. D lydian (characteristicflavor: 4th step):
Ex. 2-2 IUruïVV ,
|
(dim.) P*rIï
In the mixolydian mode with its characteristic seventh step (major scale with the lowered seventh) the primary chords are I, V, and VII and the secondary chords are II, IV, and VI. The diminished triad is III. D mixolydian (characteristic flavor: 7th step):
Ex. 2-3
,
(dim.)
tl
prinnry
In the dorian mode, with its characteristic sixth step (nâturâl minor scalewith the raisedsixth), the primary chordsare I, II, and IV and the secondarychordsare III, V, and VII. The diminished triad is VI. D dorian (characteristicflavor: 6th step):
2 . SCALE MATERIAIS
34)
Er. 24 IIIMIV
t
rJà.r
pÍiÍnâqf
In the phrygian modewith its characteristicsecondstep_(natural minor *itn ift" lowered second)the primary chords are I, II, and VII and the secondaryare III, IV, aãd VI. The diminishedtriad is V. D phrygian (characteristicflavor: 2nd step):
Er. 2-j
-rttention Modal chordsby úirds, other than triads,needspecial becausethe tritone present in many seventh and ninth chords impliesthe dominantieventhof a maior scale;the chord-maythen easily lose its tonic feeling and slip into a maior scale.useful seventh and ninú chords-in the modes (excepting ionian) are thoseinvolving no tritone. Phrygian seventh chords:
Er. 2-6
Phrygian ninth chords: Ex. 2-7
^-%-^
1
MODES
(3t
Triads, sevenths,and ninths progresseasily from one to another while in the samemode:
Ex. 2-8
I'trvII pdrnary
Chord succession of any kind is not iust a seriesof separareroor points but a harmonicrelationshipin which chordsmove forward. The selectionand distribution of primary and secondarychords within a given segmenrof music and the ways in which the harmonic rhphm is organized help give the music its individual sound. A singlemode is not necessarilyusedthroughout an enrire section. As working materialsfor composition the modes may be arrangedeffectively accordingto their tensionrelationships.The greâtestnumber of flats that can be appliedto a modal scaleon a particular tone will producethe "darkest" mode,the locrian. Subtracting flats (and then adding sharps)in diatonic signatureorder will produce ân arrangementof modesfrom "darkest" to "brightest.2'The dorian modeis the middle point and setsthe norm.
Er. 2-9
2 .SCALE MATERIALS
t6)
mixolydian
Within this related order â flexible set of modesis at the composer'sdisposal,and definite control of thesescaleformationswith their inherent qualitiesis possible. Although sÌiiftittg modes are effective on a stationary-key center,múch melodic referencemust be madeto the tonic if one wishesro stay within the mode; otherwisethe tonaliry will switch to major under the ionic power of the tritone. Melodic circling or chánt-like repetition of the tonic tone and frequent_cadences will help maintain the center. The following i9 a melody with a cr"r"eodo in register, dynamics, rhythm, and modal materials; the tonic center is A throughoue
Ex. 2-10 (J =ee)Clarinet
-=----> cresc.e acêel.poco n poco,
4 r A aeolian
l A mixolvdian
A doriàn
I Jl roruil
Chromatic alterations, both melodic and harmonic, are devices naturalto modalwriting.
(37
MODES Ex. 2-11
,W tenerntente
The diminished triad is a frequent subiect for chromatic alteration. This chord has a restlesstendencv becauseof its tritone and is altered to give the tritone perfect-fifth stability and resonancel the root is lowered or the diminished fifth raised. This dissonanrtextured diminished triad is found on a different scale step in each mode. In phrygian it occurs on the fifth scale step, and when altered, forms an additional dominant equivalent (three in all).
Er. 2-12
elt. dom.
alt. dom.
In locrian, the diminished uiad occurs on the tonic, but if úis diminishedtonic is alteredchromaticallvin order to avoid tritone involvementwith the key center chorá,'úe locrian flavor is lessened.Therefore the tonic of this mode is often soundedwith no fifth, or with an addednote. The useof first inversionsubduesthe tritone and the omission of the third and fifth in a total unison obliteratesie
2 . SCALE MATERIALS
38)
Ex. 2-13 (
"f no 5ú
*ddeã-notc
lst inn
It mav be observedthat since the locrian tonic triad contâins the unsiabletritone, melodic use mây be made of the chords on the first and fifth scalestepsand the tritone relationshipconsideÍed a thematiccharacteristic.
Ex. 2-14 Mârziel€ 1J=tzO;
\
is one in which a modal melody is harA pure modal passage moniied with chõrds from úe samemode and on the sametonal center.
Ex. 2-15
(Bptuyean)
Polymodaliry involves two or more diÍferent modeson the same or difierent tonal centers.The modal strandsmay be melodic or harmonic.
(J=6s1
(E aeolian)
2 Cls. 7' etpr.
,r{
J
When the samemode occurs simulrâneouslyon different ronal centers,the pâssageis polytonal and modal, but not polymodal. Ex. 2-17
When different modes occur on different tonal centers at úe sametime the passageis both polymodal and poly"tonal.
E . SCALE MATERIAIS
40) Ex. 2-18 (J=r2o)(G PhrYgtân)
(C doriaú)
A melody may move from one mode to another with a different tonal center. If a melody fluctuates through several modes the harmony may follow wíth the same or with a difierent set of modes. When the same mode is moved from one tonal center to another a modal modulation existq
Ex. 2-19
doriaa)
(A dorian)
-------i---/
(Ft dorian)
but when the modes change while the tonal center remains, modaÌ interchanges result.
(41
MODES
Ex. 2-20 Andante
3 CIs.
: (E locrian)
(E lydian)
In twentieth-century music, key signaturesare seldom used becausetonal centers and modality shift rapidly and because atonality is often present.The enharmonicchoice of spelling is determinedby the easeof readability.
Sowce Materiul -Dorian writing: Bmest Bloch, Concerto Grosso No-t+J
(Buchard)
r
(Dgrlndf "4r".TBJg:!9g*"-gjp-ç 9egg,ryqst' +[As :t.Mjlisanqerkd),p. t 1_6 arris,,fmerican-Tãllils, p. ísõlieO**Ottorino Reqpighi, Concerto Gregoriano, p. 9 (Universal) Erik Satie,Socrate (red.), p. 35 (Sirène) Jean Sibelius,Symphony No. ó, pp. 3-4 (Hansen)
'- Phrygian writing: / Ernest Bloch, Visions et Prophéties f'\ Carlos Châvez,Piano PreÌudei, p. 3 Claude Debussy,-Strrn-eUíartêt, p.
))
IldebrandoPuzettt so,,;r;;Ë f;'ëuï")Jiï.ìí o. tu (Ricordi) SymphonyNo. 5, p.4 (Musicus) Dmiui Shostakovich,
42)
2 . SCALE MATERIALS
Lydian writing: Beaiamin Britten, Seven Sonnets of Michelangelo, p. 14 (Boosey) Roy Harris, Strins Quaftet No. 3, p. 10 (Mills) Giánfrancesco Ma-lipiero,Rispetti e Strambotti' PP. 4, 8 (Chester) Darius Milhaud, Prõtée (red.), p. I (Durand) Maurice Ravel, Trois Chansons,p. 12 (Durand) Jean Sibelius, Symphony No. 4, p t+ (Breitkopf)
-*
Mixolydian writing:
, . J
Béla Bartók, Piano Concerto No. 3 (red.), p. 3 (Boosey) Beniamin Britten, SerenadeOp. 31, p. t (Boosey) Gedrse Gershwin, Preludes fõr Piúo, p. 5 (Harms)
{ ( \
\
p+'ç Ekgqt,LïFry::(#*Èril,t (Deiss)
p. 2 (Gehrmans)
Aeoüan writing: Luis Escobar,Piano SonatineNo. 2, p. 9 (Peer) Carl Orfi, Carmina Burana, p. I (Schott) Ottorino Respighi, Pines of Rome, p' 34 (Ricordi) Domingo Santa Cruz, Three Madrigals, p' 3 (Peer) Randall Thompsorq The PeaceableKingdom, p. 3a (E. C. Schirmer) Virgil Thomson, Four Saints in Three Acts (r"d.)' p. 90 (Arrow) Wiiliam Walton, Façade,p. 8l (Oxford)
eailos Chávez, Preludes for Piano, pp. 5' í-f,(G. Schirmer) Claude Debussy,Sonatafor Flute, Vìòla, and HarP, P. 11 (Durand) Klaus Egge, Symphony No. 1, p. ó (Lyche) Paul Hiíãemilh, Ludús Tonalis, p. a-(fthott) Gofiredo Petrassi,Magnificat (red.), p. 76 (Ricordi) Jean Sibeüus,Symphoãy No. 4, p. 37-(Breitkopf)
Modal interchange: Alfredo Casella,ll Peza Infantili, p. 12 (Universal) Paul Hindemith, Das Marienleben-(1948)'p' 18 (Schott) Zoltân Kodály, Sonatafor Solo Cello, p. 5 (Unive_rsal) -. Darius Milhaüd, Le Pauvre Matelot (rèd.), p. 1 (Heugel) Vincent Persichetti Piano Soaatinas,pp. 18-19 (Elkan-Vogel) Bernard Rogerg Characters frqn Hans Chriçtian Andersen, PP. 4-5 (Elkan-Vogel)
SYNTHETIC SCALE FORIVÍATIONS
(43
Ned Rorem, A Christmas Carol, pp. 3-5 (Elkan-Vogel) Igor Stravinsky, L'Histoire du Soldãt, pp. 59-ó0 (Philharmonia)
Polymodality: Béla Bartók, String Quartet No. 3, p. 10 (Boosey) Carlos Chávez, Soìratinafor Violirrand Piano' p' 4 (New M"sic) Paul Hindemith, Nobilissima Visione (ballet), p. + lSchott; Arthur Flonegger, Sept Pièces Brèves, p. 4 (Eschig) -. Olivier Messiããn,Vingt Regards (piano)' p. 18 (Durand) Darius Milhaud, Protée (red.), p. 56 (Durand) CarÌ Orff, Die Bernauerin (red.), p. 85 (Schoa) Francis Poulenc, Mouvements Perfetuels, p. 2 (Chester) Maurice Ravel, Piano Concerto in G (red.)' p. 38 (Durand) Igor Stravinsky, Oeüpus Rex (red'), p. 79 (Russe)
SYNTHETIC
SCALE FORMATIONS
Although a single tone, through its overtone series, suggests most obviouslythe maior scale,úe formation is partly rationalized. The major is only one of mâny scalescontainedin the basicrwelvetone chromaticscalethat is found in the upper region of the overtone series.Free placementof scalestepsresultsin original scale formationsbeyondthe sphereof maior and minor modes. Most original scalesâre constructedby placing any number of maior, minor, and augmentedsecondsin any order. The permutation possibilities are staggering and the mâthemâtical processhas little creative connection with composition. It is advisablethat scalesbe allowed to form as a result of the impetusof melodic or harmonic patterns;the material generatedby thematic ideasmay then be gatheredup and placedinto scaleformation. Some "original" or synthetic scalesare used more often than others.These better-known scalesoften coincidewith folk scales namedasfollow* and aresomedmes
44)
2 . SCALE MATERIALS
Ex. 2-21
(4ú mode of Double Harm.)
The synthetic seven-tone,one-octavescale, like a ma]or or minor, is made of a pair of four-note groups (tetrachords) that repeât the tonic at the eighth step. These tetrachords may be similar,asin major and Double Harmonic scales,or different, asin harmonicminor and HungarianMaior scales. The modal construction principle that produced the seven diatonic modes (dorian, phrygian, etc.) may be applied to any scale,creating multiple versions.The first modal version of any scalebeginseÍr the _tonic,the secqndon the supertoniçof that scale, etc.
STT{THETIC SCALE FORMATIONS
(4t
Ex. 2-22
Transposedto srme tonic for compar.isoo
The harmonic usefulnessof new scalesis determined by surveying their indigenous chordal materials. Each synthetic scale contains a set of chords within its own intervallic make-up. The primary chords are the tonic plus the two triads that include the scale step or steps containing the most determinable characteristic colors of the scalein question. If a maior-scale tetrachord is present the color tones are those outside the tetrachord. But if the scale contains no major-key tetrachord, the primary chords other than the tonic are those triads that are enharmonic spellings of a major or minor triad. If enharmonically spelled major or minor triads do not exist, the characteristic tone or tones are found in the notes forming augmented or diminished intervals with the tonic. The remaining triads are the secondary formations that function within the gravitation of the primary chords.
2 . SCALE MATERIALS
46)
Ex. 2-23 Original Scale characteristic rcale stepr
ru1- tott tetrachorô
III
minor
!'II maior eúarmonic
A harmonic problem is created by the fact that mosr syntheric scalesproduce one or more triads with diminished or augmented thirds and often these triads are primaries. They are usually chromatically converted into one of the four basic triads: major, minor, augrnented,or diminished. Altering the harmonic texture should not disturb the strict scale tones in the melodic writing because the burden of maintaining the flavor of the prevailing scale is placed upon the melody. The sooner the melodic voice includes all the tones of the scale,úe greater úe chance of projecting the synthetic scaleasa unit.
Er. 2-24
Further harrnonic possibiüties may be tested by considering the mirrored version of the scale. Scanning intervallic points between the original and mirrored versions reveals hidden potentialities of the scale.Fresh material such as cadential patterns, passingtextures, -and and outer-voice movement is suggested brought into focus by reflection.
(47
S]TNTHETIC SCALE FORMATIONS
Ex. 2-2í
:@l
Some scalesare reflectively identical, inversion producing exactduplicationof the original scalein retrograde.
Ex. 2-26
As in previously discussedmodal writing, the melody and harmony of a passageinvolving synthetic scalesmay stem from the samescaleoi difietent scales,and be placedon identicalor different key centers.The following passageis built of different scaleson the sametonal center:
Ex. 2-27 C HungarianMinor "
C Hungarian Maior
,
2 .SCALE MATERTALS
48)
This next passâgeis built of different scaleson different tonal centers: Ex. 2-28 go14y (J= 128 '(cg!?oa|
D HungarianMaior
,
G Oriental
New scalesmay be so built with similar or dissimilar tetrachords that the tonic is not repeâted at the first octave. When the octave is missed and the tetrachords âre continued, a two-octave scale or multi-octave scale may evolve.
Ex. 2-29
Multi-octavc
(4e
SYNTHETIC SCALE FORMATIONS
A secondqype of two-octâve scaleis built by combining rwo different one-octavescaleswith commontonics. Ex. 2-30
Tones 9 through 15 of a rwo-octave scale are not necessarily duplications of tones 2 through S. This tremendous span of intervallic color makes shifting of modal versions impracticable. The principal chords of the two-octave scale tend to be large, complex structures which clearly define the two-octâve compass. The fifteenth and seventeenthof a chord by thirds from the two-octave scale are not necessarily duplications of the root and third. These two-octâve scalesserye as a unifying element in music of complex chordal formations.
Ex. 2-31 Lento Ww. H.
,rf ,tpr. Buít on 2-8vcscalc (8x..2-29>
ffiì= -1-#-
Two or more tonal levels of intricate two-octave formations appearing at the same time (polymodal or polytonal) are dif6cult to project, and are best contained in music for a medium of wide color palette.
2 . SCALE MATERIALS
t0)
SourceMaterial Passages basedon syntheticscales: Féla Bartók, Sonata for Two Pianos and Percussion,p. ó5 (Boosey) Niels Viggo Benrzon,Third Piano Sonata,p. 17 (Hansen) Benjamin Britten, Turn of the Screw (red.), p. 180 (Boosey) RossLee Finney, Piano Quintet, p. 33 (U. of Mich.) Charles Griffes, The Pìeasure-Domeof Kubla Khan, -p. 14 (G. Schirmer) Lou Flarrison, Suite for Cello and Harp, p. l0 (Peer) Arthur Honegger,Symphony No. 5, p. 49 (Salabert) Alan Hovhanãís,Loísnàg Kisher, pp.'2-5 (Merion)' Olivier Messiaen,Vingt Regards (piano), p. 128 (Durand) Gofiredo Petrassi,Mà'gnific-at (red.), p. aà (Ricordi; Manuel M. Ponce, 3 Poemasde Lermontow, p. 6 (Universidad,Argentina) Maurice Ravel,Concertofor Left Hand (red.), p. 20 (Durand) Harald Saeverud,SiÌjuslâtten,p 5 (Norsk) Jean Sibelius,Symphogy No.4, p. 13 (Breitkopf) Igor Stravinsky, Fire-Bird Suite, p. 25 (Kalmús)
PENTATONIC
AND
HEXATONIC
SCALES
There âre variouskinds of basicfive-tone or pentâtonicscâles. Someof the better known are: Ex. 2-J2
The modal construction technique thât produces the seven diatonic modes produces five modes of each rype of pentatonic scale. The five modal forms of the diatonic pentatonic are as follows:
PENTATONIC AND HEXATONIC SCALES
('I
Ex. 2-33 lst modc
ü
2nd modè
3rd mode
-'C diatonic pentatonic scde
A
Trrrsposed to sarnêtonic for comparison 4th modc
5th mode
ü
^
Diatonic scales of five tones are hârmonically limited in scope becauseof the lack of semitones (when all five tones of a penratonic scale are sounded together they form â somewhat srâtic chord). It is therefore extremely dificult to achieve harmonic and melodic direction in a pure pentatonic form. When melody and harmony âre pentatonic, changing the modal versions of the pentatonic or moving from one pentatonic to another will help prevent monotony.
2 .SCALE MA,TERIALS
t2) Ex. 2-34 orgâa _
(c dieronicpenatonic)
Ândantc
lst mode
Lavish use of ornamental tones, pedal points, and frequent modal interchanges or modulations to other pentatonics will also help prevent harmonic monotony; but pure pentatonic music (nonpolymodal, etc.) is most effective when used for short spans of time. Pentatonic materials function well melodicallv or harmonically, but seldom both. Pentatonic melodies are often harmonized with foreign chords.
Ex. 2-3Í (J=12\
3lÍ*')/
One type of pentatonic scale combines well with another type on the sâme or different ke'y centers.
PENTATONIC AND HEXATONIC SCALES
(t3
Ex. 2-36 Piano Moderato
fl
:e,,rL-e '
-
t#t
atonic on B ílst mode
Diatonic pentatonicon C (5ú mode)
.._- )
Ê r'g
There âre vârious kinds of basic six-tone or hexatonic scales. Someof the better known are:
Ex. 2-37
The modal construction technique that produces the seven diatonic modes and the five modes of the pentatonics, produces six modes of each qFpeof hexatonic scale except the whole-tone scale.Harmonic monotony is somewhat more easily avoided in pure hexatonic scales than it is in pentatonic scales because of the additional interval. Melodic material from these scales is usually harmonized with chords from other scales or with chords in non-scalar relationship.
2 .SCALE MATERIAI^S
'4)
The hexatonic scale (excepting the whole-tone) has a primarily 'When melodic function. it is used as marerial for melodic writing a complete and fully independent line evolves. At times the harmony is drawn into the tonal orbit of the melody, but for the most part the harmony is non-hexatonic and moves independent of any implications of the melody. The consonant-dissonanr tension causedby the fwo sepârateforces creâtesits own fluctuating design and shape. In hexatonic pâssagesthe two stong forces, melody and harmonf t ãre often in polytonal relationship.
E*. 2-38 C Promeúeus Neapoütan
, Ddiatonicpentatonic
, G mixolydian
,
The whole-tone hexatonic scale offers a limited basisfor extended musicalexpression. When the scaleis mirrored there is no changeexcept in register. A secondwhole-tone scalelies a half step abovea first but any âttemprto producemore will result not only in a transpositionbut in a duplicationof the notesof the first or second.Modal versionsof either of the two scalesresult in an
(tt
PENTATONIC AND HEXATONIC SCALES
exâct úansposition of the original forms. Its equidistantintervallic make-up deprives the scale of the fundamental intervals, the perfect fourth and fifth, and of úe leadingtone. A real feeling of tonality, therefore, must be establishedby harmony outside the whole-tone category. The chords furnished bv the whole-tone hexatonic scale are meâger harmonic material. The six triads of the scale are all augmentedand four of them are, in effect, but inversionsof the first two. There is only one type of seventh,one type of ninth chord, and one categoryof chordsby seconds
Ex. 2-39 aue.6ús
Nevertheless,whole-tone materialshave possibilitieswhen certain devicesare employed to prolong úe harmonic interest. These âre: contrary motion,
Er. 240
alternating the two scaleg
2 . SCALE MATERIALS
,6)
Ex. 2-41
soundingall six tonestogetherharmonically,
Ex. 2-42 Strings
1J=sã;u:
changing the density and spacing,
Ex. 2-43 (J=ee1
'lVw.
\\--:-. I
and usingboth whole-tonescalessimultaneously. Ex. 2-44
PENTATONIC AND HEXATONIC SCALES
(t7
The true value of the whole-tone scale lies in the contrast it provides when it is used in combinadon with other scales and techniques. When amalgamated with other materials it can be creatively stimulating, as in: a whole-tone melody harmonized with chords other than wholetone,
Ex. 2-4Í (J :120)
'ú? Str.
I
a diatonic melody created over whole-tone harmony,
Ex. 2-46 Allegreno
ob. u vl.I ,ú VI.II Va.
2 . SCALE MATERIALS
t8)
whole-tone chords changed to added-notechords when minor secondsare attached,
Ex. 247
whole-tone passages alternatedwith non-whole-tone passages,
h.248 Atlogt'o :>
non-whole-tone
PENTATOMC AND FIEXATONTC SCALES
(t9
and the whole-tone scalecombined with another kind of scale.
8r.249 whole-tone
SourceMaterial Pentatonic writing: Béla Bartók, Mikrokosmos Vol. III, p. 22 (Boosey) Claude Debussy, Preludes Vol. I, p. 1ó (Durand) Charles Grifieó, Five Poems of the Ancient Far East (voice and piano), pp. a-l5 (G. Schirmer) Gianfrancesco Malipiero, Pausedel Silenzio, p. 37 (Philharmonia) Maurice Ravel, Trio for Violin, Cello, and Piano, p. 21 (Durand) Albert Roussel,Douze Mélodies (voice and piano), p. 49 (Lerolle) Pentatonic and non-pentatonic
combinations:
Béla Bartók, String Quartet No. 3, pp. 7-8 (Boosey) Paul Hindemith, Tanzstücke (piano), p. 18 (Schott) Arthur Flonegger, Trois Chansons,p. 2 (Senart) Burrill Phillips, A Set of Three Informalities for Piano, p. 4 (G. Schirmer) Maurice Ravel, L'Enfant et les Sortilèges,pp.4243 (Durand) Ralph Vaughan'Williams, A London Symphony, p. 24 (Stainer)
'Whole-tone writing: Béla Bartók, Mikrokosmos Vol. V, p. 32 (Boosey) Alban Berg, SiebenFrühe Lieder, p. 3 (Universal) Claude Debussy,PreludesVol. I, p. 3 (Durand) Paul Hindemith, Neues vom Tage (red.), p. 171 (Schoa)
2 .SCALE MATERIALS
60) Whole-tone
and non-whole-tone
combinations:
Béla Bartók, String Quartet No. 1, p. 1l (Boosey) Ferruccio Busoni, Piano SonatinaNo. l, p. 11 (Zimmermann) Paul Hindemith, Piano Sonata No. 1, p. 15 (Schott) Jacqueslbert, AngéÌique (red.), p. 24 (Heugel) Charleslves, Thirty-four Songs (Mists), p. 4ó (New Music) Maurice Ravel, Ma Mère Ì'Oye (4 hands), pp. 18-19 (Durand) Igor Stravinsky, Le Sacre du Prinremps,p. ó7-(Kalmus)
THE CHROMATIC SCALE The chromatic scale is made of úe octave divided into nryelve half steps. It is used as an omamentarion of a diatonic scale, or as an independent scale (dodecuple) with twelve equâliy important steps.This chromatic scale may impose tonic feeling through fixed or shifting centers or may have no definite tonâliry. Modal versions in the eqúdistant chromatic scale are no more possibleto consüuct than in the equidistant whole-tone scale. Ffowever, chords of equidistant intervals or any combination of mixed intervals may be built from the scale. They may be constructed upon âny or all chromatic tones and, if desireá, brought wiúin the gravitation of a tonic cenrer through establishment of any plan of chordal relationships. Chromatic harmony often contains miscellaneous intervaÌlic building materials. This complex harmony forms a compound qFp" that is discussed in a later chapter. There are various kinds of chromatic writing: chromatic figuration of non-chromatic harmony,
THE CHROMATIC SCALE
Ex. 2-í0 Ándante
cr. .rd b
"*.
lnt
chromatic harmony with diatonic melodic writing,
Ex. 2-Í1
2 Tpa. p Bn.
diatonic melodv
chromaticmelody generatedby chromaticharmony,
Ex. 2-Í2
(61
2 .SCALE MATERTALS
62)
mixed chordalstructuresformed by the chromaticmotion of parts, h.2-Í3
2 CIs.
and chromatic harmony generatedby chromatic melodic writing. Er. 2-Í4
íJ.orr
Ë-'
a\, When characteristicgroupsof melodic noresare usedvertically, asabove,chordsare formed by intervalsfrom the horizontalmotif. Compositionwith twelve notes can generatethis kind of harmony.
Sowce Morerial Chrornatic figuration of non-cüromatic harmony: Henry Cowell, Symphony No. 11, p. 15 (Associated) Arthur Flonegger, King David (red.), p. ó (Foetisch) SergeProkofiev, Piano SonataNo. 2, p. 3 (Leeds) Dmitri Shostakovich,Piano Prelude No. 1 (Leeds) Igor Suavinsky, Symphony of Psalms (red.), p. 2 (Boosey)
Chromatic harmony with diatonic melody: SamuelBarber, Piano Sonata,p. 42 (G. Schirmer) Roy Harris, Litde Suite, p. 5 (G. Schirmer) Paul Hindemith, Sonata for Piano, Four Hands, pp. 1e-11 (Schott) Charles lves, Violin Sonata No. 4, p. 19 (Arrow)
THE CHROMATIC SCALE
(63
Chromatic harmony with chromatic melody: Alban Berg, Fünf Orchester-Lieder, Op. 4 (red.), p. 5 (Universal) Bruno Bettinelli, Sinfonia Breve, p. 52 (Ricordi) Gotdried von Einem, JapanischeBlâter, p. 2 (Universal) Howard Hanson, Symphony No. 2, p. 2 (C. Fischer) Carl Ruggles, Men and Mountains, p. t5 (New Music) Arnold Sõhoenberg,Violin Concerfo (red.), p. 33 (G. Schirmer) Alexander Scriabine,Piano SonataNo. 9, p. I (Leeds) Roger Sessions,Piano Concerto (red.), p. 3a (Marks)
Applicati.ons l. Write a short piano piece in the rnixolydian mode, with a minimurn of chromatic alteration. 2. Extend theseopening suing quartet measuresusing the lydian mode.
Et. 2-i Í
3. Write a pâssagefor organ employing modal modulation. 4. Write â passagefor harp illustrating modal interchange. 5. Write a short recitative for violin using fluctuating modes. 6. Write a gay and quickly moving vocalise for soprarrc basedupon úe darker modes. 7.'Write a slow and melancholy vocaüsefor baritone employing only bright modes. 8. Construct a solo clarinet line in the lydian mode supported by
2 .SCALE MATERIALS
64)
phrygian string-quartetharmony. Set both the melody and harmony on the tonal centerBf. 9. À4ovea woodwind quintet rapidly through a section of mostly mixolydian music. 10.Harmonize alocrian English horn melody with locrian divisi cello harmony on the samecenter. 11.Extend the following polymodal and polytonal passage.
Ex. 2-Í6 Blydian
,
12. Write original melodies for various insuuments using original scales. 13. Write a one-voice fantasy for organ, pedalsalone, using several synthetic or original scales. 14. Construct a canon for three clarinets in which each performer plays a different synthetic scaleon a different tonic. 15. Createan original two-octave-scaleharmonic texture in a scherzino for piano, four hands. 16. Write a purely pentatonic section of a scherzo for woodwind quintet. 17.Allow an oboeto sing a slow pentatonicline over a non-pentatonic chordal string background. 18. Move the orchestraquickly through a florid pâssâgebasedupon shifting pentatonic scales. 19. Construct two melodieson a whole-tone scale,one suitable for the themeof a lyric movementand the other for the theme of a scherzo movement. 20. Harmonize a descendingwhole-tone scalein the tuba with major and minor triads in the trumpet, horn, and trombone,
THE CHROMATIC SCALE
(6t
21. Harmonize an ascendingmajor scalewith variouskinds of wholetone materials.IJse any medium. 22.P\t high brasses(using one whole-tone scale) againstlow brasses (using the other whole-tone scale). 23.Writea chromaticbassoonmelody under three-partdiatonic string harmony. 24.Extend the following chromatically ornamentedpiano Passage.
Ex. 2-Í7
25. Harmonize an ascending chromatic scalein the soprano saxophone, with major and minor triads in an alto and two tenor saxophones.
""fil.":an"rdsby Thirds I
TRIADS
Tnrers AREusED by composers of the twentieth century in ways not emphasizedin the eighteenth and nineteenth centuries. Chords of the earlier period revolve around úe tonal pillars-tonic, dominant, and subdominant-and gravitation is created by the anticipation of harmonic arrival. The dominant and subdominant balance the tonic on either side in intervals of the fifth, and these relationships (V-I and IV-I) dominate all others. The remaining chords are secondary and furnish variety once the primary color has been established.The motion to and from the primary material gives úe key its identity and úe music its balance. Since thb dominant-subdominant harmony is used for cadential feeling, the progression is unquestionably established as being governed by a 6fth relationship or a cycle of fifths.
66
(€7
TRIADS
Er. 3-1 .IV
V,
I
Triadic materialswithin a scalemay be set in motion by relationshipsother than that of the fifth' In thei': mrlsic-comPosers have sËownthat, âs it is possibleto have a cycle of fifths, so it is possiblero movein a cyclè of úirds or seconds.Theserelationships can be convincingto ihe ear when the cycle in force is confirmed by passingand cãdentialchordal movements.In third relationship llycte oithirds) the mediantand subme{i1t- give balancedsuppú to the tonic from their positionsa_thirdaboveand below the ionic. The primary chordsthen are I, III, and VI and thoseremainrng are secàndary.The relationshipsIII-I and VI-I dominateall othem"
Ex. 3-2 ,vI
I
m,
(5ï
In second relationship (cycle of seconds) the supertonic and leading-tonechordshólp establishthe tonic center{rom úeir_positions ã secondin either direction. Primary chords are I, II, and VII and the remaining chords secondary.The relationship II-I and VII-I dominatethe others.
Er. 3-3 ,\.fi
(r{)
I
II,
when determining the successionof chords in a third or seeond relationúip otr" *ay proceedin their equivalentof the traditional fifth relationship of rãots. The most nâtural root progressionsof the secondand third relationship parallel the usual roor pxogres-
3 . CHORDS BY THIRDS
68)
sionsin musicbasedupon the cycle of fifths. Here are corresponding chords of all categories,their tonal functions (cadêntial, modulatory,and so on) being paralleÌ: C;rcle of 5ths 3rds 2nds
IV -VI VII-IV
ru -II
_VII _VI
-v
VI _VII_IV -ilI II -v
v -ru -II I
:I
:I
and conespondingharmonicprogressions: Cycle of 5ths I III IV VI V I Cycle of 3rds I II VI VII ruI Cycle of 2nds I V VII IV I I I In the following examplethe root progressionis created by descendingin successive intervalsof the cycle relationshipin force. Here the passages are different only in that they are governedby different cycles-fifths, thirds, and seconds. Ex. 3-4
Cycle of Sths
Cycle of 3rds
Cycleof 2nds
(69
TRIADS
These cyclic relationshipsmay be constructed in any scale, synthetic or other'ü/ise.In a major key the primary chords in a fifth relationshipare mafor, in aeolianthey are minot, and in many synthetic scalesthey are mixed. In secondand third relationships, asin the fifth, the colors of primary chordsare determinedby the intervallic make-upof the scalein force and will vary considerably. A third relationshipin a major key producesthe following harmonic colorsin primary chords: I major, III minor, and VI minor. There are major as well as minor secondarychords, thesetriads creatinguseful color tensionin a secondarychordal function. In this context a C major E-G-B "dominant" is as refreshingas the secondaryG-B-D. Ex. 3-5
In modes,the primary chords of a particular cycÌic relationship may not coincidewith the natural modal primary chordsexpÌained in Chapter 2. For example,a secondrelationshipin the phrygian happensto include the natural primary chords of the mode (I, II, and VII). The dominantequivalents,II and VII, contâin the characteristic phrygian second scale step. A third relationship in phrygian producesthe primary triads I, III, and VI, but these chords do not include the phrygian flavor tone. Even though the it phrygian soundis difficult to captureunder thesecircumstances, upon is quite possibleto establishthis third relationshipby emphasis the secondarychords of the cycle which do contain the phrygian color. Ex. 3-6 E phrygian-third
E phrygian-+econd
I U VU I
II(ru)vII
I
m(ry)vI
3 . CHORDS BY THIRDS
70)
The harmonic rnotion to and from primary chords may change to a motion created by shifting from one cycle to anorher. Interchange of the three relationships (second, third, and fifth) affords complete freedom of root movement within a scale. Every intervallic root progression is possiblebecausemovements of the second, third, and fifth are identical ro rhose of the sevenrh, sixth, and fourth by inversion- And since the intervals belwegn moving roots âppeâr as major, minor, perfect, and augmented (depending upon úe scalein use), the whole rwelve-tone compassof intervallic root progression is automatically available. To find ornamental tones, any chord of the harmonic progression may be considered a "ronic" of any scale, synthetic or otherwise, and ornamental tones mây be derived from that inferred scale.
Ex. 3-7
<-
9Ncap. Mi., f'Enigmatic -G,Lead.Wh.+onc,,CDoublcHarm,
Synthetic scalesoften contain uiads that have augmentedor diminishedthirds. These are awkward becausethey sound like fourths or secondsand usually result in misspellinga chord.
Ex. 3-8
DfFrAl
F!AICT
cf (E) GB
AbC (Eb)ct (or aug.ó$)
TRIADS
GI
S'uch chords are often afueredto one of the four basic triads, maior, minor, diminished, or augmented, in whiú only major and minor thirds âre present. Chords may move âs part of a cycle within a scale,or independentof scalerelationshipin triadsbuilt upon any tone. In music that lacks a definite scaleor modality, any triad may be followed by any other triad and any sequenceof key centersmay be used. The root movementof a perfect fifth has a strong tendency to establisha definite modality and tonaliry, and therefore is seldom usedin a chromatically free triadic context. Root movementsof major and minor secondsand malor and minor thirds occur more often becausethey are lesslikely to defineany one scale,the root of one triad moving up or down to the root of anothertriad more often in intervalsof secondsand thirds than in fifths or the tritone. Both triads involved may be of any type, but are usually maior or minor.
Er. 3-9 CE'DFI
When triads progress chromatically â root movement of the augmentedfourth producesa chordalrelatiorshipthat addsvariety to the basicsecond-úLd relationship.
Es. 3-10
l-l Irn,2nd
ma.Znd
oi 2nd
mi 3rd
The wide selection of triads made available by chromatic progression often creates harmonic and tonal restlessness.But if each voice has purpose and design any triad may progress freely and with harmonic meaning. When chromatic triads wander har-
3 . CHORDS BY THIRDS
72)
monically and make vague phrase-shapes a diatonic melody may bring the chromaticisminto clearfocus. Ex.3-11
diatonic bas
At any point chordal materialmay be chosenby consideringa prominentnote in the strongestvoice asthe root, third, or fifth of a major or minor (lessoften, diminishedor âugmented)triad. Any note hasthreemajor and three minor triadic possibilities.
Ex. 3-12
Even an unadornedscaleline producespotential chordalvariety. Ex. 3-13 aeoüansoprano
SuperLocrian soprano
_ =-ç,_v
1,- l^-
út
t-'-
!
ut
L
L r tL^ be ,b- -#3
In musicof suchchromaticshifting, an underlying scaleor mode is sometimes a resultantfactor but nevera governingone.Although the center of the following exampleis indisputablyF, the passage
(73
TRIADS
is not governed by a prevailing mode or â preconceivedtonal framework. Ex. 3-14 lowlVw.
()=72)
Triads are frequently used in fundamentalposition while the voices containing the root and fifth (usually the two bottom voices) move in parallel6fths. This type of movementis efiective if attention is diverted from the fifths by extensivecontrary motion. Periodic inversion of the triads will relieve the binding parallelism. Ex. 3-1Í
2 (Xs'
I 2 Bns.
In the last chord of the above example, the minor six-three functions as an incomplete major triad with an added sixth (Ff tonic). The six-four chord with its characteristic interval of a fourth is often heard in the company of simple chords by founhs. The
3 . CHOR.DSBY THIRDS
74)
mild tension of the second inversion and the punctuation of rectrring cadenceshelp define the formal arc- of longer triadic In thesesurroundingsmodalcadencesof seconãand úird pâssages. relationshipsfind their narural habitat.
SourceMaterial Triads moving by third relationship: SamuelBarber, Dover Beach (red.), p. 12 (G. Schirmer) Benjamin Britten, Piano Concerro (red.), p. +O (BooreyÍ Frank Martin, Golgoúa (red.), p. 12 (Unìversal) *Ige Prokofiev, March from L'Amour des Trois Oranges (Breitkopf) ' Willialq Schuman,Symphony No. 4, pp. 34-35(G. Schírnrei) Virgil Thomson, A Solemn Music, foiband (red.), p. 7 (G. Schirmer)
Triads moving by secondrelationship: SamuelBarber, Adagio for Strings, p. 3 (G. Schirmer) Aaron Copland,CÌaiinet Concerïo (red.), p. 2 (Boosey) Arthur Honegger, King David (red.), p. iS qchesteri DouglasMoore, The Ballad of Baby Dde (red.), p. 155 (Chappell) Serge Prokofiev, ClassicalSymphoiry,p. 5l (Barôn) EriÉ Satie,Socrate (red.), f. ri 1Súariey
Triads moving by trirone relationship: DomFick.Arrylqg,Thu Bool (red.),-21 p. 29 (Boosey)
Béla Bartók, Violin SonataNo. t, p. (Universâl) Mysterious Moumãin, p. 64 (Associated) $an F{ov_haness, Gyn Carlo Menoni, Amahl and úe Nigtrt Visltors (red.), p. 21 (G. Schirmer) Willem Pijper, Piano Sonatina No. 3, p. 6 (Oxford) Erik Satie,Sonneriesde la Rose * Croix, p. 7 (Lerolle)
SEVENTH AND NINTH
CHORDS
The seventh and ninth members of chords are traditionaly üssonaüt tones but úey have been freed of some of their fãrmer
(7t
SEVENTH AND NrNTH CHORDS
restrictions.These chords have becomestableentitiesin themselves with their dissonanttones not necessarilyprepared or resolved. Seventhand ninth chords, like triads, may progresswithin or outside any scale formation, original or traditional. Under certain formal conditions the seventh and ninth are treated as dissonant tones needing resolution; but as independent seventh and ninth chords they have the faciliry of uiads.
Er. 3-16
It is possibleto build sevendifferent seventhchords with malor and minor third construction. Seventh chords with augmented and diminishedthirds are misspellingsof oúer chords.
Er. 3-17
aug.6 Ft7ú
DTrh B9rô
Great varieqy in seventh chord texture can be had through doubling (any note may be doubled) and inversion.Seventhsmay be inverted and spacedin any manner without destroying their The first inversion,spacedin fifths, is parharmonic suppleness. ticularly useful becauseits unique soundenablesit to act as a key centerchord.
3 . CHORDS BY THIRDS
76) Ex. 3-18
I
senplibe mesto
E
C_ D_.F_ (seventhchordsonly)
C
8b_
.Àb_ G_D|
Er
All types of harmonic progressionpossiblewith triads âre possiblewith seventhand ninth chords.Seventhand ninth chordsused âs consonântformationsfunction well in relationshipsestablished by a cycle of fifths, thirds, or seconds.The augmentedfourth root relationshipprovidesfresh activity from chord ro chord, particularly when the chordsare dominantsevenths. Ex. 3-19
,
tritonc
,
.
tntonc
, tritone ,
A feeling of "progression"may be created by moving voices through various forms of different seventhand ninth formations on the sameroot.
(77
SEVENTH AND NINTH CHORDS Ex. 3-20 (J =s0)
l-t--l
Mathematically,it should be possibleto build with maior and minor thirds sixteendifferent ninth chords on one note; but becauseof enharmonicduplication of certain notes'only twelve are possible.For scanningpurposesthe ninth chord is analyzed as òonsistingof two triads, úe top uiad anchoredto the uppermost note of the bottom triad. This dual chording has polychordal implications Ex. 3-21
mÍL ma"
mâ, di*. ,
Tr ma.
mi. di*.
diÍrl . rnâ.
dim. fu,
me. mi.
aug: me"
âug. fu. t
mâ. I aug.
D:ri. mi.
rni. aug.
dim. mi.
dim. âug'
aug. mr.
âì19. âug. r
A workable order of the twelve ninth chords from darkest to brightest is material for a composer's craft (the chords connected by arrows may be interchanged).
Ex. 3-22
mi. nu. dim. diIÍL
diÍrI. dim. mà. ni
eug. dim.
mi. mi.
mi. m?. me. dim. aug; rnt rne. mi. nrá. âug. tm. aug.
78)
3 . CHORDS BY THIRDS
'When
color gradations of the ninth formations are made part of the composer's aural âppârâfts, textural control of the various ninth chords will be possible. Ninths used with technical faciüry add freshnessto harmonic progression.
Ex. 3-23
One of the thirds that makesup a ninth chord may be (but rarely is) smallerthan a minor third. The harmonicsqueezecaused by the diminished third, or its inversion the augmented sixú, createsa needfor chromatic resolution.
Er. 3-24
In ninth chords members a.re omitted as follows: fifth-for richness;third or seventh-for less color. Chord membersare doubledas follows: root or 6fth-for solidity; third or seventhfor densiry of color; ninú-for increasedtension. When úe ninth of the chord is below the roor the chord b less agile; fluent part-writing helps úe progression.
(7e
SEVENTH AND NINTH CHORDS
Er. 3-2Í
The fourth inversion (ninth in the bas) is a hard texnue and effective in a rough-herÃinpassage. Omitting the fifth here produces more suppleness.
Ex. 3-26
Ì;:
=-t.
The minor dominant ninth in the fourth inversion is often found with its sevenú omitted in parallel harmony. In fourth inversion the interval of the minor ninth is sometimesqpelledasa diminished octâ\reto facfitate reading.
Ex. 3-27 e=?6J >
t
IF
>
+ din
8vc
vrl
+ alio"Evc
3 . CHORDSBY THIRDS
80)
Extensive rnaterials are made available bv ninth formations. Sinceany note may be consideredthe root, third, fifth, sevenrh,or ninth of twelve different ninth chords,a singlerone may be harmonized with sixty different ninths. With the note E in the top voice, the five minor-minor ninth chords might be written:
Ex. 3-28
Imi. CtLmt
f mi. ELmi
Successions of ninths of varying intervallic texruresare effective in sequentialpatterns, Ex. 3-29
diatonic (tonal)
.chromatic (red) ;--:
Li...-
rnd in combination with sevenths.
Ex. 3-30
mixcd r --\
SEVENTH AND NINTH CHORDS
(81
The increasedharmonic weight of ninths often presenrsthe problem of immobility. This may be solved by merely touching the ninth with a voice moving from a uiad or seventhchord. Ex. 3-31
'When
ninth chords are used with chords by fourths or orher non-third categoriesthe members of the ninth are spacedso that ar least one of the intervals of this chord resemblesthe building interval of the non-tertian harmony. For example, if ninth chords are followed by chords built of fourths, the members of the ninth are arranged so that an interval of the fourth is formed by two of the voices. This fourth is given emphasisin the phrase to prepâre the texture for the entrance of the chord by fourths. Progressions that combine chordal textures are, however, a matter for study under Harmonic Synthesis; see Chapter 13.
SourceMaterial Various kinds of seventhand ninth chords: Alban Berg, Piano Sonata,p. 10 (Universal) Paul Creston, Symphony No. 2, p. 5 (G. Schirmer) Klaus Egge, Symphony No. l, p. 74 (Lyche) Lukas Foss,The Jumping Frog (red.), pp. 84-85 (C. Fischer) George Gershwin, Porgy and Bess (red.), p. 8 (Chappell) Roy Harris, Soliloquy and Dance, for viola and piano, p. 4 (G. Schirmer) Charleslves, Walking (Arrow) Goffredo Peuassi,Magnificat (red.), p. 56 (Ricordi) Maurice Ravel, ValsesNobles et Sentimentales,p. 3 (Durand) Erik Satie, SarabandeNo. 2 (Lerolle) Arnold Schoenberg,Six Little Piano Pieces,Op. 19, p. 4 (Associated) Alexander Scriabine, Piano Sonata No. 5, p. 16 (International) Igor Suavinsky,Threni (red.), p. 44 (Boosey) Guido Turchi, Preludi e Fughette per Pianofone, p. 3 (Zerboni)
3 . CHORDS BY THIRDS
82)
ELEVENTHS
AND
THIRTEENTHS
Large tertian chords, no mâtter how many thirds have been added,form only a small portion of the harmonic palette. The multiple tones of eleventhand thirteenth chords add density but Thesesix- and seven-noteformationsare cumreducesuppleness. bersomein harmonic progressionsbut useful in the generalharmonic scheme. An eleventhchord is easilyidentified by consideringthe formation a combinationof two triadsa major or minor third apart.
Ex. 3-32
A thirteenth chord may be identified by consideringthe formation a simultaneouscombination of three triads with tones in commonât two points.
Ex. 3-33 TÌüI. lnÊ. tlur.
aug. ma. mi
IIu. TIÌT. mi.
The thirteenth chord is non-invertible; any attemPt at inverslon will produceanothereleventhor úirteenth.
En.3-34 c 13
(c13) 2ndin%
ïïrt:
ï*#;,3
i?
Eleventh and thirteenth sounds are often created by pedal tones or melodic ornamentation of uiads and seventh chords. In thesein-
ELEVENTHS AND THIRTEENTHS
(81
stancesthe harmonic background is not one of eleventh or thirteenth chords but a smaller chord with the addition of ornamental tones. In analysis the apparent eleventh or thirteenth is broken down to the chord with the fewest notes and this considered the basic chord; otherwise ornamental tones are mistakenly considered part of the chord.
Er. 3-3Í Anirlantino
Oe
,---
+^4
'tf
If some members of the eleventh and thirteenth chords are omitted it is possible to âttain a certain freedom of harmonic movement. Eleventh and thirteenth chords usually contain two sharp dissonant intervals. Omitting one of the tones that forms a sharp dissonant interval lessens the dissonant content and makes relatively supple harmonic movement possible. In the following thirteenth-chord example, CB and EF are members of the sharp intervals contained in the chord. E, B, or F are choice notes of omission; if C, the root, \yere omitted an elevenú chord would resrdc
Er. 3-36
no 3rd
no 7ó
no Íltü
Chord membersare bestarrângedin resonantintervallic relatiop ship; but if the arràngementproduces two separatetriadic units a
3 'CHORDS BY THTRDS
84)
polychord results;and if fourths predominatethe chords sound not aseleventhsor thirteenths but aschords bv founhs.
Er. 3-37
polychord
The intervallic make-upof eleventhand thirteenth chordsoften coincideswith variousscaleformations, Ex. 3-38
SuperLocrian
phrygiur
Hung. Ma
Leading Whole-tone
and the chords become excellent six- and seven-note tonic formadons around which polychords and compound structures may function. These eleventh and thirteenú formations are usually guided by a melodic line derived from the scale implied by the rich tonic chord; they are seldom found in extensive part-writing. Eleventh and thirteenth chords combine well with seventh and ninth chords.
Ex. 3-39
,rf Hn.
FIFTEENTHS AND SEVENTEENTHS
(8t
SourceMateri.al Eleventh and thirteenth chords: AÌban Berg, Iü/ozzeck (red.), p. 39 (Universal) Benjamin_Britten,Peter Grimés (red.), p. 27 (Boosey) Arthur_Horegger, Jeanned'Arc au Bücher (red.), p. A+ (Salabert) Darius Milhaud, Les Malheursd'Orphée (red.), p. 27 (Heueet) Walter Piston, Carnival_Song(men's chorus anã brasses),-p.Ze la.rrow) M_auriceRavel, ValsesNobles et Sentimentales,p. 1 (Duranã) â1"*1"dgi Scriabine, Piano SonataNo. 8, p. f (Leeds) Sh.apero, Iltrold ^Sonarafor Piano, Four Éands, p. I (Affiliated) Igor Suavinsky, Ocruor, p. 52 (Boosey)
FIFTEENTHS AND SEVENTEENTHS As the tonal system expanded into one rhat accommodated more than seven different chord tones, thirds were added to the thirteenth chord as a fifteenth and â sevenreenthwithout duplicating chord members.
Er. 3-40
86)
3 . CHORDS BY THIRDS
In tertian chords larger úan the seventeenth,not every tone is necessarilydifferent; the size of the chord is determinedby the distancebetween the root and the highest new noce that rises in thirds abovethe rooc
E* 341
For purposesof manipulation, úe texture of theselarge chor& drould be thinned by omitting two or úree inner tones.Separated triadic units must be avoided unless polychordal structure is deúed.
Er. 3-42
#; Í,oo
Euph.,Saxes., Bna
chor,lsarç çffeçuvein parallel Completefifteenth or seyenteenth in harg.nonic or punctgatio4g, belglonl
(n
TWELVE-NOTE CHORDS
Er. 343 AIl.g-
Sowce Material Fifteenth
and seventeenth chords:
Henk Badings,Louisville-SymphonI, p. ó3 (Peters) Alban Berg,ïiolin Conceúo ïred.), p. +z (univeisal; Arthur Honegger, Symphonie Liturgique, p. 106 (Salabert) Charleslves, ïí Songs (on the Anti!ódeij, p. aa'(New úusic) Giselher Klebe, Moments Musicaux Íor Orchestrâ, p. I (Bote) RiccardoÌ{alipiero, Sonata for Violin and Piano, p. tS (Zerboni) Maurice Ravel, ChansonsMadécasses(red.), p. 12 (Durand) Alexandre Tansman, Quatre Préludes, p. 5 (Demets) Heitor Villa-Lobos, Rudepoema, p. Z2 (Eschig)
TWELVE-NOTE
CHORDS
Mixed thirds may be superimposeduntil all twelve tones are present. The unwieldy terms "nineteenth," "tweng/-firsq" or "twenty-third" chord are seldomused.Twelve-note chords containing t\pelve different member tones are so complex and thick that specialattenrion must be given to the register and instrumentation. The thick rexrure lightens when the chord is placed in dE lpp"t register or when corÌsonântportiorÌs of the clrord de pbyed by separateorche$trâlchcirs
3 . CHORDS BY THIRDS
88)
Ex. 3-44
This is an extremely limited speciesof harmony, *q"h oPerâtes in a confined area; iis harmonió functions are few. Twelve-note chords are used for punctuationn
Ex. 3-4Í (J =laa).,
i^
rËí
for quiet and sustainedtension,
Ex. 3-46
su' Orch.
p r
rhat answerunisonor two-Part writing. and for short progressions
TWELVE-NOTE CHORDS
(8e
Ex. 3-47
TweÌve-note chords by thirds span â wide register and their members are normally spaced in thirds. Parallel movement of all voices provides temporâry "s-oppl.tt"r." but when contrary motion rn some vorces rs used the distances between some of the voices change. This results in the twelve-note chords by thirds moving to one formed by fourths or seconds, or to a polychord, heterogeneouscompound chord, or mirror chord:
3 . CHORDS BY THIRDS
e0) Ex. 348
polychordal
compound
v=
.u}lffot
SourceMaterial Twelve-note
chords:
Alban Berg, Fünf Orchester-Lieder (red.), p. 6 (Universal) Leonard Bernstein, The Age of Anxiety (red.), p. 59 (G. Schirmer) Karl-Birger Blomdahl, Aniara (red.), pp. 1-3 (Schott) Benjamin Britten, The Tum of the Screw (red.), p. 5 (Boosey) Vittorio Giannini, Symphony No. 4, III, at rehearsalnumber 9 (Ricordi) Michael Gielen, Musica per Archi, Pianoforte, Baritono, Trombone, e Timpani, p. 39 (Universal) Everett Flelm, Concerto for Five Solo Instruments, Percussion, and Strings, p. 15 (Schott) Cliarles lves, 19 Songs (Maioriqy), p. 42 (New Music) Rolf Liebermann, Concerto f.or lazz Band and Symphony Orchestra, p. 1 (Universal) Darius Milhaud, Piano Sonata (1916), p. 10 (Salabert) Vincent Persichetti, Symphony for Band, p. 127 (Elkan-Vogel) Bernard Rogers, The Passion(red.), p. 98 (Elkan-Vogel)
Appli.cations 'Write a dorian passagefor piano in which the harmony is dominated 1. by the cycle of fifths. 2. Set for mixed chorus a line from one of the Psalms.Let the music be governed primarily by the cycle of thirds.
TWELVE-NOTE CHORDS
(e1
3. write a mixolydian passagefor two oboes and two bassoonsin which the harmony is governedby the cycle of seconds. 4. construct a phrase on the following series of harmonic roots: A lydian, I-U-VI-VII-III-L 5. Harmonize a descendingmajor scalewith major triads exclusively. ó. Harmonize rhe ascendingEnigmatic scalewith major and minor uiads. 7. H:armsruze the following melody with chords by thirds.
Er. 3-49 () =72)
9 ilolce (legato)
8. Extend the following passâgcfor two clarinets and two bassoons.
tu. 3-50
l. !-!ing C as a tonal cenrer (but no prevaiÌing scale), creârea quier rnood in the string orchestra while triads progressin chromatic relationships of the secondand úird. End on a six-three tonic equivalent. 10. write a src.cessionof staccato chords in the brasses.Esabrish severaltritone root movements.
3 . CHORDS BY THIRDS
e2)
11. Construct a sequenceof maior seventhchords and build a string on the sequentialidea. quarrerpassage 12.Harmonize the following melody in four string pafts using dominant seventhchordsexclusively.Much contrary and oblique motion and severalinversionsshouldbe used.
Ex. 3-í I
13. Write a seriesof sequencesincluding seventhand ninth chords. 14. Include severalkinds of seventhand ninth chords in an organ interlude. 15. In a short sectionfor piano dominatedby ninth chords, use loud and rough fourth inversions. 16.Expand this piano passâgeof eleventhand thirteenth chords preserving the generalcharacter.
Ex. 3-Í2
tf
rnolto precíso
17.In string music of sustainedchords by thirds include severaleleventh and thirteenth chords. 18. Write a short triadic piece for one piano, four hands,in which suddenfifteenth formations interrupt the mood. 19.Write a lyric line for solo trumpet with a quiet divisi string background of twelve-note chords. 20. Construct twelve-notechordsfor full band that puncfuatea rapid solo timpani passage.
""iï;i Chordsby Fourths I cHÂPrER L-,,
TweNnern-cENTURy composers use quartal harmony (chords by founhs) as well as the tertian harmony (chords by'úirds) of classic and Romantic pracrice. Quartal materials Élem from ornamentation of the triad (a) and from the rechniques of medieval polyphony (ú).
Ex. 4-1 Harmonium Àndante (a)
4'CFIORDS BY FOURTHS
94)
chords by fourths are built by superimposingintervals of the fourth. In ãther spacings,most of the chord membersmust be itt oider to preservethe dislnctive-quartal placed a fourth "pãn lound; otherwiseìhe quaral st*ctures may sound üke eleventh, thirteenth, or added-notechords.
Er. 4-2
added-noo
Three-, four-, and five-note chords by perfect fourths have a pentatonic flavor. The five-note form contairs all the stepsof the diatonic pentatonic scale.
Er. 4-3
Chords by perfect fourths are ambiguousin that, like all chords built by equiãistant intervals (dirninished seventh chords or aug*"nt"d triáds;, any membercan function as the root. The indifference of this rootless harmony to tonality placesthe burden of key verification upon úe voice with úe most active melodic line.
Ex. 44 Moderato
THREE-NOTE CHORDS BY FOURTHS
THREE-NOTE
(et
CHORDS BY FOURTHS
Three kinds of intervallic aÌrangementof three-note chords by fourths are possible:perfect-perfecqperfect-augmenred, and augmented-perfect. The augmented-augmentedarrângement is irnpracticable becauseúe 6rst and úird nores are enharmonically identical.
8r,. +t
In all types of three-note chords by fourths rwo inversionsare possible.Inverting chords having rwo perfect fourths helpsprevent the harmonicmonotony of uniform intervals.Either inversioncan be usedas a fundamentalstructure becauseof the presenceof the strong perfect fifth. If rhe resonantinterval of úe perfect fifth is allowed to dominate the rexrure, the second-created by the inverted seventh
Er. 4-6
The varieqy presentedby open spacing increasesharmonic exPres$veness:
s
4 . CHORDS BY FOURTHS
e6) Ex. 4-7
(J= toq
2 Tpts. (sord.)
Any note in a perfect quartal chord may be doubledas well as âny other note. Doubling of the outer parts enflches.harmonlc doubling of inãer Pafts strengúensany moving voice' X coío. "rrd
Ex. 4-8
A successionof chords by perfect fourths does not fall within the intervallic make-up of ãny one scale. If the chords are to be (a). made to fit a scalep"tt"rtt, miicellaneousfourths must be used t9p. . Chords by perfect-fourths, therefore, are chromatically 19t" scale The fourths' ple than .hotdt with perfect and augmented íon.r used as building roots for perfect-fourth chords wili be duplicated at different to-nallevels, indicating a polytonal potential(á)'
Er. 4-9 D majorscalewiú diatonicchordsby 4ús
D major scde wiú chords by perfect 4ds
The perfect-perfectchord is seldomused as a dissonantstructure. The absenceof a sharpinïãilaÏ,-the equaliry of the perfect that fourths, and the mildnessof ihe minor seventhcreatea texture is consonanrin a quartal conrext. Any member of this chord is free to skip.
THREE-NOTE CHORDS BY FOURTHS
Er. 4-10
(e7
(J=so)
In chords comaining an augmented fourth (perfect-augmented or eugmented-perfect) the upper note of the tritone resolves best to the nearest note of the prevailing melodic or scale formation. If the neighboring tones of the scale lie equal distances ãway, cither direction is taken.
Ex. 4-11
;: ú a. I
4i
d
Ë ,{i:
1Ê,
ïii:
'è
Any chord tone in any type of three- or four-note quartal chord may skip a fourth or seventhif the other tonesremain stationary. The result is a larger (four- or five-note) version of úe same chord.
fi
Ë
Er. #12
4 . CHORDS BY FOURTHS
e8)
Any type of three-note chord by fourths can progÍess djatonically, chrómaticalll, or by a skip to âny other chord by fourths if one voice moveswith strong melodic PurPose. Er. 4-13
Clarity is dificult to achieve with chords by fourths in low registers;they tend to flow more easily in upper voices-woodany dissonanttone's *itrds or women'svoices.A pedalpoint lessens need for resolution. Ex. 4-14
f
'When
nuïc,
a florid voice is added to three-notechords by fourths greâterharmonic freedom is possible.
Er. 4-15
THREE-NOTE CHORDS BY FOURTHS
(99
Chords by fourths may !e approachedor left by uiads when the uppermostnote is prepared,
Ex. 4-16
('Ww ) = t 2)
+
J
when srryensionsâre not resolved,
Ex. 4-17
and when the sixth or ninth is added to a cadential tertian tomc. E*. 4-18
Piano
*Í
ttPr.
added*ote toob
When both tertian and quartal chords aPPeârin a progressbn, it is advisableto employ devicesin the tertian harrnony that bring out the flavor of tlie perfect fourth. Chords by fourús may be approachedor left by ninth chords when the fourth inversion of chord is usedwith the root in the top voice (the prorninent ú,ã "i"tt
4 . CHORDS BY FOURTHS
100)
seventh,spanningtwo fourths, actsasa binder for the two chordal categories); Ex. 4-19 () =s6) lVw.i
*Tpts .l
í-ú
by seventhchords when the third and 6fth of parallel seventh chords are replaced by the fourth;
Ex. 4-20
flt*:"
and by thirteenth chords when they are anângedso that fourths predominate.
Er. 4-21
(J=so)r;----
In quartal cadencesthe final chord is more powerful in its inverted form.
Ex. 4-22 ---------'-':-
FOUR.NOTE CHORDS BY FOURTHS
( 101
Quartal chord membersmove so freely that in cadencesmade pl.ly of chords by fourths the next to tú" hst fourth chord may have any bas tone. Es. 4-23
Chor$ py fourths are used as "dominants" in cadencesof any . harmonic idiom. Any mirure of chords may be used in quartal cedencesif the interval of úe fourú b preãominant in úã harmooy.
FOUR.NOTE
CHORDS BY F'OURTHS
A guartal strucnue more resonant than a rhree-note chord by fourths is madeby adding anotherfourth to the chord. The new tone forms a consonanrinterval (tenth) wiú the basstone and adds color and variety to quartalharmony.Four-note chordsby fourtlx are extremelyuseful in their three inverted forms becauseof the variety of intervals they contain.
Ex. 4-24
4 . CHORDS BY FOURTHS
r02)
Moving through inversions of the same chord will produce real harmonic movement without a root change. Ex.4-25
,r^--rÂÍìí?
FBbErAb
Four-note chords resolveeasilyto chords by thirds when rwo voicesmove conjunctly while the othersremainstârionâry.Threenote quartal chords with a doubling are useful in this conrexc Ex. 4-26
(J:84)
When the augmentedfourth is present in a four-note chord by fourths the uitone moves easily if placed at the top of úe chord.
Er. 4-27
ffi
Compound construction (thirds and fourths) brings fresh color to quartalharmony.A third may be addedaboveor below a threenote chord by fourths. If the addedthird is major úe chord sounds consonant;if úe third is minor úe chord soundslessconsonant.
(10t
FOUR-NOTE CHORDS BY FOURTHS
Er. 4-28
The compoundthree-notequartal chord with the major third addedis effectivewhen used as a cadentialtonic. When used as passingchords both types (major or minor thirds) are equally useful.A third aboveand below the quartal stmcture may appear with it simultaneouslyas a five-note chord; this formation is lush in soundand functions particularly well in progressions containing tertiân or polychordal structures. Ex. 4-29 An&nte la
-__:-:
a 'Ww.
ltü
Ft,."
íü
v
Str. ha
The chromaticintroduction of a chord by fourths may caìxrca suddenshift of tonaliry or scaleformation. Ex. 4-30 Âllegreao
cl.
ã--.---
./------\
:--l
4 . CHORDS BY FOURTHS
104)
Chordsby fourths may be arrangedin fifths as easilyas chords by thirds are arrangedin sixths.
Ex. 4-31
When fifths dominateâ quartal chord the fourths becomerestless.It is advisableto resolvethe fourth to â third of a compound quartal chord before returning to the pure chord by fourths.
MULTI-NOTE
CHORDS BY FOURTHS
Chords built of superimposedperfect fourths âre consonântto and incÌude the five-note chord. The six-note chord resultsin a categoricalchangein tension becauseof the sharp dissonantinterval. These six- (or more) note chords belong to the dissonant group of three-, four-, and five-note chords containing an augmentedfourth. It is good to exploit the relationshipof a dissonant group with a consonantgroup.
Ex. 4-32
Thirteenth chords and multi-note quartal chords often contain the same notes. The similarity is theoretical, not aural. If thirds overrun a six- or seven-note chord, the ear hears a thirteenth formation. If a six- or seven-note chord is overrun by fourths, a chord bv fourths sounds.
MULTI-NOTE CHORDS BY FOURTHS
(10t
(samenotes)
Ex. 4-33 ü*
úord by 4rbs
If the number of thirds and fourths is equal the chord may be used as a pivotal structnre and regarded as belonging to either the tertian or quartal câtegory, or to both. Twelve different notes may be placed a perfect fourth apart before one is repeated (twelve-note chords by fourths).
tu. 4-34
--1'-
\.nn"r*onic adiusr;lirera ,/
As the number of chord membersincreases,the linear potentiãl decreases.A touch of parallel movement, an interrupting unison, or a zuddenly enriched dominant will prevent harmonic suffocation- If muddy soundsare not wanted, place the larger intervals at the bottom of the chord and omit a member.Voices may be clusteredand the distinctive qualiry of quartal harmony preserved by the isolationof orchestraltimbre:
106)
4 . CHORDS BY FOURTHS
Er. 4-3J
SourceMaterial Quaral harmony: Alban Berg, Wozzeck (red.), p. 45 (Universal) Leonard Bernstein, Seven Anniversaries for Piano, p. 3 (Wiunark) Valerrtino Bucchi, Piano Sonatina (1938), p. 3 (Zerboni) Aaron Copland. Piano Fantasv. D. 2 (Boosey) Paul Hind'emittr, Nobilissim"'Úi'rioo"' ( orchótral suite), p. 49 (Schott) Arthur Flonegger, King David (red.), p. 5 (Foetisch) Arnold Schoenberg, Kammersy'rnphonie Op. 9, p. 1 (Universal) Roger Sessions,Symphony No. 2, p. 67 (G. Schirmer) IEor Stravinsky, Septet,p. 11 (Boosey) William Walton, Concerto for Violà and Orchestra (red.), p. 12 (Oford) Anton Webern, Piano Variations Op. 27, pp. 5-6 (Universal)
Applicati,ons 1. I{rite sequentialpâssagesfor flute, oboe, and clarinet Us chords by perfect fourtlrs exclusive$. 2. Write a short presto for two üumpets and trombone. Feature perfet-augmented and augmented-perfect chords by fourths. 3. Write an example of tlree-part quartal harmony for two violirs and viola over a cello pedal point. Ornament the pedal. 4. Continue the following pâssagefor tnrmpets preserving úe general úarac er.
MULTI-NOTE CHORDS BY FOURTHS
(107
Ex. 4-36
í
*0.
5. Compose an original piece for women's voices (SSA) featuring chords by fourths. Other textures may be included. Use the following text, Psâlm lA7: "They mount up to the heaven,th"y go down again to úe depths:their soul is melted becauseof trouble.' 6. Continue the following idea for piano.
Ex. 4-37
7. Add sopÍano,alto, and tenor voices;use chords by fourths.
Ex. 4-38 (bes voice;
8. Harmonize the following melody for woodwind quârtet allowing quartal harmony to dominatethe passage.
En. 4-39
108)
4 . CHORDS BY FOURTHS
9. Write severalmelodies and harmonize them with a predominandy quartal texture. Any medium and any number of parts may be used. 10. Extend the following string-quârtet opening. Feature pentatonic melodic and quartal harmonic writing.
Ex. 440
""^ïïïï Added-NoteChords | cEAPTER
|
^
Ax eouno-xorB chord is a basic harmonic formation whose textural quality has been modified by the imposition of tones not found in.úe original chord. The tones to be added form one or more major or minor seconds with any member of a chord by thirds or by fourths. These added notes âre usually placed a second above or below any member to avoid creating seventh, ninth, compound chords, etc. The added tone or tones are modifying elements attached to a chord of clear directional powers and, as color modifications, change the texture rather than the function of the basic structure. Traditional examples of added-note chords are to be found in the cadential tonic six-five and the French augmented sixth chord.
AUGMENTED SIXTH CHORDS The augmented sixth is a likely chord to add notes to because its directional pull is sufficiently strong to be unimpaired by the 109
5 .ADDED-NOTE CHORDS
110)
addition of color tones. The French augmented sixth is a prime example; here a major second is added above the middle tone of the basic Italian augmented sixth chord. This attached note alrers neither the function nor the formal meaning of the Italian chord but creates fringe color (the augmented súth interval gives the Italian chord its motivating power and the interval a thirdlrom the bottom gives it its fundamental flavor). Twentieth-cenrury added-note technique employs five basic augrnented sixth chords to which seconds may be attached. Theie chords consist of the interval of the ausmented sixth with: a major third (Italian); a"minor third; an atfumented ocrave with a major úird; a doubly augmented ocrave with a major third; and an augmented third.
Ex. Í-1 Wiú:
me.3rd from bas
mi.3ril
aug. Bve r i--l----------addeónot* added +ür
'O
added'notes
ú ' -&$ic - r(French)(whole(rtôrran) tone)
rlF-.
doubly aug.Sve
,\1./
, Basic,
added^notes
, Basic ,
ì
' Basic J
aus. 3rd
'CI
addednotes
(guatal)
The formation with the minor third is a color varianr of the Ilalian augmented sixth with the major third. The basic augmented sixth chords with the augmenred ocrave and with the doubly augmented octâve are ninth textures and are useful in passagesfeaturing ninth, eleventh, and thirteenth chords. The aúgmented sixth chord with the augmented third is useful in a quartal conrext and is ofrcn spelÌed enharmonically. In any chord containing the interval of the augmented sixth the voices spanning úe interval have
( 111
OTHER ADDED-NOTE CHORDS
a tendency to expând, descendchromaticaÌly, or move obliquely (one voiceheld).
Ex. Í-2
sutionaryvoice
Several ma]or and minor seconds may be added simultaneously to any form of the augmented sixth chord without changing its function. The chord has a strong tendency to move onward regard,lessof the number of notes attached to it.
Ex. J-3
Augmented sixth chords with two or more added notes resolve most naturally to added-notechords of another variety, because of their commonsecundaltexflrÍe.
OTHER
ADDED-NOTE
CHOR.DS
Major and minor secondsmay be addednot only to augmented sixth formationsbut to most chordsby thirds and fourths. Added nores âre nor ornamentaltones soundingwith a chord but true
112)
5 .ADDED-NOTE CHORDS
color membersthât rival the third in color potential. They add spiceand increasethe harmonic density. Ex. J-4
Majot and minor seconds may be added above or below any member of a maior or minor triad but the lower the added note is placed in the chord the less resonant the formation.
En. Í-Í
Adding â note abovea maior third diÍfusesúe color of this rich member.The minor thfud is somewharlessaffected by an added note. The diminished triad will always be a sharp-texruredchord regardlessof what addednote is appliedor where it is added.In the augmentedtriad with major secondsadded above or below any member, the texture is still whole-tone; the minor-secondadditions aremore usefulbecauseúey makepossibleintervallic variety. Additions to seventhand ninth chords âre more frequently minor secondsbecausea major-secondaddition somerimes resultsin duplication of a chord member.
OTHER ADDED-NOTE CHORDS
( 113
Ex. 5-6 dm.uiad
eug.uiad
9ú chords
In somecâses,a uiad or seventhchord wiú an addednore mây resemblea ninth chord. A look at rhe context can determineúe true identity of the chord. In an added-noteseventhor ninth chord even the sharply dissonântaddedtonesdo not competewith the sevenú or ninth for dissonant-tone movementâttention;the addedtonesare not strong contenders for resolution. They cling to inverted as well as to fundamentalchords and may be doubled at will. Doubling the addednote in outer voicesis effectivewhen it occursassuccessive octavesin melodic coupling. Over-all coupling soundswell when usedin an entire body of added-noteharmony.
Ex. Í-7 (J +zo1 'Ww. -'-
IIDs,&TbDs.(Svebwea)
Secondsare added to chords by perfect fourtlx in the following order for sonority: for mild texture, the maior second below the seventh, above the fourth, below the fourth, and above the "root"; and for sharp texture, the minor second above the seventh, below the seventh, above the fourth, below the fourth, and above the "root." The lower the second is placed in the chord the less resonant the formation:
5 .ADDED-NOTE CHORDS
114) Ex. J-8
aug.4tÌr witlr added.oote
It is possibleto regard the above chords either as uiads with addednotesor asincompleteseventhand ninth chordswith added notes.The chords will sound like added-notechords by fourths if they appearin a passagedominatedby fourth chords and like added-notechordsby thirds if a preponderanceof chordsby thirds is used. The chromatic-secondaddition to chords by perfect fourths createsa sharptexture which blendswell with the texture of augmentedfourth chordswithout addednotes.Whether the seconds fastenedto âugmented-fourthchord membersare malor or minot, the chord will always be of sharp texture becauseof the major seventhinterval in the basic formation. Ex. Í-9
(D G CD
(D GTLI)'
Augmentedfourth chords with and without addednotessound well side by side becausethey both belong to the category of sharp textures.
Ex. Í-10 (J =1oo) (trin unr. a 3)
OTHER ADDED-NOTE CHORDS
( 11t
In any kind of added-notechord two generaltexturesâre Posand a úarp type havsible,a mild type havingno sharpdissonance ing at leastone sharp dissonance. E*. Í-11
Added-notechordsof the mild type often stop harmonicflow by their tendency to form a cadence,and when used extensively causeharmonic progressionsto becomeparulyzed.A flow can be maintainedby mixing freely the mild and sharpryPes. The progressivemotion of added-notechords is govern"d by the basic harmony to which added notes are attached.Such devices as cadences,sequences,and traditional harmonic formulas help protect the basicchordsfrom the debilitatingeffect of crowding seconds.
Ex. í-12
)^
rl --2
'*
-
=Ê
+
116)
5 . ADDED-NOTE CHORDS
Added-note chords are effective as zuch only when a clear and definite harmonic progression is implied by thã basic chords or is previously established by chords without added notes. This is particularly true of those chords thar contain many notes spread over a wide range. Notes may be attached to complex basic chords if the stmctures are first clearly stated without the color tones. If notes are added to a complex basic chord without textural prep aration, a chord of a larger basic formation-not of added notes -is heard. A large compound chord and a complex added-note chord are often identical. Unless a 6rm harmonic progression is felt under the complex added-note strucrure, a compound harmonic texture will prevail. Added-note chords are ofren secundal in appearance;ân addednote chord and a chord by seconds âre somerimes identical. It b only within the general conrexr of a section of music that a difference can be seen. Occasionall/, added nores are placed outside the original octâve rânge. This wider spacing produces grearer freedom of harmonic rnovement and clearer focusing of the disonant added tones.
Ex. Í-13 1)=nz'1
rr'I6!
A special câtegory of this type of chord with its added note outside the octave is that of the triad in cÌose position with a nore added below. A triad (major, minor, diminished, or augmented) is placed in the upper voices and a ma]or or minor second above or below any of the members is added as the bottom voice. often in
OTHER ADDED-NOTE CHORDS
( 117
octâvesfor balance.A wide variety of chordal scnrctr*esis possible; there are thirry-six suchchords. Ex. Í-14 mi. triad
ma. triatl
ma.2nds
ni.2n
r-l
5 6 'A=ttí " s = 7fi7 - ú * pí' t , ,'7 orild
,t
,
rug. triad
mi.2nils
ma.Znds
| E T- ï ,t
r
nra.2nds
''t 6 cïtl
sharp
,, dim. uiâd
mi2nds
c
mild
'
rna.Znds
Although some of thesestructuresresembletraditional chords by thirds úey do not function assuch in a context of added-note harmony. Progressionin this qype of added-noteharmony is often governed by an upper melodic line. Each note of a melody, except ornamentaltones,may be considereda memberof a maior, minor, diminished,or augmentedtriad. A bassline is then constructed from notes a secondfrom any triadic member (Ex. 5-14). Bass notes for the bottom line are chosento form the kind of outervoice relatiorship that best suits the desired texture and phrase shapes:
5 . ADDED.NOTE CHORDS
1 1)8 Ex. J-LÍ me.
mâ.
rni.
mi.
mr. mr.
= n=#= ==F=
ur.2ndmi.2ndmi.2admi m+ mi nra, mL
This type of added-notechord is most eÍfective when used in harmonicprogressions consistingsolely of the samerype of addednote structures.Primary and secondaryrelationshipsare not relevant, melody_being the governing factor. Textural consistencyis insured by chordal spacing,and freedom of Ìinear movemenris madepossibleby the wide selectionof bassnores.
SourceMaterial Added-noteharmony: Paul Ben-Haim, 5 Piecesfor Piano Op. 34, p. I0 (Neqen) BenjaminBrirten, The Turn of the Screw 1rìd.), ìp.4t++ (Boosey) ^ Carlos Chávez,Sonatinafor Piano, p. I (Cos Cobf Aaron Copland,BilÌy the Kid (ballêt suite), p. 85 (Boosey) Luìgi Dallapiccola,Volo di Notte (red.), p. l7 (Universal) Alberto Ginastera,Piano Sonata,p. 24 (Bfurv\ press) !zí. Çgmargo Guarnieri, Den-Báu, p. 3 (Muiic Paul Hindemiú, Das Marienlebenf p. ó9 (Schott) {frhy Honegger, Jeanned'Arc au llücher (red.), pp.20-21 (Salaberc) Charles lves, Violin SonataNo. 4, pp. 4-5 (Arrow)^ André Joliveg BassoonConc-erto(;dd.), p. 32 (Heugel) (Zerboni) $""999 Malipiero, Sonata for Violin anid Piano, plf ' Frank Martin, Piano Prelude No. 4 (Universal) leter Mennin, The ChristrnasStory (red.), p.26 (C. Fischer) Gian Carlo Menotti, SebastianSuite,'p. ti (Ricordi) pariry Milhaud, ChristopÌre Colomb (red.), p. 8 (Universal) Igor Stravinsky, Fire-Birã Suite, p. 77 (Kâlmirs) Antoni,o Veretti, Piano Sonatina, b. 9 (Ricordi)
OTHER ADDED-NOTE CHORDS
( 1le
Applicati.orcs 1. Constrrrct a segmentof music for chamber orchestra featuring various types of augmentedsixth chords. 2. ìVÍodulate by means of various kinds of augmented sixú chords through severalkeys. Scorethe examplefor two pianos 3. Write a short triadic passâgefor woodwinds that is interrupted by a solo horn introducing an added-note variant of the initial material. in strings. 4. Write added-notechords for piano, right hand, over this left hand ground bass.Extend to sixteenmeasures.
Ex. J-16 ?reff
5. Harmonize a folk tune with added-note chords of tlre mild type. Scorefor voice and piano. 6. Write an allegro section for brassesand feature added-note úords of the sharp varieqy. 7. \À/rite a sarcastical$ rhythmic pâssagefor string qpâner. Feature augmented fourth chords wiú added notes. 8. Write an exampleof coupled added-notechords for band. 9. Extend the following piano idea, preserving úe general character.
Ex. Í-17
120)
5 .ADDED-NOTE CHORDS
10.Write an orchestralcrescendoin which the harmonic volume increases. Start with smalladded-noteformatiors and finish with a cadence of complexadded-notestrucflrres. 11. Harmonize the following melody for strings with uiads in the violins and violas, and the added notes in the cellos and basses(in octaves).
Ex. í-18
CEi{PTER
srx
Chordsby Seconds
Tnnne ARE,THREEcategoriesof intervaÌlic materials from which chords may be built: thirds or sixths (tertian), fourths or fifús (quartal), and secondsor sevenths(secundal).The addition of secondsto chordsby thirds or fourths, or the filling-in of the mixed intervals of compound chords for coloristic purposes,does not produce chords by seconds;theseare added-notechords.But out of context zuch chords may be called by eiúer naÍIÌ€.
THREE-NOTE
CHORDS BY
SECONDS
Both maior and minor secondsmay be usedin the constmction of chords by seconds(the augmentedsecondis tertian in effect). There are four intervallic rypes of three-notechords by seconds: maior-major, major-minor, minor-majornand minor-minor. Arrangedin an order of consonanceprogressingto dissonancethey âre: m
6 . CHORDS BY SECONDS
122) Ex. 6-1
Two inversionsof eachare possible.
Ex. 6-2 3und.
2ad
Chords by secondsmay be arrangedin sevenths,as chords by thfuds may be arrangedin sixths and chords by fourths in fifths.
Es. 6-3 o-
h-
CDE
CEG
CFBI
chords by secondsare usedin closeposition they cramp Shen easily and becomepercussivein the low register. Spacingin intervals of the seventhand ninth gives the muscle-bìund chords by secondslinear freedomand room for activity of the parts.
Ex. 6-4
In the preceding example,spacing produces chords similar ro ninths, but in a secundalcontext úey are chords by secondsin
THREE-NOTE CHORDS BY SECONDS
(123
oPen poslrlon. In major, minor, or the five other modal scales, only the first three types of three-note chords are found naturally; the minorminor is derived from chromatic or synthetic scales.
Er. 6-Í
For solidariqy, the bass note of secundalharmony, whether root, second,or third, is doubled (a). For mildnessof texture the most consonantnote over the bassis doubledregardlessof whether of texture the most dissonant or not it is the root (á). For sharpness note over the bassis doubled(c).
Er. 6-6
A dissonanttone is a resdesstone thât often asksfor resolution. In fundamentalposition and in secondinversion of secundalharmony of any intervallic type the dissonanttone is the secondof the chord. In the first inversionit is the third of the chord, except in the minor-maiorfirst inversion,where the root is most disonant.
Ex. 6-7
1
6 .CT{ORDSBY SECONDS
124)
In the first inversionof úe major-maiorthe roor becomesthe dissonanttone if it lies below úe úird.
Er. 6-8
ffi
l*inn
If the dissonanttone is a member of a sharp dissonantinterval (major seventhor minor second),one of the membersthat forms the shar! interval is, for smoothnessof line, best approachedand left conjunctly or by repetition.If the dissonanttonêìs not a member of a sharp dissonantinrerval, it is approachedand left freely.
Ex. 6-9
Three-note secundalharmony hasa unique flavor.
Er. 6-10 Andentc
rmt
>J í
8ú.
>J
(12t
MULTI-NOTE CFIORDSBY SECONDs
MULTI.NOTE
CHORDS BY SECONDS
Four- andfive-notechordsby secondsmove contrâpuntallywith difficulry. Linear motion can be obtained by including in the progressionthree-note chords by secondsor chords by fourths. The sevenths(inverted seconds)that are presentin chords by fourths blend with the secondsin chords by secondsand leave spacefor movementof the parts. Ex. 6-11
(J=s+)
{r
!
In the preceding examplechords by secondsare usedat the phrase breath without disturbing the parallel position of the parts. an enA singlechord by secondscan be enlargedto encompass úe scale,diatonic, chromatic, or original. It may or may not be a cluster dependingupon the type of harmony that surroundsit. This thickened harmony is best combinsd with polychordal or cornpoundharmony beforeit hardens:
]\
126)
6 . CHORDS BY SECONDS
Ex. 6-12
SourceMaterì.al Secundalharmony: Béla Bartók, String Quartet No. 3, p. 3 (Boosey) Karl-Birger Blomdahl, Aniara (red.), p. 105 (Schoa) Aaron Copland, Piano Sonata,p. l+ (Boosey) Claude Debussy,PréludesVol. II, p. 73 (Durand) Darius Milhaud, Christophe Colomb (red.), p. 143 (Universal) Francis Poulenc, Promenadesfor Piano, p. 13 (Chester) Carl Ruggles, Men and Mountains, p. 12 (New Music) Camillo Togni, FantasiaConcertante (flute and suings), pp. 4-5 (Zerboni) Heitor Villa-Lobos, String Quartet No. 3, p. 32 (Eschig)
CLUSTERS
is dominatedby chordsby secondsand arranged When â passâge in predominantlyuninvertedforms so thar most of the voicesare â secondapaÍt, the chords are called clusters.These âre not true chords by seconds,in part becauseof their generally consistent spacing but mainly becauseof the lack of defined inner voice movement.When large clustersare used, handüng the voices is âccomplishedsolely by considering the two-pa$ contrapuntal frame formed by the outer voices.The secondsfill in this frame while expandingand contracting the clustersto form good outerpart writing.
(127
CLUSTERS Ex. 6-13 Frame
Most scaleformationsor their pârtsmây be clustered.The chromatic scaleis the least useful becausewhen clusteredit becomes tiresomequickly. A seven-notescalemay be clusteredmodally in sevendifferent ways; and a two-octave scale,in fourteen. Ex. 6-14
Changing,in progression,the intervallic make-up and number of chord membersgives cluster harmony textural interest and momenüÌm. Ex. 6-1Í
Orclu
,,f
uetc.
íz
128)
6 . CHORDS BY SECONDS
Subtleties of cluster part-writing are diÍficult to compose or notate for the piano. Chamber combinations and the orchestra can more fullv utilize clusters and better accommodate notation. Chromatic cluóters are often notated for keyboard instruments with one note written so that it runs through the entire cluster, the cluster to be played with palms or ârms.
Ex. 6-16
A chromatic cluster can be scored for instruments in such a way that úe cluster is broken into chordal units.
E*. 6-17
'When
clustersmove in parallel motion the progressionis purely melodic. Changing the parallel motion to similar motion in some of the voices adds textural interest, and using occasionaloctaves in the t\Ãioouter pârts accentuates úe color. Clusters progress harmonically by expanding and contracting, changing úe intervallic construction, omitting chord members, and shifting voice colors. Large clusters are powerful in dramatic puncilations but smaller clusters âre more agile and generally easierto handle. The consonant-dissonant quality of cluster harmony may oppose
/a'
CLUSTERS
( 129
or pârallel the quality of the counterpoint of the outer voices. Consonant or dissonant clusters (diatonic or chromatic) may be used in.aÌl possible combinations with consonant or dissonant outer volces. Clusters may be formed from one complete scale of any type or from t\Ã/o or more contrasting scales.
Ex. 6-18
A cluster is not always introduced by sounding all its tones simultaneously.When the tones of a cluster are soundedconsecutively they are effective if each note is held until úe last entersThesearpeggioversionsof the clustercontribute variety ro secundal panerns.They may unfold from top to bottom, bottom to top, or from the center to úe extremities. Ex. 6-19
The consonant or dissonant aspect of a cluster's character may be accentuated by the way in which its members enter. Or accentuation may be determined by sounding consonant or dissonant intervals of the cluster beforehand:
\
ó . CHORDS BY SECONDS
130)
Er. 6-20
Large clusters may accumulatethrough the additive use of chords by thirds or fourths, polychords, or smaller clusrers. Ex. 6-21 clusterentrancc Band
I
PolYchordal
Two or more clusters,derivedfrom one scaleor different scales, may be used simultaneouslyas a polycluster. The roots of the variousclusterunits of a polyclustermây form a chord by seconds (a),atríad (b),or a chordby fourths(c).
Ex. 6-22
bv 2nds
tÍiad
by 4tbs
Spacemust be left betweenthe cluster units to allow them to sound distincdy. The larger each cluster, the wider must be the sPace. The number of contrapuntalvoicesinvolved in polyclusterharmony is automaticallydoubledif úe cluster sizesÍluctuate.Each cluste.ris úen oudined by two independentvoices.
(13r
CLUSTERS
Ex. 6-23 for clusters
Varying the outer voicesby contrary oblique, or parallel movement will produce clusters of changing sizes.As clusters increasein size, harmonic tension increases;as clustersdecreasein size,instrumentalcolor can becomeconcentratedbecauseof overlappeCand doubledvoices. Clustersmay be broken (arpeggiosby seconds)but will sound like clustersonÌy if cluster harmony has been previously established.They will sound like scalesif the broken clustersâre nor clearly part of a clustercontext.
Er. 6-24
Hní^
* nuïc.
J
broken chord
ü a*
ïL*\_*-\--* It t.b.
ì-,
-^
-^
-^
6 . CHORDS BY SECONDS
132)
Ornamental tones increase harmonic circulation in passagesof clusters. Ex. 6-2Í
ob.a Str.
,,
têncí.
Ttlldlgng aaditional harmony into cluster harmony by av -. bitrarily filling in the spaceis calculativeand usuallywithôut musical impetus.Clustersmore effectively stemfrom the secundalharmony that generatesthem becauseof the commoninterval of the second.Clustersare used with chords by seconds,but occasioni" conjunction with or in contrastto other types of harmony. 3!y When clusters or chords by secondsare used with chords by thirds or fourths they can táke part in progressionsof functional root relationships. Ex. 6-26
CLUSTERS
( 133
SourceMateri.al Clusters: Alban 9erg, Wozzeck (red.), p. 33 (Universal) Ernest Bloch, Piano Sonara,p.1 (Carisch) Henry Cowell, Silt of the Rèel (Universal) AIan Hovhaness,Magnificat, p. 26 (Peters) Charleslves, 19 Songs(Majoiity; 1ìVew úusic) Wallingford Riegger, Music for Brass Choir, p. 1 (Merrymount) Edgard Varèse, Ionisation, p. 21 (New Music)
Applications 1. Harmonize the follorr.ing melody for string trio using chords by seconds.
Er. 6-27
2. Write â three-part Elegy for two clarinets and bassclarinet featuring chords by seconds. 3. Write a short Presto for three muted trumpets featuring minorminor chords by seconds. 'Write a four-part Preludefor string quârtet employing three-note 4. chords by seconds(with doubling), four-note chords by seconds,and chords bv fourths (with the inverted seventh).
134)
6 . CHORDS BY SECONDS
5.'Write a Capriccio for two pianosin which diatonic, penratonic, and chromatic clusters are used. ó. Write a slow passagefor string orchestra allowing clusters to expand and contract. T.Write an exampleof orchestralmusic which includesseveralpolyclusters.
""ff:ï n"t chords I
A por-ycnoRDrs the simultaneouscombination of t\Ã/o or more chords from different harmonic areâs.The segmentsof the polychord are referred to as chordal units. The beginningsof polychordsmay be tracedto doubleand triple pedalpoint, where hinrs of bitonaliry, causedby the relationshipof the passingchords to the pedal chord, üe in the passingharmony.
Er. 7-1
-
(sn) p dotrr*
t
-G
71
.a-
{Èx ld I
=-=--zõ (tddcpd.)
r36)
7 . POLYCHORDS
?olyharmony is seldom polytonal. Polytonality is present only when the chordal units that makeup the structure adherero separate keys.
Ex. 7-2
D major arca 3f €ull orch.)
F mejor arca
Polychords that are not polytonal are considerablymore flexible and versatile;the harmonic areasof both chordal units shift often.
TWO TRIADIC UNITS
(Piano)
'lP <
Clear grouping of the chordal units is a requisite of polyharmony, and rearrangingúe tones of úese units can desuoy the polychordal organization.
Es,.74 ü
fi'
x (notapolyúorQ
T\MO
TRIADIC
UNITS
Overtones resulting from a fundamental tone and from those overtonesthemselves may producepolyharmony:
r.38 )
7 . POLYCHORDS
Ex. 7-Í
The resonance of a polychord is determined by the intervallic structure of the bottom chordal unit and the powãr of its separate tones to generate overtones. The second inversion of the major uiad as a botrom unit is the most resonant chordal unit upon which polyharm-ony can be erected, becauseits internal spacing is crosest to that of the harmonic series; the major third of úe fiindamental triad in close position is nor as close to the size of the perfect fifth of the overtone seriesas is the perfect fourth of the six-four chord. When the tones of the bottom triad are spread apart, the fundamental position is most sonorous. Any position or inversion of the upper triad may be used depending upon úe kind of ourer-voice relationship desired. The upper triad of a polychord depends upon its proximity to the overrones of the third and fifth of the lòwer uiìd for resonan-ce.-A complete inventory of major-major polychords may be made by b:{Fg the upper major uiads on the notes of a óycle of perfect fifths that begins with the bass nore of the bottom'sixfour chordal unit. The triads are added, in turn, to the bottom six-four chord, creating a rising order, based upon the cycle of fifths, which places the chords in a natural seqoeãceof deóreasing consonânce and increasing dissonance.The last six polychords are noticeably less resonant; úe sound of number 11 is aimost a dull
úud.
TWO TRIADIC UNITS
( 139
Ex. 7-6
The density of the polychordal strucrure is determined by spacing. Placing chordal units well aparr allows for maximum tonal vibration. Contrasting instrumentation of the chordal units clearly defines the contrasting h".*onic zones. Doubüng the consonant intervals gives strength. A tone common to the units helps blend the component parts. The relationship of the bottom and top rones of the polychord is important. Consonant outer-voice resonancespreadsits eÍfectiveness throughout the formation and dissonant outer voices do úe sâme. LX.
t-l
Moderáto
D--J
mgt
Ç
mnoro
A polychord gains resonanceif smallerintervals are placed in the upper register and wider intervals arç placed in the lower
7 .POLYCHORDS
140)
register.A polychord like number 7 (Ex. 7-6) becomeslessnebulous by careful spacing.
Er. 7-8
Although closespacingandmonochromescoringproducecloudiness,the result is a valuable addition ro the over-all fluctuating tension of harmony.
Ex. 7-9 Slowly
(3Crí.) 2
rq..
(3 nutcd IIns.;
,t
The closer úe dissonanttones are placed to each other, the higher the degree_ of tension;but unlessclearly definedas part of a chordal unit, the different harmonic areaswill run intã each other and polyharmonyceaseto exist
Ex. 7-10
TWO TRIADIC UNITS
(141
Nevertheless, this added-notechord can be projectedpolychordally by strongly contrastedinstrumentation(C maior woodwinds and Ff major strings). If the upper unit in a polychord forms a chord by thirds with the bottom unit (numbers1 and 12,Ex. 7 -6), the earidentifiessuch a stucture, out of context,âsa non-polychord.But the chord may be unmistakablypart of the polychordal category by reasonof context when surroundedby polyharmony. Ex. 7-11 Pesante ( J' 84) > QJr>
Str.
Orú.
Í
When the lowest note of the polychord is placed somewhere below the bassclef low F, the harmony becomesmuddy unless an open-position chord is used. (The "muddy" polychord is nevertheless a valuablestructure under appropriatedramatic conditions.)
Ex. 7-12
As a polychord is transposedupward it losesbody and resonance but gains brilliance (a). Drastic complexion changesoccur in lower registertranspositions(á) :
7 .POLYCHORDS
142)
Ex. 7-13
,f
Piano
ctesc.
A polychord may be madeup of any kind of triads.When it is constructedof major triads it is most consonantand resonant,becoming progressivelylessso asminor, rhen augmented,and finally diminishedtriads are included. The qualitiesof the twelve maiorminor (namedfrom the bottom upward) possibfitiesmay be observedwhen the upper units are addedto the bottom chord in a rising cycle of fifths beginningwith the bassnote of the bottom unit. Numbers 4, 5, 6,9, and 12 arc more useful becauseof their resonantcharacter, Ex. 7-14 oa.-mi polyúords
dÉ.f::
12t4.t678
ïÍ't 91011t2
+++
++
A minor over a major triad is richer than a major over â minor; the upper triad in the first formation receives additional supporr -from from tones of the lower chord other than the bottom tone which it is generated.
TWO TRIADIC UMTS
(143
Er. 7-1Í
Of the minor-majorpolychords,numbers1, 5, and 10havewider usebecausethey are more resonant. Ex. 7-16 mi.-ma. polychords
)^
+
.a*
+
'4-
r23456789101112
In minor-minorpolychords,the resonantnumbers1, 5, and 9 aremostfrequendyused. Ex. 7-17 -tÀ
mi.-mi. oolvchords L t +
,.tt
1234567891011t2
r*-
..
+
t-
144)
7 .POLYCHORDS
.AIl polychordscontainingât lea$ one diminishedor augmented triad are identified as chromatic polychords.The most süpple of the chromaticsare: Ex. 7-18
when the bottom chordal unit is augmentedor diminishedit is advisableto spreadthe voicesof the lower triad to avoid lowerregistercrowding. The mosr resonanrpolychordsin this caregory are: Ex. 7-19
dim.-aug.
TWO TRIADIC UMTS
(14t
The direction of polyharmony is determinedby linear movement.The counterpointof chords (counterchords)is derivedfrom a t\Mo-partlinear frame of single-tonelines. Two kinds of counterchordal techniquesserveâs a working basisfor polyharmonic writing: t\Mo-partcounterpoint used as the outer voicesof polyharmony, Ex. 7-20
Piem
xp
kgao
and two-part counterpointusedasúe roots of triads of both units making up the polyharmony. The notes of the basic tv/o-parr framework of roots move freely betweeninner and outer voices:
7 .POLYCHORDS
146)
Er. 7-2Ì
Any note of any melodicline can becomerhe roor, third, or 6fth of a major, minor, diminished,or augmentedtriad. Whether úe composerworks from the upper or lower triad, the great number of combinationsof triads that are possiblegiveshim a wide choice of textures within which the harmonic tension can fluctuate.
E*. 7-22
Str. Orch.
2
tener.
Cretc.
TWO TRIADIC UNITS
(147
Polyharmonic progressionstouch so mâny key areasthat tonaliry annnotbe securedthrough the harmonic personaliryof a prevailing scale.Tonality is establishedby the tonal implications of a predominatingmelodicline or by harmonicgravitationro a dominating chord. Resonantpolychords play the tonic role most convincingly; a wealth of invention must be savedfor the cadenceif a firm tonal center is desired.A tonality may be formed by the melody,
Ex. 7-23
or from a characteristicchord.
Ex. 7-24
3 Tpts. '
í.
Prolongedpassâges of pure polychords can result in tiring mass resonance;the richnessand thicknessstifle inner voices.Modification of the ìines by ornamenrâtionfreshensthe texture since attention is capturedby individual voice activity:
7 . POLYCHORDS
148)
Er. 7-2Í Slowly
Pi-o
"f
frò. -f,ò
-tò.
-Sò.
-çò.
-#
simitc
Unison and two-voice interruptions revitalize the polychordal texture.
Ex. 7-26 (J :132)
Violas and Gllos
í\
TWO TRIADIC UMTS
(14e
Omission of notes of either chordal unit lightens the rexrure and contributesharmonicflexibility.
Ex. 7-27
When polychords are used as architectural harmonic pillars, their dynamic conrrasrwith other types of harmony is refrêshing.
Ex. 7-28 Á,llegro
a
a
Winds
Í
?esox,
>
7 . POLYCHORDS
tt0)
SourceMaterial Polychords,two triadic units: Béla Bartók, String Quartet No. 5, p. 87 (Boosey) Peter Racine Fricker, Piano Concerto Op. 19 (red.), p. 40 (Schott) Roy Harris, SoliÌoquy and Dance,for viola and piano, p. 7 (G. Schirmer) Arihur Honegger, Symphony No. 5, p. I (Salabèrt) Charleslves, Piano SonataNo. 2, p. ó5 (Arrow) Albert Roussel,Bacchuset Ariane, p. 57 (Durand) William Schuman,Symphony for Strings, p. I (G.Schirmer) Igor Stravins$, The Rake's Progress (red.), p. 195 (Boosey)
THREE
OR MORE
TRIADIC
UNITS
Chordal units in polyharmony are often built upon different overtonesof the sameseries.There are four kinds of polychords with three or more units: thosewhoseupper units are built on the third and fifth of the botrom triad (rarely the root);
Ex. 7-29
rhosewhoseupperunits arebuilt on overtones(at any octavelevel) of the third andfifth of the bottom triad;
THREE OR MORE TRIADIC UNITS
Ex. 7-30 +
1 5th above Jú
(1t1
$*
5ú abovc3rd
thosewhoseupper units are built on overtonesof the overtonesof the third and fifth of the bottom triad;
Ex. 7-31 5ú of úc 5th of úc 5ú
and those whose upper notes are built on overtonesof the root, third, or fifth of triads other than the bottom triad.
tt2)
7 .POLYCHORDS
Multi-unit polyharmonyis so massiveand complexthat the notes of úe bottom triad must often be spreadâpârt. Someunits shouÌd be overlappedand others should have the spacebetween them widened.Doubling and coupling enlargea polychord without adding to its complexity.
E*. 7-33
Overlappingin a three-unit chord may result in a two-unit chord.
Ex. 7-34
Multi-unit polychords (usuallynot polytonal) are usedfor brief periodsof time. Their natural habitatis a climactic section,
(1t3
NON-TRIADIC LINITS
Er. 7-3Í (J:80)
Piano, ,t hands
-F
F I
çò.
E"
hr
E
rK -*
or a fast trut quiet section.
Er. 7-36 Prcsto
Ww.
I
leggicto
NON-TRIADIC
UNITS
Polychordsconsistingof seventhchord units are seldomusedin but more often in brief chordal groups that extendedpassages intensify a singÌeline or a two-paft statement'
7 .POLYCHORDS
1t4) Lr.
F ^ -
t-t t
Tl:y' J=ao)
nf
Full
cresc.mobo
B. Dr.
or asâ sforzandochord. Ex. 7-38
Somepolychordswhoseindividual unie are seventhchordscontain one or more notesin common,which makesfor a homogeneoussound; Er. 7-39 3 notcs in common
2 notes in common
t nco incommotr
(ttt
NON-TRIADIC UNITS and somehave no notesin coÍnmon.
Ex. 740 a
h]
tht <
When chords other than chords by thirds are used as building units in polychords,textural clariqy becomesmore of a problem. Polychordal formations of chords by fourths are, in effect, enlarged versionsof three-note chords by fourús. And if all the units are secundal,a polycluster results. However, quartal and secundalunits are used with those by thirds in a polychord of mixed chordal units. Chords by secondsfunction sonorouslyas the uppermostunit of a multi-unit polychord of mixed chordal consüuction.
Ex" 741
I I
The polychordal combinationof the triad with other chordal formationscreâtesan additional and useful polychordal category. When combining chords by fourths with triads, place the triads below for linear freedom whether the fourths are perfect,
7 .POLYCHORDS
1t6)
Ex.
t6789101112
123456
7891011t2
or augmented. Ex. 7-43
Triads areplacedabovefor lessresonanrbut usefulsubtlechords of a darkertexture.
(1t7
NON-TRIADIC UNITS Ex. 7-44 (cons.)
-oã
prfect
*---
rte-
augmented
Other polychordal combinationsare possible. Ex. 7-45
ü*r =J
7úr mi. tried l-
aqg.trid
L
7ú inc. Tth din Eüd
SoarceMaterial Polychords,three or more units: Arthur Honegger, Cris du Monde (red.), p. 9 (Senart) Charles lves, Piano SonataNo 2, p. 26 (Arrow) Olivier Messiaen,Visions de I'Amèn, for two pianos,p. 2 (Durand) Darius MiÌhaud" Cinq Symphonies (petit orchestre), p. 52 (Universal) Humphrey Searle,Symphony No. 2, p. 38 (Schct)
r.-,ì
7 . POLYCHORDS
1t8)
Polychords,mixed units: Béla Bartók, SonataNo. 2 for Violin and Piano, p. 29 (Universal) Alban Berg, Wozzeck (red.), p. 71 (Universal) Aaron Copland, Piano Fantasy, pp. 5-ó (Boosey) Paul Hindemith, Piano Sonata No. 2, p. 12 (Schott) JacquesIbert, Divertissement, p. 52 (Durand) Leon Kirchner, Duo for Violin and Piano, p. 9 (Mercury) Marcel Mihalovici, SinÍonia Partita (strings), p. 62 (Heugel) Darius Milhaud, Les Choëphores(red.), p. 41 (Heugel) Arnold Schoenberg,De Profundis, p. 23 (Leeds) Igor Stravinsky, Symphony in Three Movements, p. il (Associated) funst Toctr" The Princessand the Pea (red.), p. 26 (Schoa)
Applications 1. Harmonize the following two-part pâssagein six-part polychords for the piano.
Ex. 7-46
(1te
NON-TRIADIC UNITS
2. Harmonize the following first-trumpet melody in six-part brass harmony (three trumpets and three trombones). Use a predominantly polychordal texfure with occasionalunison relief.
3. Harmonize the following bassline for string sextet (two violins, two violas,and two cellos).
Ex. 7-48 Ândante
,f
-----:ry 4. Extend the polychordal passagefor piano:
160)
7 . POLYCHORDS
Er. 7-49
etc.
featuring polychordal ornamentation 5. Extend the woodwind passage
Er. 7-Í0
z.'---.-
êtê,
6. Extend the passageof broken polychords (three units) for piano.
Er.7-51
NON-TRIADIC
UNITS
( 161
7. Continuethe polychordal orchestraltutti.
Er. 7-52
ì-
8. Additional lines for polychordal harrnonizationin any mediurn.
Ex. 7-Í3
a -+arf?p
Â
7 .POLYCHORDS
CEÂPTER EIGET
COMPOUND
Compoundand Mirror Harmony
CONSTRUCTION
MaNv cÍroRDsâre constructedby superimposingintervals of thc third, of the fourth, or of the second.Anõther-type of chord is made by superimposingcombinationsof miscelinious intervals. This simultaneouscombination of mixed intervals, not arranged is f polychordal units, a compound chord. Compound h"rmãny doesnot include the chords of miscellaneous inteivals formed bv inverting tertian, quartal, or secundalstructures, becaurethú chordsrerain their inherenrroot feeling.when many inrervalsare combinedinto a compoundstÌucture a resoundingbody of tones results that is parcicularly effective in the orchõstra, band, and piano, four hands. Ary combination of varied intervals is possiblein a compound _ chord and the larger heterogeneousselectionsare often efiìctive through sheerenergyandtonal intensity: 163
164)
S .COMPOUND AND MIRROR HARMONY
Ex. 8-1
Intervals may be arrangedin any combination of tersions. They may be distributedso as to produce any desiredshapeand âssembled to createvariousconsonântor dissonantâreas.The combination of consonantor dissonantintervalsmay createa consonantor dissonantbottom,middle,or top portion of úe chord.
Er. 8-2
Some compound chords are characterund by an inner grzphic plan rather than an ârrângement of interval tensions. The important âspect of a chord of this kind is the logic of its inner construction rather than the motivating force of intervallic tension. Some such chords contain all twelve chromatic tones and eleven symmetrically invertible intervals.
COMPOUND CONSTRUCTION
(16t
Ex. 8-3
lg:Ë;?
1 J
w.2 w,,7
m.. ó
ha=
p.+
Other chords of this kind are arranged in alternately odd- or even-numberedintervals counted in semirones.
Er. 84
scrÌutofles
-Mr-ny other graphic interval arrâng€mentsare possible. Some chords are fashionedin the image of the on.tton. series.A pyramidal type of compound chord is composedof a seriesof-útervals diminishing from the bottom upward.
Er. 8-5
h.r+^
COMPOUND CONSTRUCTION
(tt7
Passagesmay upper sharp dissonâncesand lower open _emphasize consonances. If the upper tone of a sharp dissonant interval is placed high in the chord and anchored a fifth or tenrh below, tension and brilliance are added.
Ex. 8-8
d=uzlf gt'Ivy.# o-.
f:t
*h ']
8 . COMPOIIND AND MIRROR HARMONY
168)
Smallercompoundchords of five or six discreetly placedtones havean elasticquality becauseof the fluidiry of the smallernumber of varied intervals E*. 8-9
ob. ct. .ú
ttpr.
Bn.
Occasionally it will be difficult to decide whether certâin chords are compound or added-note chords. A satisfactory analysis can be made only by examining the context of the harmony. If the chord in question shows $rong tendencies to progress in a tonal sphere, it is an added-note chord containing notes that modify the basic structure of tonal functional powers; otherwise the chord is compound. Compound chords do not readily subordinate themselvesto the tonal regulation of root movement or key. Compound chords have litde or no root significance and are usually handled simply as massesof sound. There is no likely scale to dominate the harmony and few harmonic values that result from reÌationships within a tonality. Any compound structure mây be establishedas
COMPOUND CONSTRUSIION
(16e
â central chord by the relative tension set up by surrounding chords, and may serve âs the harmonic center to which adjacent chords gravrtate. Harmonic motion is created by the fluctuating density contained within the highest and lowest voices and by the shifting degreesof intervallic tension. The changing speeds with which the densiry and consonant-dissonant factors move create a harmonic rhythm in which compound chords mây progress. Compound chords are often large and complex and when used in successionare effective as declamations,arrival points, and opening and closing statements.They form naturally percussive chords when the smaller intervals are low in the sffucrure.
Ex. 8-10
large formations often limits their harmonic The inflexibiliqf ."f activity to percussive accentuations, sustained backgrounds, and cadences.When these chords are used for percusúe accentuation fwo textural levels of difierent kinds may be created. The harmony containing the percussive chords is compound and the other may be tertian, quartal, or secundal.
Er. 8-11
170)
8 . COMPOTIND AND MIRROR HARMONY
Compound chords may move as a background texture with no harmonichold on a voice or voicesin a solo foreground. Ex. 8-12
In cadential treatment úe compound chord of arrival is usually preceded by a structure of greater chordal densiqy. The chords that lead to the final chords of the cadence are not necessarilv compound.
Er. 8-13
Becauseof the complexity of intervallic make-upin compound harmonyeachchordalmembermust be manipulatedprecisely.The slightestmiscaÌculationcân upsetthe intendedbalance.\Ã/hencare is given aurally to interval and medium color, a homogeneous and intelligible sonority may evolve. One of the most frequendy usedcompoundchordsis the threenote chord by fourths with the addition of a third (discussedin Chapter4). Harmonically, this chord is flexible and colorful and functions well in tertian or quartal context. A specialcategory of compound chords stemsfrom the uiad with addedsecondsplacedin the bass.When formationsfrom this hybrid category (added-notechord and polychord) are written in open positiona unique type of fused,compoundharmony is produced. It is possibleto fuse two ftiads so that a single chord of mixed intervalsresults.This speciesof compoundharmony has a distinct polychordal flavor. Chords are formed by fusing two
COMPOI.INDCONSTRUCTION
(171
diÍferent kinds of triads so that two of the six noresare duplications, leaving a four-note formation. The duplicatednoresare in the middle voices and are common to boú uiads. The chord is labeledfrom the bottom uiad upwards Ex. 8-14 Primery Chords (füsç.t) 2 I
ma.-Ílug. dim,-rÍri ma.-mí 66-665 3414_'
qu.-dftrI.
dim..nu.
There are only six compound chords of this variety; other fused combinations of triads form seventh or triadic harmony. These six fused chords are completely interchangeable and are free to move to and from each other in any order. They are, in effect, the six primary chords of this category. Their secondary chords are not compound and include those seventh, ninth, and eleventh chords in root position or inversion that contain a sharp disonant interval which serves as a blending agent. These formations are numerous.
Ex. 8-1J SoconderyChorils sevcnús
elcvcnús
172)
8 .COMPOUND AND MIRROR HARMONY
Fusedharmony flows freely in four parrs. Ex. 8-16
SourceMaterial Compoundharmony: Easley Blackwood, Symphony No. 1, p. 48 (Elkan-Vogel) Pierre Boulez,Piano SonataNo. 2, p. 3 (Heugel) !g-Tir-T Britte_n,The-Turn of the Screw (red.), pp. l74, t8t (Boosey) Elliott Carter, Suing Quanet No. L, p. 29 (Assoõiãted) Charles Ives, Piano Sonata No. 2, p. 4Z (Arrow) Arnold Schoenberg,Klavierstiick Op. 33a,p. 2 (Universal) Wilüam Schuman, Symphony No. õ, pp. t, 49 (G. Schirmer) Nikos Skalkottas,Little^Suité for Striâgs, p. t0 iKalmus) Karlheinz Stockhausen,Kontra-Punkte,-p. il (Universal )' Igor Suavinsky, Le Sacre du Printemps, p.- 83 (Kalmus) Edgard Varèse, Octandre, p. 11 (Ricoldi) Anton Webem, Kantate Op.29, p. 1 (Universal)
MIRROR
\MRITING
Any chord (tertian, quartâI, secundal,polychordal, or compound) may be mirrored by adding below the original formation strictly inverted intervals in symmetricalreÍlection. One half of a mirror chord is an exact and simultaneousinversionof the other half. Mirror harmony has a textural complexion unlike âny orher çhqrdal formation becauserefleçtivç iovçrsion opposesthe natural
MIRROR WRITING
(173
âcousticalpropertiesof sound,in that the overtonesthat form the characterof a singletone are naturally generatedfrom the bottom, not from the middle, asin a mirror. The spuriousundertoneseries, an intervallic reflection of the overtoneseries,is the onÌy instance of a mirror as a natural musical phenomenonand is theoretical rather than aural.
Ex. 8-17 OYcnoneSerics
fL"çeaì;; "
-t> I
I
I I
-O
e.r--pl
(r)
=
rvo) (T) Va
=
UndcrtoncScries
In mirror harmony, fundamentalchords by thirds, fourths, and secondsgeneratelarger formationsof the samecategory.Mirroring inverted chords producespolychords, and mirroring polychords and compound chords produces more complex versions of the samekind of structure. Er. 8-18
polyúords
8 . COMPOUND AND MIRROR HARMOì{Y
174)
(chor
(chordsby 2orb)
(pol
(conpound)
'--
-í} L.-l
chordsbv,lús
diuters
polychords
L-l
compound
possibletypes of mirror chord writing âre: a srationary , ï?:r building tone usedto generarereflection (n); moving buildin'E " tone.generâtingreflection (b); the building rones theniselvesbe-coming reflective_by moving in conuary motion (c); building tonesusedfreely (d). Er. 8-19
+-+-,---+
(175
MIRROR WRITING
Any mirror chord may be doubly mirrored. These complex structures are used primarily with large unmirrored compound chords.Enharmonicchangesare madewhen spellingbecomesunwieldy.
Ex. 8-20
Even though the members of mirror chords are built from a tone oÍ tones located in the center of the chord the building tone never functions aurally as a root. It is the entire chordal bulk that emergesas a chord in its own right. Mirror chords usually assume the character of the bottom chord. Some scales are naturally reÍlective in that t\Ã/o sepârâte scales move identically, interval for interval, when placed in contrary motion. The entire diatonic scale system is symmetricaiÌy invertible. The mirrored diatonic scales appear in a reversed order of color gradation. The dorian in mirrored version produces the samescale.
Ex. 8-21 lydian
a)
--
-+lr
-t
---
L-'
+h-t
locún
brighter
mixolyüan
torum
-
-L-r
pht)'gnn
acoüan
MIRROR WRITING
(17t
Any mirror chord may be doubly mirrored. These complex structures are used primarily with large unmirrored compound chords.Enharmonicchangesare madewhen speliingbecomesunwieldv.
Ex. 8-20
Even though the members of mirror chords are built from a tone or tones located in the center of the chord the building tone never functions aurally as a root. It is the entire chordal bulk that emergesas a chord in its own right. Mirror chords usually âssume the character of the bottom chord. Some scales are naturally reflective in that t\n/o separâte scales move identically, interval for interval, when placed in contrary motion. The entire diatonic scale system is symmetrically invertible. The mirrored diatonic scales appear in a reversed order of color gradation. The dorian in mirrored version produces the samescale.
Ex. 8-21 drrkcr
=
lydian
a)
--
.r-h-t
+h-t
locrian
brightu
--
- > -
eh-t
phrysm
acolian
8 .COMPOIIND
176) fì"oorlr-d""rìt
I
AND MIRROR HARMONY
âèoliân
+
Any scalemay be reflected.The following illustratessynthetic scalemirroring. Ex. 8-22
Hung. Minor
Lydian Minor
Mrjor Locrian
MIRROR WRITING
(177
Somesyntheticscales,such asthe Double Harmonic, are inversely identical. Reflectivescalesimply mirror harmony. Ex. 8-23 Gdodao
Grnalor aJ
\t--'
/t+.lì^
v.?-
|
-
r-o--Jt-
_--_--.->
Gd"ril-
GphryS,.o
Reflective scaleswhose tonics are located ât different pitch levels also produce mirror chords. The flavor of each chord of reflective harmony becomes more pronounced as the space between th€ building tones widens. Ex. 8-24
Í'-mkolYdian ,.--->
When strict mirror writing is desired,ornamentaltonesare kept in reflectiverelationship:
8 . COMPOUND AND MIRROR HARMONY
178)
Ex. 8-2Í
Suinç qf
Greater freedomin harmony can be obtainedthrough only parúl reflection, the outer voices mirrored while the inner voices move freely. Ex. 8-26
ICL'
-
lt *d La.J:
Mirror writing may stem from thematic soÌrces; an initial melody can be constructed so that part of the melody is the inversion of another part. Subsequent simultaneous use of the original melody and its inversion breeds mirrored vertical stmctures generated by the thematic elements of the work.
(17e
MIRROR WRITING
Ex. 8-27
aÈ 1. z 3 4 5 espr.
67 I
|
231 t
6 7 a
nveËroll
Reflective keyboard writing producesunique mirror harmony that equalizesthe movementof the handsând createssimultaneous and uniform keyboard technique. When musically appropriate, reflective keyboard passages supply a fresh sound.The mirror or reflective pivotal points of the keyboard are D and Gf. Corresponding notesin the keyboardmirror are these:
DDf EFF#GG#AA#BCC# (D) DC#CBAfiAG#GFfFED#(D) Simultaneous inversionbeginningat ãrryone of the twelve pivotal points producesstrict mirroring regardlessof what rype of harmony is used;the fingering in both handswill, without exception, beidentical:
8 .COMPOUND AND MIRROR HARMONY
r80) Er. 8-28 () =126)
I
2L
í
I
t'l
1
l.
2l
4 >\---l
SourceMateri.al Mirror writing: Béla Bartók, Concerto for Orchestra, p. I (Boosey) 1çr1fBilger Blomdahl, Chamber Concêrto (red.),-p. 17 (Schott) Aaron Copland,Vitebsk (violin, cello, and piano), p. Z (Cos Cob) Luigi Dallapiccola,QuadernoMusicaledi fuúalibera (piano), p. 9 (Zerboni) Karl Amadeus Flartmann, Concerto for Piano, Winds, and Percussion, pp.32-33 (Schott) Darius Milhaud, Les Choëphores(red.), pp. i0, 7ó (Heugel) Vincent Persichetti, Sixth Piano Sonara,p. tA 1e*an-Vo!el) George Rochbe_rg,Duo Concertanre for Violin and Cello] p. 13 (Presser) Gerald Strang, Mirrorrorrim (New Music) Alexandre Tansman, Petite Suite, p. 7 (Demets) Antonio Veremi, Piano Sonatina,i. tl (Ricordi)
Applications 1. Write a sectionof a two-piano piece including the following compound chordsin any order and in any transposition.
MIRROR WRITING
( 181
Ex. 8-29
2. Write an orchestral passagecontaining a sequencehaving for its harmonicbackgrounda progressionof heterogeneous compoundchords. 3. Write â passagefor winds that includesseveralpyramidal chords. 4.Write a turbulent pâssageof tertian harmony for a chambergroup in which large compound chords are usedfor percussiveaccentuation. 5. Write a compound chordal section for oboe, clarinet, horn, and bassoonin which fusedchordsare employed. 6. Write music for two clarinets with simultaneousmirroring. 7. Move a chambergroup through severalmirror chords where the reflective harmony is generatedby the sametone and by different tones. 8. Write an openingsectionof a two-part piecefor the piano employing two symmetrically invertible scales.The mirror writing should be kept strict throughout. 9. Illustrate reflective keyboard writing in a short allegro sectionfor piano.
CEAPTER NINE
HarmonicDirection
PROGRESSION
WnrN A succEssroÈÍof chords establishesa definite direction it hasformal function and is considereda progression.The goal of a progressionmay be reachedor abandoned,a tonality fixed or forsaken. Whether a zuccession of chordsis established by root movemenr. contrapuntallines,or bedsof sound,the composóris able to guide his harmony in any direction. In root progression, inverted or otherwise,there are two directional factors: âction of the roor and location of the bass.The root, not necessarilyin the bass,may fall as the soundingbassrises,or rise as the sounding bassfalli, or úe factors mây agreein direction.
182
(183
PROGRESSION Ex. 9-1
Melodic and harmonic lines of tensionmay be placedin variable relationshipswith the root movement.
Er. 9-2
melodiclhc
ccf,turetensidl basline irngliedroots
Although register placementof the entire tonal massdoes affect the direction of sound.
Er. 9-3 FuIl Orclr" f
tuo.
9 . HARMONTC DIRECTION
184)
harmony with a strong downward pull can resista registerclimb. Ex. 9-4
Progressions basedupon the interval of the perfect fifth between roots hâvestrength;thosebasedupon rhe third, softness;upon the second,blandness;and upon rhe rritone, ambiguity (notice that theseintervalstogethersubsumeall rwelve tones). Ex. 9-Í |2,4567Ierolr17.
The root direction of I-V, I-[I, and I-II is up, regardlessof the inversionor placementof voices.The root direction of I-IV, I-VI, and I-VII is down. The uninvertible tritone is indefinite as ro direction. In tonal music of the twenrierh centu!/, the root distancebetÌveen important chords of a phraseor cadenceis usually determined by the cycle upon which the music is constructed.Music in a cyclical fifth relationshipis governedby a seriesof perfect fifths which may encompâssthe twelve differenr tones (a). In a third relationship úe chromatic compassis created by alternating major and minor thirds (á). In cyclical secondrelationshipa series of maior and minor secondsis used to encircle úe twelve tones (c).
(18t
PROGRESSION
Er. 9-6 (r) cycleof5ttr
-O
Ë
(b)
cycleof 3rds
(c) cyclcof2nds
r'.:
Harmonic writing, then, may be based uPon the fifth, third, or second relationship of chords (simple or complex), upon the tension created by moving from one kind of relationship to another, or simpÌy upon the horizontal movement of voices. Chordal relationships may be established within or without a prevailing scale formation and a tenún created by moving from one to another. Chordal movement in which the intervals between the roots are chromatically free is not governed by a scale but by horizontal movement of the voices. Harmonic movement may be created by generous chromaticism in all the voices and the emphasis placed upon a total melodic motion obliterating intervallic construction of chords. In augmented triads, diminished seventh chords, chords by perfect fourths or major seconds,roots ãre indefinite and vanish quickly. These versatile chords link one kind of texture to another while acting as binding chords in a synthesis of harmonic contexts. often acts as A melodic line, whether an inner or outer voice, 'When a complex a directional guide for harmonic progression. melody is the motivating force, the successof motivic development depends upon the abiliqy of the ear to retain melodic elements. Predominant intervals and durations must be aurally retainable, and those elements that have special significance for the formal plan should be made melodic and harmonic characteristics. Melodies i-ply tonal inflection, harmonic punctuation, and rhythmic movement, and any one of these elements may be featured. The composer is constantly aware of culminating points, general
186)
9 . HARMONIC DIRECTION
design, articulation, phrasing, dynamics, the rhythmic meaning of each note, predominant interval textures, and characteristicJ of the medium. other factors must be considered in creating harmonic progression: the texrural influence of intervals charãcteristic of'spe-cific types of harmony, the effect of frequently occurring melodic motifs upon harmonic phrase shapes,úe búavior of úe ffitone in both horizontal and vertical sitúations, the pÌacement of chords in a presiding or vanishing ronal cenrer, and tï. ,".o.r".y of harmonic. equilibrium after swift changes of compositionaí devices. A vital thematic passageshould be tested on vãrious tonal levels for brilliance. Transposition sheds varying lights upon thematic material; the slightest shift in register can change the^meaning of a musical idea. - when writing music without a given line, attention should be focused upon the- outer voices. If-undecided about upper voice motion, work a few notes ahead in the bass, and vicè- versa. If pars begin moving too fasq slow down mosr of the parts with notes and move the remaining pârt or parts by empÌoying a longer fragment of the theme. The following examplesillusrrate special kinds of chordar movement. A successionconsisting of an interchange of two or three chords may be used for "atmospheric" passiges where neither definite tonality nor forward harmonic motion is desired,
Ex. 9-7
or for musicwith folk roors.
(187
PROGRESSION Ex. 9-8
pi*o
/ oottPirito
it Any chord can return to the chord that immediately_precedes (a); ãnd succeedingchords may reflrrn to an original formation
(b ) . Ex. 9-9 (a)
+ (b)
of chords may be statedbackwardsuntil the An enúe pâssâge original chord reappeârs.Retrogressiveprogressionsbring new meaningto the original harmonicstatement. Ex. 9-10
Unexpected chords at resolution points add freshnessto harmonicflow:
9 .HARMONTC DIRECTION
188 )
Er. 9-II
,rf
r
===>
Harmonic elision brings about new relationships.Chordal relationshipsne\Ã/ro the piecemay âpp€arby omitting a chord that is expected becauseof previously estabüshedpassagesor srrong sequentialor traditionalsuccessions.
E*. 9-12 Adteio \Mwi
If a passageis thematically significant and is easily retained aurally, may be omitted or shufled in a dismembered .chords Progresslon. Ex. 9-13
1Vw. ald I tcrnPrc
CHORD CONNECTION
(18e
CHORD CONNECTION
Two inseparablefactors are involved with harmonic progression: what chord follows what chord, and how they are connected. When melodies sound together chords are formed, and when chordsfollow eachother melodicmotion is involved.Music can be primarily harmonic,melodic,or rhythmic, bur there is seldompure harmony or counterpoint for they are deeply involved with each other. Separatechord tones of any progressionhave melodic tendencies;even the most isolaredchord is full of melodic potential. Outer voicesgovern harmonicdirection and inner voicessecure the relationshipof the chords.For unrufled harmonicmotion inner voicesare moved as üttle as possibleand common tones are held. Parallelintervalslessenthe individuality of the voicesand contrary and oblique motion give the voices independence.The inherent urge of independentvoices to maintain identifiable lines can be strong enoughto ove{po\Merharmonic impulse. Smooth progressionsare but one facer of the craft. There is a danger of their becoming overly smoorh and much ingenuiqy is required to keep them fresh._Lgapingvoices,straying dissonances, escapingcommontones,modulatory twists, and chromatic daring are all part of harmonictechnique. The following deviceshelp give harmonicwriting this freshness. Inverting or transposing the interval containing common tones expandsthe registerrange:
t\
9 . HARMONIC DIRECTION
1e0) Ex. 9-14
Moving a voice to â note higher than the one just left by the voice above, or to â note lower than the note iust left by the voice below,
givesa passagea harmonic litt or drop.
A voice may be animatedby deflectingits melodic line, one more of the melody notesbeingshiftedup or down an octave. Ex. 9-16 Moderato
The registerof an enúe harmonicmâssmay be shiftedsuddenly to ânotheroctave.
CHORD CONNECTION
( 1el
Ex. 9-17
Piano I
cresc.
The range supplenes of instuments may contribute to linear flexibility. Ex. 9-18 1J.tzo;
ìÉ.
9 . HARMONIC
1e2)
DIRECTION
Melodic risesand dips may be reinforced by successive octaves, fifths, and paralielharmony. Ex. 9-19
r'G--, ü
'lteV_c í' t-i ____-_/
Piano
.Ir\_j_
A" a-
,r{
-----:.._---\
|
,/'
Eo'
Hidden fifths and octaves give coupled two-part harmony textural strengú, and thirdless harmony a freedom of movemenl
Er. 9-20
t'
(1e3
CHORD CONNECTION
The number of voicesin successive chords mây be increasedor decreased for variety in density.
Ex. 9-21 ( J= 88) Ww.
:+-
A climactic harmonicpoint may be left vacanrby rests.
Ex. 9-22
wtv and
^ ,V
cresc.moho
t + Brass
Voices may take turns soundingthe tune. When voicessharea melody in this way themâticimplicationsâre felt in the harmony. Ex. 9-23
Each voice may move chromaticallyto daringly complexchords becausewhen all voicesmove by half stepany combinationof dissonancesmay have meaning and direction. The voices containing the sharpestdissonantinterval should be well separated:
9 . HARMONIC DIRECTION
1e4) Er. 9-24
Í
feruemelte
DISSONANCE
Any combination of simultaneously sounding tones is relatively consonant if there is a more dissonantcombination in the surrounding area. An abundance of dissonancecan result in the feeìing of â consonânt textnre becausethe harmonic tension often relaxes in chords of the samevalues. The juxtaposition of chords of different values creâtes süong harmonic tension. A chord is dissonant only in relation to an over-all harmonic scheme and at times the "consonant" chord is the restless one. Because of melodic pull and chordal relationships the "consonânt" chord at (a) has a strong Ìrrge to move while the "dissonânt" chord at (b) remains unflustered.
Ex. 9-2Í
Increasing and decreasing consonance or dissonancecontributes to the shape of phrases,securescadential progressions,and articulates sectiõnal writing. Some are inherently more dissonant than otheÍs. But from the esthetic point of view the composer's ear &termines interval consonance or dissonance. Dissonance exists only where there is a norÍn of consonance implied or stated. A ninih chord may be relatively dissonant and resdessbecauseof the
DISSONANCE
(let
lessdissonantseventh and triadic material surrounding iq but the sameninth rnight be perfectly securedin consonancein a coíÌtext of ninths, elevenths,and polychords. Consonant-disonantrelationshipmay be reversedby starting and ending with a dissonantchord as the norm; consonancemay then resolveto dissonance.Extremely dissonantchords are kept in check by sequentialpatterns, overbearingmelodic lines, and characteristicmelodicintervals.A dissonantchord might represent a tonaliry and generateideasthat suggestthe form and content of a large work. A dissonantchord hasspecialusesoutsidea dissonantcontext. It sometimesends a phrasewhen used to begin the next phrase (transposed or not), Ex. 9-26 (à =e6) Tpts. rnd
or is repeated so dynamically and intensely úat the need for resolution is eradicated. In harmonic progression, each note makes its position in the chord felt as well as its position in its own melodic line. This linear force generates the harmony, conuapuntal motion, and formal design. Dissonant melodic and chordal clashes occur with less aural concern in harmony stemming from horizontal thinking-in multi-voice counterpoint (counterchords), in ornamental chords, and in reflection of some of the voices. Dissonant harmonic combinations often produce a üatonic melody.
Es. 9-27
9 . HARMONIC DIRECTION
Ie6)
This melodic writing must not be confused with artificial combinations of diatonic melody and dissonantharmony. 'When a chord is dissonant bv context it is usuallv resolved bv the movement of the voices containing the most dissonant ,orr.í. For smoothness of progression the dissonant tone resolves to the nearest note of the prevailing scale scheme.
Ex. 9-28 () =72)
ns.
The dissonânttone can resistits natural tendency to move to the neârestnote by following a scalewisemotion in the oppositedirection. If the adjacentscaletones are the samedistancefrom the dissonanttone, movementin either direction is natural.For passive non-commitmentit remainsstationary,or leapsan octave at the chord change. Ex. 9-29 +
e
A dissonanttone may evaporateby skippingto anothermember of the samechord or may freeze in parallel harmony and not The dissonanttone may skip resolveuntil the end of the passage. freely with melodicpurposein high-tensionmixed chordal forma,, rions or when suong melodic motifs overshadowthe power of the dissonanttone to resolve. The momentum of sequentialdesign Elovesdissonanttoneswithout resolution.For a suddentensionlift, the dissonanttone may resolvein another voice.
DISSONANCE
(1e7
E*. 9-30
The quality of the dissonant tone can be softened by coupüng it with consonant intervals, but doubling of the dissonant tone raises the harmonic tension. Such doubling in a simple chord enablesthat chord to function easily with complex formations.
Ex.9-31
To soften doubleddissonanttones,the voicesinvolving the dissonancemovein contrâry motion, or one of the doubledtonesmay move before the other resolves. The spacingconcern in three- and four-part harmony is often one of securingmaximum sound, but in harmony of more than four parts, doubling and spacing considerationsare directed to secur:ingvariety of texrure. Various colors and weights are obtainablethrough omissionand doubling of both dissonàntand consonant chord members.The densitv and concenrration of tonal
9 . HARMOMC DIRECTION
1e8 )
sound varies under diÍferent dramatic conditions. In an orchestral arrival of dissonant material upon a consonant climax, extensive doubling of all members of the consonant chord may be necessary to avoid loss of sound.
PARALLEL
HARMONY
When all voices in a successionof chords move in the same direction, parallel harmony occurs.Parallel harmony is found in eighteenth-centurysix-threezuccessions and in nineteenth-century diminished seventh chord successions. The term includes both strict parallelmotion in which all the chords are identical in construction, and similar motion in which the chords changeâs the voicesmove freely but in the samedirection. The direction and intervallic transpositionsmay vary and be either real or tonal.
Er. 9-32
Real parallel harmony (exact transposition) has a tendency to severconnectionswith any one key and may be used âs â meâns of enteringand Ìeavingatonality. This kind of harmony functions freely in modulatory transitionsand in thematic statementswhere tonality is meant to be obscure.Tonal parallel harmony (intervallic changesdeterminedby the scalein force) tends to preserve a modality. Parallelharmony (or chordal melody) is an expandedtextural equivalentof a melodicline; its direction is governedprimarily by melodic considerationsand its intervallic constructionby the kind of texture demandedby the dramatic form. In parallel harmony, fourths and fifths axeâsliquid asthirds and sixths, and intervals of the secondand seventhfind horizontalfreedom. Momentary parallel harmony is effective when used to accentuate a rise or fatl in a melodic line or to süp into a fresh key
PARALLEL HARMONY
(1ee
area. But extended similar morion tires quickly even úough complex chords are employed. Ways to develop the generating force of parallel harmony have become parr of the composer'i craft. Before parallel harmony becomesmonotonous one of úe following devices may be employed for a renewal of harmonic freshnessanã flow: contrary motion in one voice against the current parallel succession(a); tonal parallel motion convened to real (á);
Ex. 9-33
-à
motion of the voiceschangedro similar motion (a); the roots of parallel chords moved in the direction opposite ro the moving mass(ú);
Ex. 9-34
the direction and register changed (a); nores dropped while tlre parallelharmony is continued (á);
Ex.9-3Í
g timoroso
e . HARMONIC DIRECTION
200)
affention diverted by ornamentation and imitation (a); the octave changedin one voice (ú);
Er. 9-36 (^) G= 66)
Str. Orch.
ilf
)
::=-
the instrumentationchanged (a); different instrumentsused on differentnotes(ú); Ex. 9-37 (a) Lento (Ob.,CÌ.)
SUCCESSIVEPERFECTFIFTHS
(201
all notes raisedor dropped successivelyuntil the chord is dupli= catedat someother step. Ex. 9-38
So'pobeneptacido
Parallel harmony may be relieved by inserting fragments of nonparallel harmony, or by using two sets of parallel chords in contrary motion-the result may or may not be reflective. The chordal formation that dominates a succession of parallel chords may be broken melodically and a new set of parallel chords placed under the melodic notes of the broken chord, resulting in oblique harmony.
EÍ. 9-39
parallel added-note tertian chords
lFr I lD! | lC! | lAf I lG I
parallel chordsby 4ús
SUCCESSIVE PERFECT
FIF'THS
Unle.ss used imaginatively, successive perfect fifths become úesome; the intervallic uniformity of any combination of notes moving in parallel motion chaÌlenges a composer's inventiveness and facility. Fifths are emotionally immense, vague, and distant, or bare and dominating-they form an important harmonic in-
9 . HARMONIC DIRECTION
N2)
gredient in contemporâry composition.They are found in twopart writing, prying looseobliquemorion;
Ex. 9-40 2 Recorders
() . se). X--J----
,rf in coupledtwo-pârt writing; Er. 9-41 (J.=ss;
gp
in parallel harmony; Ex. 942
(i=
Piano $
ogüato
at the end of one sequential pattern and the beginning of the next;
SUCCESSIVEPERFECT FIFTHS
(203
Ex. 9-43 Andamc
and ât phraseioints Er. 9-44 tdi
t6
ãHo
Although perfect fifths make independenceof parts difrcult to achieve,their function in the vasttonal reserveis an important one. As part of a moving chordalbody of soundthey can be usedwithout dominating the generalrexture. The following deviceshelp push perfect fifths to rhe background. Conjunct fifths may be placedin the lower voiceswhile other parts employ conrrary or oblique motion. Es. 945
b
9 . HARMONIC DIRECTION
204)
Fifths in the upper parts becomeprominent but attention may be divertedby using rhythmically agile accompanyingpârrs. Ex. 9-46
Hn.
Chromatic fifths may be used more freely if at least one voice moves contrary to the fifths (a). Some monorony can be avoided by inserting other intervals between some of the fifths (ú).
En. 947 ( a )( J = $ )
Contrary outer pârts may be usedwith fifths in the inner parts (a). Fifths in the upper pârts are softenedby placing the third of the fifth in a lower voice (á).
SUCCESSIVEPERFECTFIFTHS
(20t
Ex. 9-48
l'Ìf*-
---\
úttpr. Va. (div.)
Skipping fifths are subduedwhen they leap to membersof the samechord (a). Florid inner voiceshelp divert the attention from fifths in the outer pans (á). Ex. 9-49 (4) (J=r16)
ttf Ha. -
9 . HARMONIC DIRECTION
206)
CADENTIAL DEVICES A cadence is an organization of melody and harmony in time, having a connotatior, ãf ,"rr. The cadencËis created harmonically through a pattern of chords, and melodically through the direction of each voice. Both are positive forces only when verified rhythmically. Cadential breathing places may occur at ends of phrases and sections and finally at the end of the piece. Under certain formal conditions, however, the final cadence may find that a prominent subject in a different key has made a bid for a new tonaliry, causing a cadence of two or more simultaneouskeys. Regardless of the complexity or inversions of the cadential chords, the two final roots will set the quality of the cadential feeling. The first chord in a two-chord cadence progresses"perfecdy" to a tonic whose root lies the interval of the existing cyclical relationship below its own.
Ex. 9-Í0
5ú rel
3rdrel.
T
m
'-T
2ndrel
-ü
T
I
The plagalequivalentsare these:
Ex. 9-í1
Íú rel'
T
TV
I
Í T
VI
I
Fvü
Any cadencewill acquire a passivequality if a dissonantton€ remârnsstaüonary.
CADENTIAL DEVICES
Qm
Ex. 9-Í2 a)
Tension and relaxation of consonanceand dissonancehelp mold cadential shapes. However, a succession of chords can produce positive cadential finality only when the underlying rhytlim confirms them. The rhythmic placement of the final chord afiects the strength of the cadence; when the last chord falls on a weak beaq repeated notes, ties, or melodic ornamentation are used to regain balance.
Ex. 9-J3
*.9*
In chromatic cadences, common rones âre avoided in order to strengthen the final tonic footing.
Ex. 9-54
#
w
The purpose of temporary cadencesis to rest briefly on a harmonic slant, thereby creating a need for harmonic, rhythmic, and melodic continuance. Deceptive cadencesare usuaÌly of this type and imply morion from one chord to anorher whose root relatiõn to the first forms an interval not characteristic of the prevailing chordal cycle. In fifth relationship, the chord of weaker i*p.ké
208)
9 . HARMONIC DIRECTION
moves to a chord whose root lies a second above its own root (a). In third relationship, root movement is up five (ú). In second relationship, root movement is up three (c).
Ex. 9-Í Í r--l
rì
Deceptive cadential progressionsare also obtained through movement to a chord outside úe establishedmodal or key realm, or by chromatic root movement. Other caclencesare created by the obliteration of all voices but one, or obliteration of all voices save a percussion note of indefinite pitch. When the final tonic establishesa positive tonality, notes mây be added freely, and if undertones are added, the tonic meaning is not disturbed. The final chord may be identical with the opening chord regardlessof tonal relationships. Cadences may include any rype of harmony: tertian, quartal, added-note, secundal, polychordal, compound, mirror, pandiatonic (Chapter 10), or twelve-note.
Ex.9-Í6
CADENTIAL DEVICES
SourceMateri.al Harmony with characteristic doubling, spacing, or omission: Aaron Copland,Piano Sonata,pp. 5,29 (Boosey) Darius Milhaud, Protée (red.), p. 8ó (Durand) Luigi Nono, Incontri for 24 Instruments, p. 14 (Scherchen) Igor Stravinsky,Mass,p. 13 (Boosey) Anton Webern, Kantate Op. 31, p. 3 (Universal)
Retrogressivewriting: Béla Bartók, Music for String Instruments, Percussion, and Celesta,p. 14 (Boosey) Alban Berg, Lyric Suite, pp.3945 (Universal) Luigi Dallapiccola, Quaderno Musicale di Annalibera (piano), n. 11 (Zerboru) Paul Hindemith, Ludus Tonalis, pp. 13-14, 57-ó0 (Associated) Olivier Messiaen,Sept Piècespour Orgue, pp. 3-4 (Leduc) Darius Milhaud, The Household Muse,p. l4 (Elkan-Vogel) Anton Webern, Variationen Op.27, p. 3 (Universal)
Real parallel harmony: Niels Viggo Bentzon, String Quartet No. 3, p. 11 (Hansen) AÌban Berg, Wozzeck (red.), p.219-22L (Universal) George Gershwin, An American in Paris, p. 48 (Harms) Karl Amadeus Hartrnann, Konzert für Bratsche mit Klavrer, p. 3 (Schott) Anaké Jolivet, Piano Concerto (red.), p. 42 (Heugel) Roger Sessions,Symphony No. 2, p. 99 (G. Schirmer) Ralph Vaughan Williams, Pastoral Symphony, p. 49 (Boosey)
210)
9 .HARMONIC DIRECTION
Tonal parallelharmony: Elüott Carter, Variations for Orchestra, p. 52 (Associated) Goffredo Petrassi,Toccata for Piano, p. 5 (Ricordi) Francis Poulenc, Les Soiréesde Nazelles (piano), p. 19 (Durand) Igor Stravinsky, Le Sacre du Printemps, p. 39 (Kalmus) Virgil Thomson, Four Saints in Three Acts (red.), p. 139 (Arrow)
Altered parallel writing: Béla Bartók, Piano Concerto No. 2 (red.), p. 38 (Boosey) Alban Berg, Lyric Suite, pp. 12,25 (Universal) John Alden Carpenter, Skyscrapers (red.), p. 39 (G. Schirmer) Frederick Delius, Requiem (red.), p. 54 (Universal) Roy Harris, Symphony No. 7, p. 89 (Associated) Maurice Ravel, L'FIeure Espagnole (red.), p. 113 (Durand) F{enri Sauguet,Concerto d'Orphée (red.), p. 38 (Heugel) Igor Stravinsky, Persephone(red.), p. 29 (Russe) Hugo Weisgall, The Tenor (red.), p. 145 (Merion)
Passages of barefifths: Georges Auric, Les Facheux (red.), p. 14 (Lerolle) Aaron Copland, Billy the Kid (ballet suite), p. t (Boosey) Manuel de Falla, Nuits dans les Jardins d'Espagne (red.), p. 17 (Eschig) Roy Harris, Symphony No. 3, p. I (G. Schirmer) Giãn Carlo Menoìti, The Uni"õ.n, the Gorgon and the Manticore (red.), p. 44 (Ricordi) William Schuman,Symphony No. 3, p. 70 (G. Schirmer)
Harmony containingp€rfect fifths: Alberto Ginastera,Piano Sonata,p. 7 (Barry) Roy Ffarris, Piano Quintet, pp. 8-9 (G. Schirmer) Bernhard l{eiden, Sonata for llorn and Piano, p. l't (Associated) Paul Hindemith, Ludus Tonalis, p. 15 (Schott) Charles lves, Piano SonataNo. 1, p. 21 (Peer) Dane Rudhyar, Three Paeansfor Piano, p. ó (New Music) William Schuman,Credendum, p. 12 (Presser) Roger Sessions,Piano Sonata No. 2, p. 8 (Marks) HaIsey Stevens, Quintet for Flute, Violir\ Viola, Cello and Piano, p. 1 (G. Schirmer for S.P.A.M.) Igor Stravinsky, Les Noces, p. 36 (Chester) $tefan Wolpe, Passacagliafoi Piano, p. 8 (New Music) Characteristic cadences: Pierre Boulez,Piano SonataNo. 2, p. 15 (Heugel) Carlos Chávez, Sinfonia India, p. 82 (G. Schirmer) Aaron Copland, Music for the Theatre, p. 67 (Boosey)
(21r
CADENTIAL DEVICES
Andrew Imbrie, Piano Sonata,p. 9 (Valley) Bruno Maderna, SerenataNo. 2 (for 11 instruments), p. 54 (Zerboni) Francis Poulenc, Mass in G maior, p. 24 (Rouart-Lerolle) Arnold Schoenberg,Erwamrng (red.), p. 47 (Universal) Gunther Schuller, Contours (small orchestra), p. 99 (Schott) Camillo Togni, Fantasia Concertante (flute and strings), p. 38 (Zerboni) Ilhan Usmanbas,String Quartet, p. 31 (Boosey) Roman Vlad, Sonatinafor Flute and Piano, p. 18 (Zerboni) Ben'Weber, Serenadefor Strings, p. 24 (Boosey)
Applications 1. Write a sustâinedpassagefor organ in which the melodic and harmonic ünes of tension are in variable relationships with the root movelïÌ€nt. 2. Write an ariosofor viola and piano (or harpsichord) in which the enúe circle of thirds is coveredby transientkeys. 3. Write a chromatic lamentation for strings where emphasisupon total melodic motion obüteratesroot feeling. 4. Shedvaryrng lights upon thematic orchestralmaterial by shifting the register severaltirnes. 5. Write an extendedsuccessionconsistingof only three chords for (AAT and Bar). four saxophones ó. Write a woodwind choralefeaturing retrogressiveprogressions. 7. Shuffie the chords of a passageso that pizzicato strings can project dismembered a progression. 8. Write a martial section for winds featuring leaping voices, straying dissonances, escapingcofilmon tones,modulatory twists, and chrornatic daring. 9. Write an abundance of dissonancefor the chamber orchestra so that a relatively consonant texture errÌerges. 10. Write an orchestral variation on a folk tune featuring various parallelharmony devices. 11. Place I great number of perfect fifths in the background of an agile dance for two pianos and brasses Write -.12. _" g-*tT or harp piece with several tempo changesand different kinds of cadences.
CIIá,PTER TEN
Timrngand Dynamics
RHYTHM
Tnnoo FoRcEsimportant to harmonic progression âre the linear motion and outline of outer voices, úe pull of harmonic or tonal centers and of the relationship of chords, and the time duration of stressed and unstressed chords. Coupled with these forces are graded tensions of texture and pitch and the rhythm created by phrasing, bowing, and tonguing indications. Harmony is always feìt in its relation to rhythmic smucture, and not until cLords .rrólrr. in a rhythmic form does harmony become wholly articulate. Harmonic rhythm is the underlying rhphm that plays a large part in controlling and stabilizing musical flow. If the harmonic changes are quick, there is an undercurrent of restlessness;if widely spaced, there is breadth. Various combinations of fluctuating melodic and harmonic rhythms give the composer a creative rhythmic potential. Tempo can be a determining factor in harmonic rhythm. Quick tempo may cause chord changes to sound like ornamental chords. Simple chords moving at a high rate of. speed may create relatively
RHYTHM
(213
complex sounds (a). Harmonic rhythm does nor move when chordsarerepeated(á). Ex. 10-1
Meter is a meâsure of rhythm. It has no rhythm of its own; it only appearsro have when rhythmic pulse coinóideswith the metric points. Strong and weak beats occur wherever the musical line placesthem, regardlessof meter.
Ex. 10-2 () =1'J2)
.f vns.I,IIva"
,
Simplerhythmsmaybecombined underonetimesignature. Ex. 10-3 ().=s6)
10 . TIMING AND DYNAMICS
2r4)
If patterns of shifted accents remain relatively consistent dte asymàeuical divisions are often indicated by compound time signaturesor dotted lines These compositemeters generte aqymmetricâl phrases. Two patterns of varying note values coinciding at occasional points will flow without a feeling of chaos. Er. 10-4 r-$-r
p Ín))i-i1 ( tr t'ílcJJÍ'í-lí
^
JJ , ) ) ),J til
r I rl
,í,ÍÍtí
Two or more rhythmic phrasesof unequallength may eachbe repeated until the return of the original combination (polyrhythm). Ex. 10-Í r
lTl
o.
)fOt
)tut.t
-T-
o.
.i..
n1.o2.l?
#
r-l
t
??
r ".?
Fl iT]
.oi...
.
el+rc,pe
iTì .
.1.
el
i-i t
o
r
F
ttll
''1e1.1.7741
'When
the pulse is irregularly but consistentlysubdivided,different time signaturesâre usedsimultaneously(polymeter). Ex. 10-6
ã)J)))tJ
i)r)li)
\ïj: â)
J ) li.
J))l)))
) [
r ll l; ,h.l) lj J_.-J-JIlll
(2rt
RHYTHM
of voicesis obtainedby using _-Completerhythmic independence different time signatureswith bar lines falling at difierent places. Et. 10-7
,=rlï
lJ. .blJ-j-tll ) lJ. .btJJ_! ) J J lJ. .b) trï;;f]T1 IJJ
Change of meter is a common meâns of achieving rhythmic variety. The fluid bar line adjusts easily and accommodates fractional meâsures.Rhythmic freedom of the bar line may result from úe demands of voial texts (prose rhythm). Musical stressis creared by pitch, intensity, color, or duration; the more factors contributing to an âccent the more complete the accent. Rhythmic pulse is most cÌearly defined when the related meÌodic, contrapuntal, and harmonic functions are emphasized. Alúough syncopation implies a dislocation of an establishedpulse, it does not necessarily oppose the meter. If the established pulse is not in accord with the merer the syncopated accents might parallel the meter.
Ex. 10-8
tuÍír_tíÍtí'| 0íÍtíf r tÉtrííf F'r'EII syncopation
Any part of a rhythmic figure may be lengthenedby a note (a), a rest (á), or a dot (c). The rhythmic rransformarionproducesametricalpatterns:
IO .TIMING AND DYNAIVÍICS
216)
Ex. 10-9 ():rr
The melodic and harmonic lines may be syncopated in opposing ways: the melodic line syncopated against harmonic pulse, harmonic rhythm syncopated against melodic pulse, or both harmonic and melodic pulse heard in comparison with a contrasting pulse o{ preceding measures.Changes of time signature may be made so ihat the syncopation falls after the bar line. Dissonant-chord syncopatiorìs urge the succeeding harmonic rhythm to move faster and consonant-chord syncopations tend to slow it down. Rhythmic forces mây sprout from the percussion line of instruments or vocal sounds of indeterminate pitches. The meÌodic and harmonic rhythms may coincide or oppose the percussion line in various ways. The following example illustrates melodic and percussiverhythm opposing the harmonic rhythm.
Ex. 10-10 ()=r20)
When one or more voices of changing notes adhereto a tinglo rhythmic pattern, isorhyúm existc
RHYTHM Er. 10-11 çJ=aa
E.H.I
í
<.--.--L-f:'
Different voices may foÌlow individual isorhythmic pâtterns. Ex. 10-12 ë.=
Isorhythmic patterns mày ylry in length. When the pattern is r long one, the device is often beyond immediate aural perception. In isorhythm, the pitch levels are free and used with a repeated rhythmic pattern, but when the rhythm is free with a repeated melodic pattern, a device called isomelos exists:
10 . TIMING AND DÌINAMICS
218) Ex. 10-13 Allegretto
n.I
1
13
,lf Vcl. (div.)
In a combination of isorhythm and isomelos, the melodic ând rhythmic pâtrerns may staft rogerher, but one of the pafterns may begin the reperirion before the other.
Er. 10-14
pi*o
/
isorhythm I
isomelos
RHYTHM
(219
SourceMaterial Irregular harmonic rhythm: Milton Babbitt, Three Cornpositions for Pìano, p. ó (Bomarr) Beniamin Britten, Serenadefor Tenor, I{orn anã Strings, - p. 34 (Boosey) Jeari Françaix, Piano Concerto (red.), p. 25 (Schott) Paul Hindemith, Sonata for Viola and Piano, p. 15 (Schott) André Jolivet, String Quartet No. 1, p. 26 (Hèugel) Ernst Krenek, Piano SonataNo. 4, p. 21 (Bomart) Quincy Porter, String Quanet No. 8, p. 21 (Valley) Serge Prokofiev, Piano Sonata No. ó, p. tZ (Am-Rus) Arnold Schoenberg,Das Buch der Hdngenden Gârren, p. l0 (Universal)
Meter changes: John Becker, String Quartet No. 2, p. 9 (New Music) Boris Blacher, Divertimento, p. 3 (Associated) Aaron Co_pland, Sextet for String Quartet, Clariner and Piano, p. 5 (Boosey) Roman Haubenstock-Rarnati,Les Symphoniesde Timbres, pp. 10-11 (Uiúversal) Paul Hindemith, Neues vom Tage (red.), p. 198 (Schott) Peter Mennin, String Quartet No. 2, p. 2a (C. Fischer) Silvestre Revueltas,Sensemaya,pp.27-37 (G. Schirmer) Roger Sessions,S1'rnphony No. 1, p. 7 (Arrow)
Polyrhythms: Samuel Barber, Vanessa(red.), p. 172 (G. Schirmer) Aaron Copland, Symphony No. l, p. 20 (Cos Cob) Charleslves, Symphony No. 3, pp. 26-27 (Arrow) Ârnold Schoenberg,String Trio Op. 45, p. 13 (Bomart) Gunther Schuller, String Quartet No. l, p. 27 (Llniversal) Alexander Scriabine,Tenth Piano Sonat4 p. 2 (Leeds) Kârth€itrz Stockhausen,Nr. J Zeiunasse,p. 21 (Universal)
Poly-tirne+ignâtures Béla Bartók, String Quartc No. 3, pp. 9,23 (Boosey) Jack Beeson,Five Songs,p. ó (Peer) Ellioa Carter, Sting Quartet No. 1, p. 5 (Associated) Paul Hindemith, SymrphonieMathis der Maler, pp.2o-22 (fthoa) Maurice Ravel, Sonate pour Violon et Violoncelle, p. 5 (Durand) Igor Stravinskn Petrushka" p. 10 (Kalmus)
10 . TIMING AND DY}TAMICS
220)
Passages featuring percussivesounds: Carlos Chávez, Toccata for PercussionInstrumenrs (Affiliated) ' Karl Amadeus Ffarrmann, Symphony No. 6, p. t02 iSchoa) Uil9emit\. Symphonic'Mètamórphosis,'. 36 (AssociatÉd) laU ^f Gustav Holst, The Plânets,p. I (Boosêy) Lev Knipper, Symphony Nõ. +. p. 49 (ïeeds) Luigi Nôno, Coro ãi Didone, ppl tz, zì (Ars'Viva) Silvestre Revueltas,Sensemayã,-p. 2j (G. Schirmei) -( _Gynth9r,Schuller, Contours small orchestra), p. tó ( Schot) Edgard Varèse, Density 21.5 (New Music)
Isorhy.thmand isomelos: Samuel Barber, Piano Sonata,p. 38 (G, Schirmer) Beniamin Btitten, Peter_Grimes(red.), p. i72 (Boosey) ' Aaron CopÌand,Piano Sonara,p. 14 (Bóosey) Arthur_Flonegger,Cris du Mõnde (red.),-p. 23 (Senart) (Sena Peter.ÌVÍennin,Symphony No. 3, pp. 128-l2b (Hargail) Burrill PÌtilhps, Burrill It_uffü Phillips, Sonara Phillips, Sonãtafor CeUo Cello and Pianoo. 3l (Wash. 1\ürsh Univ.) Piano, p. (Associated) ]{attel Piston,Symphony No. 4, pp. 99-100 (Associared) Alan Rawsthorne, Quúet for CÍarinet. Clarinet, Violin. Violin, Viola and (Cello. p. 17 (Oxford) George Rochberg, Sonata-Fantasia for Piano, p. 1g (presser) Igor Stravinsky,Symphony of Psalms(red.), fip. 3f-32 (Boosey)
PERCUSSIVE
USE oF
HARìVIONY
Accenrs may be produced by any mâteriâl that cails amention to itself-throrrghstress,duration, pitch level, tone qualiqy,relative harmonicvâlues,or repedtion.The tonal equivaleniof percussion rhythms (instrumentsof indeterminarepir.h) is the -.lodi" r.peâtednote. Reiteradonof the melodicìone is a rhythmic force that often stimulatesrepeâted-chordactiviry. Th; rhythm of chordal repetirion may âct as a tonal stimulant in slow úarmonic rhythm.
PERCUSSIVEUSE OF HARMONY
(221
Ex. l0-1J
Rhythm, both accentual and durational, can for a span of time serve as a chief compositional element. In answer to a drum figure, a chord may function percussively.
Ex. 10-16 Vivace
Su.
An isolated chord mây command attention when substituting for a bassdrum stroke. If the chord is a sudden large compound chord or a low cluster, a harmonic sforzando may be produced. The introduction of a chord outside the key realm or a sudden increase in the number of parrs may also produce a harmonic âccenL Smaller intervals placed at the bottom of chords may produce harmonic percussiveness.
Ex. 10-17 harmonic accenB
10 . TIMING AND DYNAMICS
222)
instrumens soundingtheir lower notesaccentuâte Miscellaneous of chords âs the pitch projection is dampened. the percussiveness fu. IA-18
(J=76't
(crs.)
SourceMaterìnl Pasagesfeaturing repeatednotesor chords: Ernest Bloch, Piano Quintet, p. 72 (G. Schirmer) Henry CowelÌ, Homage to Irán (violin and piano), p. 4 (Peters) for String Orchestia, p. t iElkan-Vogel) David Diamond, Rouids'Wind lrving Fine, Partita for Quintet, p. 32 (Boosey) Brunó Maderna,SerenataNo. 2 (for liinstruments), PP. 25-3A (Zetbronr) SergeProkofiev,Violin Concerto in D (red'), p' 21 (Breitkopf) CarI Ruggles,Evocations for Piano, p. 3 (Am. Mus. Ed.) Dmitri SÉostakovich,Symphony Nô. 10, p. 151 (Leeds) Roman Vlad, SonatinaÍor'Fluté and Pianó, p. 18 (Zerboni) Ànton Webern, Symphonie OP. Zt' p. 12 (Universal)
featuring percussiveharmony: Passages George Antheil, Five Songs 1979-1920,p. 8 (Cos Cob) Béla Éartók, Piano Sonatalp. 13 (Univèrsal) Alban Berg, Wozzeck (red.), p. 215 (Universal) Carlos Chãvez,Sinfonia de Antigona, p. 4 (G. Schirmer) Luiei Dallapiccola,ll Prigioniero (red.), p. 17 (Zerboni) Maiuel de iìalla, Harpsichord Concerto,f. + (Eschig) Arthur Honegger, Pacific 231,p.4 (Senart) Alan Hovhaness,Magnificat,p. 3 (Peters) Iacqueslbert, Angélúue (red.), p. l3 (Heugel) Ântãn Webern, Sïi* pìec.i for Orchesàa O-p. o, pp. L6-17 (Universal)
PANDIATONIC WRITING
PANDIATONIC
(22t
WRITING
A lack of harmonicrhythm (one chord) createsstatic harmony and a feeling of breadth or relaxarion. Ex. 10-19
4rcryo. v* *' ^1'
--
T--
8-r
Sqatigharmony is useful when attentionis to be focusedupon a tln!*t: motif, or when it is usedin repeatedchords,announcing the rhythm of an unaccompanied melody to follow.
Ex. 10-20 Vïvace Winds
Pandiatonic writing is a specific kind of static harmony in which ân enti-rescaleis used to form the members of an implied secundal, static chord. The vertical structures are combinations of any number of tones from the prevailing scale, placed in variable spacings. The horizontal chord successionhas no tonal direcdon; scale tones are manipulated as basic chordal material without creating harmonic motion outside the underlying static and unalteredscale. The_harmony has no characreristic functions; the counterpoint is rh;ythmically acrive, and the chord spacing erraric. Melodiì, con-
t
t
ii
224)
IO .TIMING AND DYNAMICS
uapuntal, and vertical combinations mây- be underpinned- by persistint intervals in the lower voices. Fifths and tenths from the bassare more fluent than úick thirds or srubborn fourths; fourths tend to predominate in the uPPer part of the chord, and seconds and sevenths harness the texture for early cadential arrivals. One mode is seldom used for an entiÍe pandiatonic section, particularly a mode with no flats or sharps, for "white-key fever" is contracted easily. In three-paft harmony each succeeding chord often contains three fresh notes bringing all scaÌe tones to aural consciousnessin seven-tone static harmony. If ornamental tones are used in one chord, fresh notes are used as members of the following chord.
Ex. 10-21 _
}d"Ct
Fl.. Vibn.
t1 bl+
IIn. (sorQ'Va. pize
Doubling is seldomemployed,even in five- or six-part harmony.
Ex. 10-22
In seven-part harmony, the seven scale steps âre constântly sounded.
PANDIATONIC WRITING
(22t
Ex. 10-23
Str
õl"r' ,,f
Any scalemay be used âs a basisfor pandiatonicism.All the intervallic characreristicsof any scale,synthetic or otherwise,can be projected pandiatonicallyat once.
SourceMateri,al Static harmony: Béla Bartók, Herzog BlaubartsBurg (red.), p. 5l (Universal) Carlos Chávez,Sinfõnia India, p. ó3-(C. Schiimer) Wgl"gt- E_gk,La Tentation de Saint Antoine, pp. 3842 (Schoa) Colin McPhee,Four Iroquois Dances,pp. 3-9 (New Music) Cinq Symphonies (pêrit orchestre), pp.'Z-+ (Universal) ?-.*: {itl*{,. Carl Orff, Die Sângerder Vorwelt (rèd.), pp. 3-16 (Sihott) Maurice Ravel, Concerro for Piano and-ôrchesra in G (red.), p.26 (Durand) Silvestre Rel'ueltas,Cuauhnahuac,p. 14 (G. Schirmer) Jean Sibelius,From the Land of Thousand Lakes, p. 9 (Boston) Igor Stravinsky, Mass, pp.6-7 (Boosey) Pandiatonic writing: William Bergsma,Tangents,Vol. II, p. 2l (C. Fischer) Aaron Copland,AppaìachianSpring, pp. 5l-52 (Boosey) I"qo.ff.Qi{,Diveiiimento foi Viãidãnd piano, p.4e qC. Schirmer for S.P.A.M.) Hoyard Ffanson,The Lament of Beowulf (red.), pp. ló-19 (Birchard) ._A.rthyHonegger, Jeanned'Arc au Bâcher (red.), p. 53 (Salabert) Igor Stravinsky, Duo Concerranr for Violin and piano, p. 13 (Russe)
IO .TIMING AND DYNAMICS
226)
DYNAMICS
AND
RESTS
Dynamics a.re ân essentialelement in composition. Harmonic progressionis affectedby the degreeof dynamic nuâncein which it is conceived. A dissonant and restless progression set in a pianissimo contexr is likely to explode into a subito forte of violent polychords, while the sameprogressionin a forte conrext might find harmonic satisfaction in its overbearing tension and remain in úe same harmonic sphere. Higttly chromatic chords blend with more harmonic easein soft passages than in loud. Dynamics have a rhythrn that is projected by meansof piano, forte, crescendo,diminuendo,sforzando,and subito directiônsof a99entu1ti9o.Tl"y reinforce úe natural rhythm when they coincide with it, and crearea conrrary line of tensionwhen they'oppose ie If a crescendois used through a passâgeof growing h"t*ãnic tension, overwhelming cumulative povrer may be obiained. If a diminuendo is used út""gh úe same kind-of pâssage,quite a different kind of tensionresuls. The rhythm of mèloay, harmony, and dyrramic nuance generatesmusical forces that cãn be iuxtaposed in many ways to creare a variety of climactic conditions The rest is a potent crearive factor. It may help lighten texrure and project motivic figures.
Er. 10-24
In multi-voice florid writing, voices rest periodically so that in-Rests dividual imitative pârrs are nor obscured. preôeding fresh 'when entrancesadd interestto long melodiclines. transparãncyin texture is soughtvoicesare widely spacedand rest often. Resrscan increaseharmonic momenrum; an interruption of a high-tensioned
DYNAMICS AND RESTS
(227
chord by silence produces an undercurrent of harmonie expectation. In a whispering diminuendo temporary silences imply unwritten harmonic innuendos. Rests have rhphmic power. In an establishedpattern of accents, a silent pulse has more strength than one sounded.
Ex. 10-2J
cresc. moho
g wb.
A rest before a climactic chord addspower to the arrival. Ex. 1A-26
SourceMaterial Passageswith characteristic dynamics and rests: Franco Donatoni, Composizionein Quatuo Movimenti (piano), p . 3 (Schott)
228)
10 . TIMING AND DYNAMICS
Bruno Maderna, SerenataNo. 2 (for 11 instruments), ^p. 2l (Zerboni) WiÌliam Schuman, Judith, pp. óGól (G. Schirmer) Igor Stravinsky, Symphoúês of Wind Instruments (rev. L947), p. 26 " (Boosey) CamiÌlo T9Sd, Fantasia Concertante (flute and string orchestra), p. 32 (Zerboni) Anton Webern, Variationen Op.27, p. ó (Universal)
Applicati,ons 1. Write a duettino for snaredrum and tenor drum using asymmetric divisionsof the measure. 2. Write a dancefor piano in which changeof merer is exploited. 3. In a three-pârt songform for clarinet,piano,and snaredrum (snares off) manipulatethe melodic rhythm of the clarinet, the harmonic rhythm of the piano, and the percussiverhythm of the snaredrum so that each of the three formal sectionscontains a different set of rhythmic relationships 4. Write a woodwind scherzoof erratic harmonic rhythm. 5. Write a fast passagefor string quarret with slow harmonic rhythm. 6. Write a lyric piano prelude in which the harmonic accentsfrequently opposethe barline accents. 7. Write a Vivo for two pianos using simple chords that move so rapidly that they createa harmonically complex sound. 8. Syncopatethe harmonicrhythm of four noisy stoppedhornsagainst a regular rhythm in low unison strings and brasses. 9. In a woodwind duo allow an oboe to play in triple time simultaneo_uslywith a bassoonplaying in quadruple time. Adiust rhe tempo so that the bar lines coincide. Wrile a string trio passagein vrhich each insrrument employs a -.10. diÍferent time signaturewith bar lines falling at difierent places. 11. Illustrate isorhythm in a dute, clarinet, and bassoonpassageof quartal harmony. 12.IiÌustrateisomelosin a flute, oboe,clarinet, and bassoonpassageof tertian harmony.
D'IôTAMICS AND RESTS
(22e
13. Employ melodic lepe.atednotes and chordal repetition in a fiery passagefor trumpet and string orchestra. the strength of percussiveorchestralchords againsta po\Mer" !+.Pit ful, opposingtimpani part. 15. write â pâssageof percussiveclusters in the lower regions of the orchestra. 16.Write a rough passâgein the strings using percussivechords. , 17. Exploit the principle of pandiatonicismin a short section for double string orchestra. 18.Write a gradual diminuendo for piano, four hands,in which the harmonic tension gradually increases. 19. write a brasspassageconraining rests of grear rhythmic po\Mer.
CEÂPTER ELEVEN
Embelhshment and Transformation
ORNAMENTAL
FIGURATION
VBnrrcer, srRUcruRESform a harmonic skeleton upon which melodicfiguration may rest. Thesemelodicembellishments may be harmonic or nonharmonic ornamentaltones. The ornamental harmonic tones consist of repeatedchord tones and broken-chord tones and create no intervallic resistanceto the harmony. When ornamentalfiguration is createdby chords that are broken in two or more voices,the individual pans gain freedom.Harmonic ornamentationmay increaseúe spacebetweenchord changesand relax harmonicrhythm. Membersof a broken chord soundedby a single voice may i*ply meaningful harmonic progression.
230
ORNAMENTAL FIGURATION
(23r
Ex. 11-1
Ornamentalnonharmonictones are inherently restlessbecause of their intervaÌlic counteractionto rhe chord. Nonharmonic tones may be either accentedor unaccenred;they âre accentedwhen they occur with the changeof harmonR regardlessof their place in the measure.There are four general kinds of nonharmonic tones: passingand auxfiary roneswhich are approachedand left without skip; Ex. 11-2
D.È
changing tones which are approachedconjunctly and left by a skip (a); appoggiaturaswhich âre approachedby a skip and left conjuncdy (á); Ex. 11-3
and a hybrid group which includesthosenonharmonicronesthat are formed by the rhythmic misplacementof chord rones. In the movementis delayed (a), and in anticipationthe suspensions, movementis hastened(á):
11 . EMBELLISHMENT AND TRANSFORMATION
2t2) Er. 11-4
It is possibleto skip to and from a noúarmonic tone if that tone becomesa memberof the following chord (a); while implying a larger formation over the sameroot (á); and while resistingany chordal affiliation (c). Ec. 11-Í
Before resolving, úe nonharmonic tone itself may be ornamentedby and combinedwith other ornamentaltones. Relatively simpleharmony or held chordsmay be spicedby dissonantand free ornamentation. Ex. 1I-6 (J=ó0)
Ornamental tones mây be derived from a scale built upon the root of the chord; each root is embellished as though it were a tonic.
ORNAMENTAL FIGURATION
G$
Ex. 11-7 Moderato
,
.* maior
,
Ornamental patteÍns may be derived from contrasting key centers creating temPorary polytonaliqy. Er. 11-8
gt
Nonharmonic tones may be grouped chord-wise and used as ornamentalchords such as passingchords, auxiliary chords, and so on:
234)
11 . EMBELLTSHMENT AND TRANSF'ORMATION
Es. 11-9
The ornamentaltone may rernain unresolved,causinga change of harmonic texflrre.
Er. 11-10 unrrs alP. T
r
teftiâtr
r,
rutr€$ sus. *:
compound,,
grrartal
,
Simple chords may be ernbelÌishedin such ^ way that one chord penetrâtesanottrcr, creating polychordal soundswhere they meet Ex. 11-11
(2tt
D(TENSION AND IMITATION
Sou.rceMateri.al Pasagesfeaturing ornamentalfiguration: Luciano Berio, Cinque Variazioni per Pianoforte, p. 10 (Zerboni) Werner Egk, Die Zaubergeige(red.), p. 173 (Schott) Paul Hindemith, Sonata for Piano, Four Flands, pp. 3G-31 (Schott) Vincent Persichetti, Fourth Symphony, p. 107 (Elkan-Vogel) Goffredo Petrassi,Invenzioni per Piano, pp.20aL (Zerboni) W'alter Piston, Trio for Violin, Cello and Piano, p. 1 (Arrow) SergeProkofiev, Piano SonataNo. 3, p. 5 (Leeds) Arnold Schoenberg,Gurre-Lieder (red.), p. 1ó5 (Universal) Hugo'Weisgall, Purgatory (red-), p. 4 (Merion)
EXTENSION
AND
IMITATION
The rrrany motivic cells that make up a theme are the concern of úe cornposer when extending harmonic material. The motivic fragments he chooses ând the way in which he transforms them are elements that give a work its personal identity. Repetition is one of the most important devices in musical composition. Repetition emerges as sequence, imitation, variation, ostinato, and in various other guises.Of the many techniques used by úe composer to extend harmonic fabric, none is rnore trying than literal repetition. A strong senseof timing and a discriminating tâste will determine when reiteration will not hinder musical Ílow. Development of thematic material involves motivic metamorphosis; the life of a structural unit depends to â greât extent upon the uansformâtive character of its elements. Ascending sequence adds dynamic tension and descending sequential figures relax dynamic movement; sequences,whether melodic (tonal or real), harmonic, rhythmic, or in combinatior\ soften extremeÌy dissonant pâssages.In diminution, shortening of the rhythmic unit promotes drive; lengthening the time values (augmentation) lessensmovement tension. Musical ideas may be extended in many wâys. Characteristic elements may be intervallically expanded (a) or conrÍacred (á),
236)
11 .EMBELLTSHMENT AND TRANSFORMATTON
Ex. 11-12
'-r. lvpr
and the order changed. Ex. 11-13
Whole passagesor small segments may be inverted, revealing fresh melodic and harmonic aspects.Removing certain notes of the line creates hidden tone-relationships, and filling out of thematic material with ornaments produces additional segments for further extensi.on.Part of an idea may be omitted by dismemberment and held for later expansion. Repeating tones and shifting their octave placement adds new color and meaning. Variants of the motif are made possible through retrogression, retrograde inversion, and rhythmic transformation, and alúough the original identiqy b often obscured, a unified musical expressionmay unfold. Imitation is a form of repetition in which the motivic elements move frorn voice to voice. The imitation may be literal or it may
CHROMATTC ALTERATTON
(237
occur in any of the forms of extensionvariation. Imitation ir, by natuÍe, a ünearprocessand a valuabledevicein achievingmeaningful part-writing and harmonicsuppleness. The strictnessof imiration is no measureof estheticevaluation,nor is free imitation necessarily a sign of inventiveness.The successof the use of linear devicesin a harmonic context dependslargely upon úe needsof the expressiveclimate in which they operate.
SourceMaterial Harmony containing extensiveimitation: Béla Bartók, Suing Quartet No. 5, p. 27 (Boosey) Boris Blacher,Stuã-ieim Pianissimo(brchestra), p. ZA lBote) Roy Harris, Symphony No. 3, pp. 85-91 (G. Schirmer) Paul Hindemith, Symphonie Mathis der Maler, pp. 1ó-20 (Schoa) Arnolcl Schoenberg,Verklãrte Nacht (sting órthestra), pp. 4-5 (Associated) Anton'Webern, Symphonie Op. 21, p. 8 (Universal)
CHROMATIC
ALTERATION
The primary effect of chordal alteration is a changeof harmonic color without a changeof chordal function. Dissonancemay r be intensified(a) orlesseãed@) by the alteration. Ex. 11-14
An alteration does not exist as such unless a scale area is defined or unless a characteristic chord is used as a harmonic norm. In C
238)
11 . EIVTBELLISHMENT AND TRANSFORMATION
maior, the foüowing example illustrates an altered first measurel but in C minor. the alteration is contained in the Picardian second
meâsure. Ex. 11-1J
O=126)
Piano ,rf dr*
The alteredformation must be foreign to the scalepresendyin effect. The chord G-Bb-Eb is an altered six-three (Neapolitan sixth) in D malor, but in the D Double Flarmonic scaleit is the unalteredsupertonic. Ex. 11-16
Altered chords in the Oriental scale have "unaltered" major freshness. Ex. 11-17 almed
Chromatic lowering as an alteration causes a drop in textural 'When tension, and chromatic raising gives a succession tonal lift.
(23e
CHROMATIC ALTERATION
altered chords are used in excessthey lose touch with the unaltered harmonic norm and fail to function as altered stmctures. Common alterations are those derived from the closest related keys. The maior key based upon the cycle of fifús may borrow its accidentals from the major keys a fifth above and below the tonic, and from its relative minors and the tonic minor.
Ex . 1 1 - 1 8 n (Cma.) ï
-;--r----o-
.,
È
L
h
iïÍ:ilH:::'
G'F'cm'
Minor keys of this cycle may use accidentalsfrom two tonal strands,thosekeys relatedto both the relativeand parallelmajors. Etc. 11-19 accidentalsfromrel keys ofEbandC
In keys basedupon a cyc{e of thirds, accidentalsare derived from the keys that lie a maior or minor third aboveor below the tonic.
E*. 11-20
In rynthetic scales,coÍÌÌmon alterationsmay be derived trom areasreachedby modulation.If chords from C Leading Wholetone scale have rnodulatedto chords of the Neapolitan Major scale,accidentâlsof D NeapolitanMajor may occur in C Leading "Whole-tone as common alterations:
240)
11 .EN{BELLISHMENT AND TRANSFORMATION
Ex. 11-21 C Leading'Whole-tone music
Ma. music
A cross relation exists when a tone in one voice of a chord is altered in another voice of úe following chord. The tension createdby this deviceis greaterin simpleharmony and barely felt in highty chromatic harmony. In harmony that uses all twelve tones with equal frequency, no such relationship is feh Cross relation occurs quite naturally in triads moving in chromatic úird relationship.
Ex. 11-22
Crm relation between a chord tone and a nonharmonictone is lessnoticeable.
Ex. 11-23
The simultâneous sounding of altered and unaltered tones has a pungent flavor. When it is created by ornamentation, the effect is fleeting. In major-minor compound harmony this sound is firmly 6xed.
PEDAL POINT AND OSTINATO
(241
SourceMateri.al Ifarmony with extensive alteration: Alban Berg, Violin Concerto(red.), pp. 4748 (Associated) ErnestBloch,ConcertoGrossoNo. 1, p. 5 (Birchard) Arnold Schoenberg,Das Buch der Hângenden Gârten, p. 28 (Universal) Roger Sessions,From My Diary, p. ó (Marks) Dmitri Shostakovich, Piano Quinteq p. ó5 (Am-Rus)
PEDAL POINT AND OSTINATO A pedal is a tone or tones sustained, repeated, or ornamented while other voices move úrough a successionof chords, some of which may be foreign to the pedal.
Er. 11-24 Q=92) Sax
*
f'**o
If three or moÍe tonesâre heÌd,a pedalchord evolves
E*. 11-25
2 CIs.
Polytonality is often suggestedby uiple pedalpoint. Tonic pedalshavereposeand non-tonic pedaÌshaveresdessness. Final pedalsare used to reinforce a tonality or allorv time for a
242)
11 . EMBELLISHMENT AND TRANSFORMATION
figuration to conclude its ornamentaldesign. When pedals are placed a fifth or ninth below the main body of harmony, sheen and resonance âre added. An ostinato is a well-defined melodic segmentinsistendy repeated. The tonal simpliciry of ostinato helps elarify úe texture of polytonal writing. Ex. 11-26
The ostinato becomesmelodically obstinate in an upper voice 'When and obtrusive in a middle voice. ostinatos occur simultaneously,harmonic tension rises.
Er. 11-27
Ft
rob. 8l
Ël 'Ël õL
lcL
LBn
\\\rt-J
ìÊ )
.-J
(243
UMSON WRITING
SoarceMaterial Examplesof pedals: Lukas Foss,A Parableof Death (red.), p. a0 (C. Fischer) PauI Hindemith, Sonatain C for Violin and Piano, p. 21 (Schott) Arthur Flonegger, Sonata No. I for Violin and Piano, p. 2 (Salabert) ZohânKodály, MissaBrevis, p. 45 (Boosey) Ârnold 'William Schoenberg,Suite für Klavier, Op. 25, pp. 1G-12(Universal) Schuman,New England Triptych, pp.24 (Presser) Igor Stravinsky, Perséphone(red.), pp. 4345 (Russe) William'Walton, Viola Concerto (red.), p. a3 (Oxford)
Examplesof ostinatos: SamuelBarber, Excursions,p. 3 (G. Schirmer) Norman Dello Joio, Meditations on Ecclesiastes,p 20 (C. Fischer) Carlisle Floyd, Susannah(red.), p. 44 (Boosey) Wolfgang Fortner, Mouvements (piano and orchestrt), p. 69 (Schott) Paul Hindemith, Das Marienleben (i948), p. 57 (Schott) Arthur Honegger, King David (red.), p. 9 (Foetisch) Paul Nordoff, Lacrima Christi, pp.24 (Mercury) Robert Palmer, Toccata Ostinato for Piano (Elkan-Vogel) Igor Stravinsky, Symphony of Psalrns(red.), p. 3 (Boosey) 'William'Walton, Belshazzar'sFeast (red.), p. 11 (Odord)
UNISON
WRITING
Unison writing implies the sounding of â line by various media at the same pitch or at different octaves. Much use is made of unison texture in twentieth-century composition; it has significant formal and coloristic functions. Its chief value in a harmonic schemeis its textural contrast. The successof unison writing dependsupon keen formal ti*i"g. Unison may be used for opening or interrupting calls (a); fmÍare flourishes (ú);
11 .EMBELLTSHMENT AND TRANSFORIVTATION
244)
Ex. 11-28 @) Q=1261
>-
,t 2T
pastoralinterludes(a); veiled linesplacedoctavesapa* (b); Ex. 11-29
I
ft) 1J=6e1 ($rno) F
(a); addedstring power (á); antiphonalâns\Ã/ers Et. 11-30
>'>aJ
t(str.) :>
(wïdr)
(str')
UMSON \ryRITING
(24t
or oudiningharmonicactivity with brokenchords Ex. 11-31 (J=il2)
Unison writing is effective when stating a rheme without its harmonic fabric, contrasting a single line with a chordal mass,or adding strength to a loud, full passage.Unison is also used for subsidingsound, rushing ocravesgathering power for a climax, to inuoduce â new tonal area by oudining the fresh scale,or ro project rhythmic varianrsin a reciative styIe.
SourceMaterial Unison writing: Conrad Beck, AeneasSilvius-Syrnphonie,p. 28 (Schott) Bruno Bettinelli, Fantasiafor Pianà, p. + (ÏUcorài; B^:"ji*ol!l*en,.String Quartet Nõ. 2, p. a4 (Boosey) Charles Griffes, Piano Sbnata,p. 15 (G. Schirmer) Camargo puarnien Piano Concerto No. 2 (red.), p. 3 (Associated) Roy FIarris, Piano Suite, p. a (Mills) Marcel Mihalovici, Sinforiia Partita, p. 27 (Fleugel) SergeProkofiev, Piano SonaraNo. 7, p. 2 (Leeõs) Arnold Schoenberg,String Quartet No. 4, p. 61 (G. Schirmer)
tl
246)
11 . EMBELLISHMENT AND TRANSFORMATION
Applications 1. Write a shorc piece for two flutes and two clarinets featuring nonharmonictones. 2. Harmonize the following melody (for piano) so that eachchecked note becomesa nonharmonictone.
Ex. 11-32
3. Write a woodwind passagefeaturing ornamentalchords. 4. Write a melodic line for clarinet that stemsfrom broken chords of various kinds 5. Write severalphrasesfor piano in which ornamentalfiguration is createdby chord tones. 6. Write imitative music for fwo flutes at the interval of the tritone. 7. Write music for horn and tuba with imitation in augmentation. 8. Write a pâssagefor two cellos that has imitation at a dissonantinterval. 9. Createa pyramid in brassesby employing closeimitative entrances. 10. Write â pâssagefor string orchestra using several effective cross relations. 11.Write a short piece for organ featuring harmonic alteration. 12.Write an expressiveharmonicproglessionfor stringsover or under a pedal tone in the French horn.
UNISON WRITING
(2,41
-13. Extend the following pâssagefor rwo oboes and two basoons, featuring the double pedal.
h.
11-33
14. Write melodic fragments, appropriate for use as ostinatos. 15.'Write a lively flute tune over a double-bassostinato. 16. write a string quarrer pâssagein which rwo osrinaros are used simultaneously. 17.Write a unison theme for violas or cellos 18. Increasethe intensity of a harmonically strong orchestralpassage by employing suddenunison writing.
I
-al
'"ï::ïi I K"y Centers I
TONALITY
Tno roNer- MEANTNGof an isolated chord is indefinite; it may be a crucial oÍ an ornamental chord of many keys, or it may belong to no key. When surrounded by other chords its meaning may-be restricteã to a single tonality, to t\À/o or more wavering tonalities; or if it has atonal intentions the fact can be made obvious. Tonaliry does not exist as an absolute. It is implied through harmonic articulation and through the tension and reÌaxation of chords around a tone or chord base. A panicuÌar style or period is not always limited to a predilection for a single kind of tonality. Twentiethceffury motic makes use of many degreesof tonaÌiry and employs mâny meânsfor establishingthem. In a strong tonal context, all elements of progression are subordinate tó the pull of the tonal center and a drive towards cadential realization. Traditional tonality depends upon scale and chord relationships for its organization. Usually three basic chords are needed to produce a feeling of tonality: one built upon a scale step above thã tonic, one below the tonic, and the tonic itself. Harmony with tritone gravitation is helpful in establishing the center' 248
(24e
TONALITY
by using tonesof a scaleas chordal Tonality may be established roots in varying degreesof support of úe central tonic: in balancedsupport by the subdominantand dominantto the tonic (a); in balancedsupport by the submediantand mediant (b); Ex. 12-1 (r)
(b)
aür. lni. Neep. ML
DoubleHarm. Hung. Mi. phrygrân LydianMi. locrian Me. Locrho
Neap. Ma. Symmetrical dorian
Hung. Ma Oriental ' tydian
in balancedsupportby the leadingtone and suPertonic(a); and in varying supportby scalestepsembracingthe tritone (á).
Ex. 12-2
phrygira SrryerLocrian
Neap. Mi. DoubleHarm, Enigmatic
lydian Hung. Mi Overtooe
locriatr Oricntal Eight-tone Spaniú
Orienal
19â. lydian teadinglVhole-toae
The remaining secondary scale roots decorate the three tonal pillars in each case. Music may be brought into key focus by forces other úan the tonal pull of chordal pillars. Key feeling may be created-by "tt extremely dissonantchord refusing to becomeconsonant'from a successionof simple chords resisting complex harmonic forces, from two culminating tonalities merging finally as a dominating polychord, from a group of important-tonesrecurring at decisive points,or from atonalmusicsearchingfor a key at cadentialpoints.
12 . KEY CENTERS
2t0)
Key consciousnessmay vanish temporarily only to make stonger an emerging key's return. The search for tonality or key center feeling may become a creâtive forcç in music. The tonaliry of a structure may be generated from a unifying harmonic idea from which musical gro\Mrh extends. An initial major-minor compound chord may promote polychordal writing that instigates â triâdic struggle between major and minor structures; the formal conflict may not be resolved until an obstinate melody note, corrÌmon to both triads, anchors them in a malor-minor formation quite transposed from the original chord. A work may be built tonally upon an initial harmony that falls cadentially; the final cadencemay find refuge in a group of tones far removed from the tonal implications of the first harmonic fall. A successionof chords ar an opening may, in microcosm, suggestthe tonal shapeof the enúe work. An insistent chord may establish a cenrer by resisting pressures from various tonalities.
Ex. 12-3 d.ua)
:>
t
úú
(2t1
MODULATION
Tonaliry may be established through contradictory tonal eÌements or through a streamlined drive to the tonic. In equidistant rootless harmony, âny note may be made úe tonal center through melodic insistence,spacing, or instrumentation. Music may hold its tonaliry loosely, elements of atonality being inherent from the onset. There are many degrees of key-center gravity or of keylessnessin the general area of tonaliqy or atonaliqy. At one extreme of the concept of key is tonality, the other extreme is atonality, and the point at which one ends and the other begins is indefinite. MeÌodic iines in a tonal framework can become so free that the implied harmony becomes evasively dissonant and a point reached where key feeling is lost. Partial atonality is useful in vague introductions and transition pâssages,and when preparing for a returning tonal thematic idea-
MODIJLATION
The ambiguity of any chord is such that it can be related to any of the twelve tonal centers. This is an important fâctor when modulating, â process of changing the tonal center. If a definite key change is desired, both keys should be firmly estabÌishedby at least three center affirming chords. A pivotal chord is one that is common to both keys; it is diatonic when belonging to both scale formations and chromatic when it belongs to neither, or only to one. It is not always clear ]ust which formation is the pivot chord -this only enhancesmodulatory beauty. When modulating to â permanent key, chords other than the tonic may be aimed for so that time can be made for settling into the feeling of the ne\Mtonality. A premature cadence is avoided by lumping to a distant key, then working gradually toward the desired kev. Chromatic modulation is attained by shifting an entire chord a half step in sudden parallel harmony. Abrupt modulations make the arriving tonic felt as a distant chord; to establish a firm feeling of the new key, an extended harmonic progression is necessaryin order to secure the new center. All chromatic tones are in the domain of a key when the vertical aspect g-ivesway to the hori-
12 .KEY CENTERS
2t2)
zoÍtãl movement of voices; therefore, all keys have twelve tones in common and may be reached quickly chromatically. Modulation may be realized through the semitone or orher intervals. A fresh change is felt when the modulatory interval is one other than the characteristic interval of the prévailing root progression. Modulatory changes of the third relationship are effecdve in passagesof second relationship harmony,
Ex. 12-4 A center
C
D
E
F->A mod.(3rd)
ClB
A
and changesof the secondin third relationshipharmony. Ex.
12-5
G ceirter ---'-
E center -------
Ft *Gt mod. (2nd)
Key changeshave speciallift when modulationis accompanied by an octaveleap in register. Ex. 12-6
Continuous,quickly shifting keys produce a senseof displaced tonality rather than modulation
MODULATION
Ex. 12-7
Key feeling may be gradually loosened or tightened. The gravity of a tonal center is decreased by moving a new voice through notes that give an important chord new roors.
Er. 12-8
l9dtcred(nb;
* aus. óú -(F)
A distant tonaÌity may be establishedby the reinforcemenrof the new centerby auxiliary chords,
12 .KEY CENTERS
2t4) Ex. 12-9
ë,Bq f
t&rc. ctLz^
or by the pneumatic action of violent repetitions of the neìü toÍìrc with color and spacing changes. Transient modulation is an important meansof securing variety It is lesseffectivein very dissonant in relatively consonantpassâges. harmony doesnot need,thecolor complex Chromatically passages. õf transitorv modulation. In this harmonic context, modulation is used to moïe from one section to another, rather than within a itself. progression Modulation from a single tonahqy to a polytonaliqy may be attained by moving double strands of uansient modulation in a contrâry motion of keys. A coupled tonic makes an excellent starting point.
Ex. 12-10
music
When modulating from one polytonal ârea to another, each key zone usually moves to the new zone by independent modulatory rneans; the over-all harmonic total must, however, have textural design and intelligible tension fluctuation. Distant tonal centers are reached in countless ways' but unless
(2tt
POLYTONALITY
this facile techniqueis held in careful check, harmonic growrh \rill be replacedby superficial variety.
POLYTONALITY
Polytonal writing is a procedure in which two or more keys are combined simultaneourly. If only two keys are sounded" the ryecific term bitonality may be used, but polytonality has come generally to imply the use of more than one tonal plane at the sametime. The scalesthat form the different tonic cenrersmay be intervallically identical or conrrasring, traditional or qFnrheric. Ex. 12-11 major
+
2
2
maior Hung. M,inor
=e
Hung. MiÃos.
lYdiaa
.sr t-2
phryg"tr
b+ r-!
Enigmatic
.i>
SuperLocdao
Great concern must be given the vertical factor; if tonal planes are arbiuarily combined the harmonic result will be haphazard. The music mu$ be conceived in polytonal context, not cloaked in accidental texture. Each melodic line should rerain its own individuality yet the harmonic total must have direction of flow, tension design, and textural consistenry. Although each tonal plane has its own organizational cenrer, a single over-all tonic structure is usually felt from the bass.From this basic polychordal tonic stems the polytonal texture. The following example employs C, E, and G areas at different levels, but they combine in a total harmonic sound with C functioning as the fundamental:
s
12 . KEY CENTERS
2t6) Et. 12-12
Polytonaliry, then, is a specific kind of tonal organization, a means of moving groups of voices within confined harmonic register areas.Polychordal writing is often tonal, and when each group of voiceswithin a chordal unit functions wiúin the confines of a stablescalezone,polytonaliqyoccurs. Polytonality is effective as such only when each tonal plane is kept within a clear scaleformation. Shifting of modaliry through chromaticalterationcÌoudsthe texture or simply producesmiscellaneouspolychords.For maximumclarity in the pro]ection of ditferent tonalities, one key is introduced and as the next key is becomesless added,the precedingkey, having been escablished, obvious.
Ex. 12-13
í
The scalestepsspanningthe tritone shouldbe brought into play âs soorl as possible;otherwise polponality will fail to operate. In
(2t7
POLYTONALITY
the following example,the lower F mafor strand hasno B! or E, and the upper C major strand has no F or B; the result is ambiguouslymajor.
Er. 12-14 J=120
Closelyspacedpolytonal areasbecomemuddy. The keys shouÌd be kept far enoughâpart to allow room for voice activity. Harmonic parts of three keys placed a small interval apart run into eachother. Crampedpolytonaliqyof this type is possiblebut lacks versâtility. Independentlines should not be placed at random without an understandingof polytonal construction.The fundamentalquality of polytonal texture is determinedby the key relationshipset up by the tonics. In major-key combinations,â polytonal order of tensionfrom consonantto dissonantis securedby combining fwo keys that lie a perfect 6fth, mafor ninth, major sixth, major third, major seventhapart-and so on up the cycle of fifths. The high point of resonancein the order is at the center. Ex. 12-1J j a-
Loú
1t
b-.
ma.9 rra.6 ma.3 ma.7*r9,4 ml 9 mló
Those keys that âre not closely related accordingto the circle of fifths will more easilyset âpârt the tonal key spheres.The tritone as a basisfor key coalition forms a prime polytonal relation-
12 . KEY CENTERS
2t8)
ship becauseit is the most resonantof the dissonantcombinations of keys. Polytonal combinationsof ma]or keys are: Ex. 12-16 consonâít
Similarinventory shouldbe madeof all key combinations.When minor keys are at the bottom (major or minor at the top), fewer consonantcombinationsof keys are possiblebecauseof the minor third in the lower key. When combining more than two keys, the consonant-dissonant order of resonanceis: all keys separatedby a perfect fifth, a maior ninth, a major sixth, a major third, etc.
Ex. 12-17
'When
the intervalsbetweenthe keys âre not the same,the larger interval is found between the bottom keys. When combining three or more mixed keys, the uppermostkey is governedby the resonantrelationshipto the bottom, not inner key. The resonanceof polytonality dependsupon the resonanceof the over-all tonic formation as determinedby its intervalÌic tension. The passingsecondarytextures are maneuveredaround the rnost resonantpolychords úat form the structural pillars of the particular key combination.
(2te
POLYTONALIfi E*. 12-18 Ama.
polychordalpíllars
polichordalpillars F lydiau
Fma"
These secondarytexturesoften becomethick and troublesome and are madeworkable by omissionof chord members,doubling of stronger intervals, ornamentalcoloring, unison and two-part interpolations,or by ostinatos. Polponaliry may be establishedby two or more tonal planes of harmonic writing (chordal polytonality), Ex. 12-19
or through imitative writing (horizontalpolytonality). Real canons at intervalsother than the octavecan imply polytonaliqp.Two or three lines may produce transpârentpolytonality.
Ex. 12-20
su, Trio
\canon by 4o
espr,
canonat úe uitone
12 . KEY CENTERS
Block chords againsta single contrastingkey line createsupple polytonal patterns;shifting pedalseâsethe polytonal texture.
va.(a;.i{
Well-balanced polytonaliry is secured through mirror scales (polymodality).
Er. 12-22 D lydian
I
legúo
-o--ã
(261
ATONALITY
JnJ
ATONALITY
Atonality is a term loosely applied to music in which a definite key feeling has been weakened or lost, and to music in which no key gravitation ever existed. Atonal writing is the organization of sound without key establishment by chordal root relationships; but tone combinations or âreas may form an atonal equivalent of tonality. In atonal music, relations between tones occur without reference to a diatonic scale formation. There is movement to and from characteristic intervallic formations but the central force is usually melody, and not a governing harmonic base. Atonality operâtes within â syntax that favors dissonant formations, and its organization is based upon shifting intervallic tension or an order of tones. Atonal movement is often linear but may produce vertical combinations of mixed intervals (compound harmony) that are free from the power of an overbearing tonic. When the motion of voices câusesâ constant and total dissonance,beds of sound are created upon which prominent melodic lines may lie. If chromatic chordal mixtures accumulate, formal coherence is achieved by repetition, variation, or mutation of úe chromatic sound groups. Although the harmonic factors are dependent uPon melodic relationships, these vertical structures are often manipulated as a c.ontributing element in atonal composition. The various elementsin atonal music are tightly knit by extreme motivic concentrâtion, and reference is constantly made to Previous material. There is litde regular rhythmic stamping and no
12 ' KEY CENTERS
262)
continuous chain rhythms; the rhythmic patrerns are asymmetrical and the meters irregular and often complicated. When the controÌling principle of scalar tonality is abandoned, chordal root organization of the rwelve tones ceasesto exist, and form and unity are creared by meiodic and rhythmic development. A basic order of tones, alÌ twelve or fewer, may be used as a unilying basis for a work, and formai devices evolve from the basic shape. Twelve-tone technique or composition with "rwelve notes related to one another" is primarily â conrrapuntai practice. It is essentiallya polyphonic conception with some points in common with the pre-"tonal" music of the Middle Ages. Twelve-rone writing is, therefore, mosr naturally approached in a treatise on counterpoint.
SERIAL
HARMONY
Harmony, even when secondary, is an important consideration in linear music. When harmony is regulated by a horizontal, unifying idea (twelve-tone or nor), rhe texrure may be serial; this kind of writing creates harmony of extraordinary compâctnessthrough the manifold variations of the motif relationships. Chordal formations that arise from serial linear writing have little or no function in a scalar tonal sense.Harmonic obligations arise from a chromâticism set up in harmonic areas from a characteristic series or portion of a series of tones. Logical meÌodic thinking gives the individual par$ their dtection and the ear of the composer gives them the quality of chordal movement. Some directions in serial composition point away from the specialized craft of strict "atonal" writing, where all elements are generated from a single germ cell, toward a flexible creârive process úat includes the vast musical resources of composition, both tonal and atonal. The techniques and materials of atonal music are often amalgamated with those of many types of tonal idioms; the harmonic stock includes endless possible harmonic combinations. A qynthesis of harmonic potentialities includes chord materials governed by root progressions, intervallic texture tensions, and serial
(26t
SERIAL HARMONY
devices.At any point in the formal shapea melodicgroup of notes may control harmonic texture. Any successionof any number of tones, not necessarilyall different (a), may be used in two or more voicesat once,forming harmony from horizontalmovement (b) or divided between voices, forming harmony from vertical telescoping(c).
Ex. 12-23 melodic set
ç)=ne1
4
56
:l',*.
non+erial
82
10 11
Invenim I ---------------->
tF!
2
34
Original (transpositionno. 1)
f-íã.--c
Original (tranqpositionno. 2)
ll (7)
f
12 . KEY CENTERS
264)
OrìginaÌ (uanspositionno. l)
-
senalrow extrectron
|
2 3 r
4 | 6 7 I t-------Ì-J
9'1,0 lt
9
l0ll
r
(identical notes) Inversion (transposed)
Original (transpositionno 2)
9 1011
In an extended passageor secrion of free serial music, any combination of tones may be ser up as a tonaliqy. A successionof three or more notes from the selectãd melodic ser or row of rones may be used âs a center chord (a).Atransposition of the cenrer chord erected upon its uppermosr note may form a cadential chord above the center (b); a mirror of the cenrer chord may form anorher primary chord below (c). Changing the octave pitch of one or more tones produces inversions. Inversion of the center chord may yield a new set of primary chords (d, e, and f). All other combinations of tones may form secondary harmony.
Ex. 12-24
(26t
SERIAL HARMONY
When a melodic set includesone or more identical notes,doubling of chord membersproducescolorful serial doublings.Parallel harmony may be used momentarily at points where doubling occurs.
Es. 12-2Í (J=8ob r òü.
>
1l
,Qew'
HH
In serial harmonic progression, the order of chords is often changed to increase the gravitational tendency of the chordal formations to move to the center chord.
Ex. 12-26 ccffer x
ctntet x
Transpositionof úe melodic set causesmodulatory shifting of the harmonicâreas.
Ec. 12-27
12 . KEY CENTERS
266)
When a chord from one form (original, retrograde, inversion, or retrograde inversion in any uansposition) of the melodic set is identical to a chord of another form of the set, it may be used as a pivot formation when entering new "ronal" areas. Closely related harmonic areasare those that may be found by constructing an inversion or retrograde inversion of the melodic ser starring a perfect fifth above or below the original set. Strong cadences may be formed by the primary chords (Ex. l2-2+) or by ornamenral movemenr of the parts directed toward the center chord.
Ex. 12-28 Perfect
PI.g"l
Complete (c)
(b)
Omamental (e)
+
(r) Chords may be ornamented by nonharmonic tones (a), by harmonic tones (â), or by serial tones that result from the simultaneoususe of two or more forms of the set (d).
Ex. 12-29
(267
SERIAL HARMONY
Contrasting thematic mateúl mây be built upon a new but related melodic set. The original set may be converted to another by selectingthe top notes of a seriesof telescopedchords.
Ex. 12-30 oenr9-nctmeloücsct
DFGDTFSD3CIÂB r23456789
When melodic sets employ twelve different notes, successive chords encompassthe entire twelve-tone field. A strong center or harmonic areamay result from the completion or fulfillment of úe twelve-tone set. Serial music of any type of rov/ or set constructionmust be aurally createdby melodic, harmonic, contrapuntal, rhythmic, and formal elementsof the musical structure and not alone by manipulativeprocedures.Serial technique doesnot in itself insure communication or even effective sound orthan any other.techniquedoes.When autoganization lnymore matic writing is avoided, the unifying power of serial practice allows great hannonic variery.
SourceMaterì,al Modulatory pâssages: Ernest Bloch, Piano Quintet, pp. 57-59 (G. Schirmer) Aaron Copland,The Tender Land (red.), pp.67a8 (Boosey) Ingolf Dahl, Sonata Seria for Piano, p. 14 (Presser) Jacqueslbert, Histoires for Piano, p. 3 (Leduc) Gian Carlo Menotti, The Unicorni the Gorgon and the Manticore (red.), p. 56 (Ricordi)
268)
12 . KEY CENTERS
Vincent Persichetti, Hymns and Responses for the Church Year, p. 1 (Elkan-Vogel) SergeProkofiev, SecondViolin Concerto (red.), p. 21 (Russe) Arnold Schoenberg,Gurre-Lieder (red.), p. 14ó (Universal) Harold Shapero,Sonata for Violin and Piano, p. 13 (Southern) Igor Stravinsky, Symphony in Three Movements, p. 78 (Associated)
Tonality createdby non-traditionalmeans: Peter Racine Fricker, Concerto for Piano and Orchestra (Schott) F{ansWerner Ffenze,Concerto for Piano and Orchesta (Schott) Paul Hindemith, Sonata in C for Violin and Piano (Schott) Arthur Honegger, Violin SonataNo. I (Salabert) Franco Margola, Piano Sonata 195ó (Ricordi) Francis Poulenc, Mass in G mafor (Rouart-Lerolle) Harold Shapero,Three Piano Sonatas(G. Schirmer) Igor Stravinsky, Symphonie en Ut (Schott)
Examplesof polytonality: Benjamin Britten, The Turn of the Screw (red.), p. 158 (Boosey) Alfredo Casella,ll Pezzi Infantili, p. 20 (Universãl) Manuel de Falla, Harpsichord Concerto, p. 3 (Eschig) Rodolfo Flalffter, Piano SonataNo. 2, p. 31 (Peer) Paul Hindemith, String Quartet No. 3, p. 21 (Schott) Arthur Honegger, Symphony for Suings, pp. 28-30 (Salabert) Darius Milhaud, Cinq Symphonies (petit orchesue) p. ó1 (Universal) Wallingford Riegger, New and OId (piano), p. 31 (Boosey) Igor Stravinsky, Symphoniesof Wind Instruments (red.), p. 14 (Russe) Karol Szymanowski, String Quartet Op.37, p. 19 (Universal)
Worlis with prominent atonality: Alban Berg, Wozzeck (Universal) Arthur Honegger, Pacific 231 (Senart) Charles lves, Aeschylus and Sophocles(from 19 Songs), (New Music) Carl Ruggles, Evocations for Piano (Am. Mus. Ed.) Arnold Schoenberg, Pierrot Lunaire (Universal)
Works written in free serial technique: Aaron Copland, Piano Fantasy (Boosey) Luigi Dallapiccola, Il Prigioniero (Zerboni) Irving Fine, String Quartet No. 1 (C Fischer) Wallingford Riegger, Symphony No. 3 (Associated) George Rochberg, String Quartet No. 1 (C. Fischer) Roger SessiongSymphony No. 2 (G. Schirmer) Igor Stravinsky, Agon (Boosey) Fartein Valen, Sonetto di Michelangelo (Norsk)
SERIAL HARMOÌ.{Y
(269
Applications 1. Write a woodwind pâssage whosebasictonality is E! with a stÍong titone emphasison A major. 2. Harmonize the following melody for string iluartet, preservingthe E tonal center.
Ex. 12-31 Ândantc
ú rtp.
3. Write a passagefor piano, four hands,in which an insistentchord estabÌishes a center by resistingtonal pressuresfrom various keys. 4. Composea short dancefor clarinet and piano which employsshifting tonality. 5. Write two-part counterpoint for the harpsichordwith eachpart in a different tonality. ó. Extend the following polytonal passagefor harpsichord (C mixolydian and Ef aeolian):
Ex. 12-32
12 . KEY CENTERS
270)
7. Extend the following polytonal pâssâgefor string trio (Ffi maior and F lydian):
Ex. 12^33
8. Extend úe following polytonal pâssâgefor piano (D[ and C rnajor):
Et. 12-34
9. Write a shortpianopieceasfollows: A-rwo distant---l r."u,- l-ï-,tingle
üne
LH-broken chords
õ-two closekeÏs
RH--chords LH-ostinato
A-modified repetition with coda. 10. Write an orchestral example of polytonality with agile ninth chords in the woodwinds, sustainedtriads in the horns, and an ostinato (in tenths) in the low strings and winds. 11. Write a non-serialstring-quartet exampleof atonal music. 12. Write a short piece for woodwind quintet that conains boú serial and non-serial music.
CEÂPTER TEIRTEEN
HarmonicSynthesis
COMBINING TEXTURES CoNrsrvÍpoRAnv harmonic writing b often a composite process which may involve varying placement of the norm of dissónance, choice of a single harmonic idiom or the coalition of one with anoúer, fusion of tonaìities, singlenessof sound organization or the juxtaposition of tonal and atonal aspects. The amalgamation of divergent concep,tionsof tonal formations is part of our harmonic language. Acceptance of one procedure does not necessarily mean the exclusion of others. A fugue may be written over a cântus placed under a rone row, and quartal harmony fI-T,-" lI*" blended with tertian. The vertical combination of harmonic rexrures produces polychordal and compound formations, but successive combinations entail movement from one kind of texture to another and the functioning of heterogeneous harmonic materiais side by side. A textural problem arisesfrom the manipulation of the transitional materiaÌs that lead from one type of harmony to another. The characteristic interval of one kind of harmony b contained in any other n1
272)
13 . HARMONIC
SYNTHESIS
kind of harmony and may be brought to the surface by intervallic inversion. In all textural changes,an inten'al may be featured that, when inverted, produces the characteristic interval of the new harmony. The interval of the fourth is given a prominent position in chords by thirds to allow chords by fourths ro enrer; the fifth contained in the triad is inverted to allow for oncoming fourths (a). In seventh chords the inverted fifth from the root or third may be used to introduce quartal harmony (ú). The voices of an inverted seventh chord may be arranged so that the interval of the second is emphasizedand the contextual way prepared for secundal harmony (c). In ninth chords the interval of the sevenrh from the root or third is inverted to suggestthe secundal texture of clusters or added-notechords (d).
Ex. 13-1
When moving from one rype of harmony to another the characteristic interval of the new harmony is best introduced well in advance. The doubling of a colorful tone (major third, maior seventh, or prominent nonharmonic tone) strongly suggestsoctave or unison writing that in turn makes way for foreign harmonic re-
(273
COMBINING TEXTURES
sources.The unison can becomea suppledevicefor moving from one kind of texture to another.The harmonicambiguiq' or sudden unison allows for the entranceof any texture. The versatileornâmentaltone also providestextural meânsfor entering any harmonic region. The appoggiaturaand suspensionare particularly eÍfective in preparing the intervallic texture. The melodic freedom of broken chordspermitsthe fluctuation of chordsof varying construction, Ex. 13-2
Accenting melodic tones that outline úe characteristic intervallic formation of the new âreâ creates a tonal bond between the contrasting harmonic materials.
Ex. 13-3
4,
(Pi"z)
teni*'
quâftd
-
l---------€
13 .HARMONIC SYNTHESIS
274)
The rypg of chordal formation may be changed by subtracting from a melodic morif rones that leave only the tones of the new textÌrre.
Er. 134
ct
rúr--:
Hn. 2 Bns.
.? Sn only
ouartal ----+
The equidistant chord has neither root nor power to resisrhomogeneous chordal formations and can, by chromatic motion, v/eave one harmonic fabric into another. Rough tritone relationship or prominent hidden fifths divert artention from harmonic rransformations. Sequential patteÍns can drive varied chords over many harmonic barriers. A common transitional harmonic device involving clusters is the gradual subtraction of cluster members, leaving chords that suggest the kind of harmony to follow. The reverse is no less efiective.
Ex. 13-Í
Polychords are approachedthrough coupled uiads (a), or chromatic conversion of chords (ú). Motion from polychords
(27t
THEME AND FORM IDEAS
to triads is createdby the evaporation of one triad of the polychord (c). Ex. 13-6 1J-tzo1
Full -, Orch.
(c)
Ì
Í
aí
The harmonic units of a tonal polychordal successionmay meet at a point where each progressesin a sepârâteand consistentkey zone.The polychordal progressionthen becomespolytonal. Atonality may be entered through florid writing when the individual lines are given such freedom of c{rromatic movement that the implied harmony becomesindefinite and úe feeling of key disappear*
THEME
AND
FORM
IDEAS
A melodic kernel of two or more tones may form the nucleus from which the subject matter of an enúe work is shapedand harmony derived. The compositional process is meaninglessunless
276)
13 . HARMONIC S\T{THESIS
thematic stateÍrlentsare identifiable, for continuiqy and coherence are effected through aural rerention of modfs. It is imperative that a s€nseof tempo, dynamics, and medium be part of thematic conception. Even a single tone can serveas a point of departure through dynamic and timbre implications; a pianissimo and expressivemiddle C played by a solo viola has musical impetus while a rough, staccato, and loud middle C played by three rrombones has a quite different kind of musical energy. Creative momenrum might stem from a scale formation, a series of non-scale ton€s, a chordal stmcrure, a lone tone repearing itself before finding â ne\Ãrtone from which flight can be made, the rnelodic contour formed by a complex opening chord âtrempting to shed its dissonant tones, or themes shaped by brassesanswering a loud timpani. Material might be born of creative tension caused by pattern shapes: the excitement of fast-moving voices of sopranos, the intrigue of brass figures accompanying a resounding sringsection, or the richness of strinç under a unison melody in the solo piano. Careful inventory of melodic, rhythmic, and harmonic aspects of thematic ideas must be taken, becauseas a work progressesihese elements are often used independently of each other. Not until full thematic intelligibility is realized do hidden meanings of the theme come to the surface. Thematic ideas may be purposefully enigmatic and vague, positive and complete in themselves,or musically. neutr_al,but they should be positively vague, not vaguely positive. The composer musr be fully awâre of the potentialitiés of his material so thât full advantage can be taken of ihe phenomenon of thematic uansformation. Thematic meaningfulnesscan arise only from úematic uniqy and purpose. If a themeis not nourished by its motivic consriruents it wilÌ lack significance. Form and style are inseparably related. Form is the outward eqúvalent of instinct, taste, and style, and is the manner in which kinds of materials âre presented. Divergent musical materials may be brought out of conrexr into a piece, but the successof the décision to change the prevailing milieu depends upon creative sensitivity.-ConÍlicting formal elemenrsoften result in free and imaginative forms, and the whole course of a maior work is altered. The impulse that incites the composer to deviate from the predictable must at the sametime create a feeling of inevitabiÌiqy of form.
THEME AND FORM IDEAS
(277
Associationof musical ideas is created by the melodic motif, the harmonic succession, and the rhythmic pattern; none of these three formal elementsbecomesfunctional until it is transformed by the creativemusicalprocess.It is during this growth that specific ideasfor shapingthe formal strucrure stimulatecrearivewriting: a succession of simplechordsfighting dissonantforcesmay succeed or fail; an extremelydissonantand overbearingchord refusing to becomeconsonântmay produce a distinctive harmonic progression; a succession of chords,dramaticallyplaced,may indicate the formal direction; a work may be built upon initial harmony falling cadentially; provocative formal elementsmay be inuoduced by brightening the harmony as nores get slower and darkening the harmony asnotesget fasrer;six tapedmicrotonesmay be elecuonically upset by hexachordal diapasonsthat push agitated Sprechstimmefragmentsagainstruned oriental blocks. Any tone cansucceedâny other tone, any tone can soundsimultaneouslywith any other tone or tones,and any group of tones can be followed by any other group of rones,just as any degree of tensionor nuancecân occur in any mediumunder any kind of stressor duration.Successfulprojectión will dependupon the contextual and formal conditionsthat prevail, and upon úe skill and soul of the composer.
SourceMateriul Passages containingvariouskinds of harmonic textures: Albln Berg, Violin Concerto (red.), pp.47a8 (Universal) Paul Hindemiú, Six Chansons(II), (Associated) Althgr F{onegger,Piano Concertino, pp. 1-4 (Sena*) Charleslves, Violin SonataNo. 4, p. 8 (Arrow) Michael Tippen, Suing Quartet No 3, p. I (Schott) Works
contâining
contrasting
techniques:
Béla Bartók, Piano Concerto No. 2 (Boosey) Karl Àmadeus Ffartmann, Symphony No. o'(Schott) Charles lves, Piano Sonata No. 2 (Concord), (Arrow) Vincent Persichetti, Quintet for Piano and Strings (Elkan-Vo,sel) Roman Vlad, Divertimenro for 11 Instruments (Éoosey)
13 ' HARMONIC SYNTHESIS
n8) Unique thematic idea*
Béla Bartók, String Quartet No. 4, p. 3 (Boosey) Alban Berg, Violin Concerto, p. 1 (Universal) John Cage,Amores for Prepared Piano, p. 1 (New Music) Carlos Chávez,Sinfonia India, p. 1 (G. Schirmer) Aaron Copland, Vitebsk (violin, cello and piano), p. 1 (Cos Cob) Roy Harris, Concerto for Piano, Clarinet and String Quartet, p. 39 (C,s Cob) Luigi Nono, Coro di Didone, p. 1 (Scherchen) Wailingford Riegger, Dichotoiry, p. I (New Music) Guido Turchi, Preludi e Fughetti per Pianoforte, p. 4 (Zerboni) Roman Vlad, Sonatinafor Flute and Piano, p. 2 (Zerboni) Ralph Vaughan Williarm, Symphony No. ó, p. 143 (Oxford)
Works with unique forms B€la Bartók, fti[tsic for String lrstru:ents, Percussion and Celesta (III), (Boosey) Aban Berg, Lyric Suite (III), (Universal) Luciano Berio, Cinque Variazioni per Pianoforte (Zerboni) Piere Boulez, Improvisation sur MallarrrÉ (Universal) Sylvano Bussotti, Five Piano Pieces for David Tudor (Universal) Elliott Carter, String Quartet No. 2 (Associated) Carlos Chávez, Sonatina for Violin end Piâno (New Music) Alois Hába, Suite No. 3 for Quarter-Tone Piano (Universal) Roy Harris, Symphony No 3 (G. Schirmer) Paul Hindemittr" Hin und Zurück (Schott) Charles Ives, The LJnanswered Question (Souúern) Bo Nilsson, Zwnzig Gruppen (Universal) Vincent Persichetti, Harmonium (soprano and piano), (Elkan-Vogel) Gunther Schuller, String Quartet No. 1 (ilI), (Universal) William Schuman" Symphony No ó (G. Schirmer) Karlheinz Stockhausen"Klavierstücte I-IV (Universal) Igor Suavimky, Symplroniee of Wiad kstrurnents (Russe) Edgard'Webern, Varèse, Ionisation (New Music) Five Pieces for String Quartet Op. 5 (Universal) Anton
Applications 1. Write â passagein any medium containing the following chords _ (among others) in any order a4d in any transposition
THEME AND FORM IDEAS
(27e
Ex. 13-7
2. Extend the following idea in the string orchestraand include various categoriesof harmony.
Ex. 13-8
3. Weave â passâgeof organ music through tertian, quartal, secundal, polychordal, and compound harmony. 4. Construct thematic material on the following pattern ideas: rich string harmony under a solo trumpet; fast-moving woodwinds; huge declamatorychords for two pianos;solo timpani answeredby full orchestra; string and woodwind chords surrounded by virtuoso figures in the brasses;coupled two-part writing in the band; percussiveharpnichord chordswith abbreviatedornaments;lyric polytonality in the oboe and guitar; dynamic chords in the harp with frequent two-parr interruptions in the flute and viola; a sopranovocalisewith mirror writing in the piano; clusteredbrasseswith melodic writing in the timpani and xylophone; quiet ornamentedpolychords in the organ; quartâl harrnony in the woodwind quintet with erratic harmonic rhythm; vivacious pandiatonic writing in the mixed chorus on a phrase from one of the Psalms;and a virnroso keyboard mirror for solo piano. 5. Make piano reductions of provocâtive passâgesfrom severaltwentieth-century orchestral works.
Index of Composers
Antheil, George, 222 Argento, Dominich, 74 Auric, Georges,210
BouÌez, Piete, 27, 172, 210, 278 Britten, Beniamin, 28, 42, 50,74,8t, 90, 118,172,2r9, 220,245,268 Bucchi. Valentino. 10ó Busoni,Ferruccio, ó0 Bussotti,Sylvano,278
Babbitt, Milton, 219 Badings,Henk, 27, 87 Barbei, Samuel,62, 74, 219,220,243 Cage,John, 278 Bartók, Béla, 27, 28, 42' 43,45, 50, 59' ó0' Carter, EÌÌion, 28, 172, 210, 219, 778 74, 126,150,158,180,209,270,219,222, Carpenter, John Alden, 210 225,237,277,278 CaseÌla,Alfredo, 42, 268 Beck. Conrad, 245 Châvez,Carlos,41, 42, 43, 118,210,220, Becker,John,219 222.225.278 Beeson,Jack,219 CopÌand,A,aron,27, 28, 74, 106,118,126, 118 Paul, Ben-Haim. 158, 180, 209, 210, 219, 220,225, 267, Bentzon, NieÌs Viggo, 28, 50, 209 268,278 Berg,Alban, 28, 59,63,81,85,87,90, 10ó' CorveÌÌ,Henry, 62, 733,222 133, 158,209, 2r0, 222, 241, 268, 278 Creston,Paul, 81 Berger, Arthur, 27 Bergsma,William, 28, 225 Dahl, Ingolf, 22t,267 Berio, Luciano,235,278 DaÌlapiccola, Luigi, 118, 180, 209, 2?2, Bernstein,Leonard, 90, 106 268 BettineÌli, Brrno, 27, 6f , 245 Debussy,CÌaude, 41, 42, 59, 126 Blacher, Boris, 219, 237 Delius,Frederick,210 Blackwood, EasÌey,172 Dello Joio, Norman, 243 Bìitzstein.Marc. 28 Dianrond, Davìd, 28, 222 Bloch, Ernest,41, 131,222,241,267 Donatoni. Franco.227 Blomdahl, Karl-Birger, 90, 126, 180 281
282)
INDEX OF COMPOSERS
Egge, Klaus, 42, 81 Egk, Werner, 225,235 Einem, Gottfried vorq 63 Escobar,Luis, 42 de Falla,À{anuel,210,222,268 Fine, In'ing, 222,268 Finney, RossLee, 50 Fìoyd, Carlisle,243 Former. Wolfgang, 28, 243 Foss,Lukas, 81, 243 Françaix, Jeen,219 Fricker, Peter Racine, 150,268 Gershv'in, Gecrge, 42, 81,209 Giannini, Vittorio, 90 Gielen, À,Íichael,90 Ginastera,Alberto, 27, ll8,710 Griffes, CharÌes,50, 59,245 Guarnieri, Camargo, 118,245 Hàba, Alois, 278 Haieff, Alexei, 28 Halffter, Rodoìfo, 2ó8 Flanson, Hou.ard, ó3, 22Í Harris, Roy, 41,42, 62, 81, 150,210,237, 'r4!-
)41
Lees, Benjamin, 27 Liebermann, Rolf, 90 Maderna,Bruno, 211,222,228 Malipiero, Gian-Francesco,42, 59, 87, 118 Margola, Franco, 2ó8 Martin, Frank, 7,1,118 Martinet, Jean Louis, 28 À{artinu, Bohuslav, 27 McPhee, Colin, 225 Mennin, Peter, 27, 118,219, 220 Menord, Gian Carìo, 74, 118,210,267 Messiaen,Olivier, 28, +3, 50, 157,209 Mihalovici, Marcel, 158,245 Miìhaud, Darius,42, 43,85,90,118,126, 157,r58, 180,209,225,268 Moore, Douglas,74 Nilsson, 8o,278 Nono, Luigi, 209, 220, 278 Nordoff, Pari,243 Orf, Carl, 42, 43,225
)13,
F{arrison,Lou, 50 Flartmann, Karl Amadeus,28, 180,209, 220,277 Flauberstock-Ramati,Roman, 219 Heiden, Bernard, 210 Helm, Everett. 90 FIenze,Hans Yrrcrner, 27, 28, 268 Hinc'lemith,PauÌ, 27. 28, 42, 43. 59, 60, 1 0 2 ,1 0 ó ,1 1 8 .1 5 8 .2 0 9 . 2 1 0 , 2 1 9 , ? 2 0 , 2 3 5 ,2 3 7 ,2 + 3 ,2 ó 8 ,2 7 7 ,2 7 8 lJolmboe, Vagn, 27 HoÌst, Gustav, 28, 220 Honegger,Arthur, 27,28, 43, 50, 59,62, 7 4 , 8 5 ,s / , 1 0 6 1 1 8 ,1 5 0 ,1 5 7 ,2 2 0 , 2 2 2 , ))<
Kodály, Zokân, 42,243 Krenek, Ernst, 28, 219
)í,R )17
Hovhaness,Alan, 50, 74, 113,222
Paìmer, Robert, 28, 243 Persichetti, \/incent, 42, 90, 180, 235, 268, 277,278 81,210, Petrassi, Gofiredo, 2.8,41,42,50, Pizzetti, Ildebrando, 41 PhilÌips, BurrilÌ, 59, 220 Pilper, Willem, 74 Piston, WaÌter , 27, 85, 220,235 Ponce, llanuel, 50 Porter, Quincv, 219 PouÌenc, Francis, 27, 43, 126, 210,211, 268 Prokofiev,Serge,27 , 62,74,219,222,235, 245, 268
Ravel, ÀIaurice, 27, 28, 42,43, 50, 59, 60, 8 1 , 8 5 , 8 72, 1 0 , 2 1 9 , 2 2 5 Ives,Charlcs,ó0, ó2, 81, 87, 90, 118,133, Rarvsthorne,AÌan, 220 Respighi,Ottorino, 41, 42 150,157,t72, 210,219,268,277,778 RevueÌtas,Silvesue, 219, 220, 225 Riegger, Wallingford, 133,268. 278 Jolivet, Andró, 118,209,219 Rochberg,George, 180,220,2ó8 Kabalevsky,Dmitri, 28 Rogers, Bernard, 42, 90 Kirchner, Leon, 158 Rorem, Ned, 4J Kìebe, Giselher, 87 Rosenberg,HiÌding, 28 Knipper, Lev,220 RousseÌ,AÌbelt, 59, 150 Ibert, Jacques,ó0, 158,222,267 Inrhrie
Ânrìrprr'
?11
INDEX OF COÀ{POSERS Rudhyar, Dane, 210 Ruggìes,Carl, ó3, 126,222,268 Saeverud.Harald. 50 Santa Cruz, Domingo, 42 Satie,Erik, 41, 42,74, 81 Sauguet,Henri, 210 Schoenberg,Arnold, 28, 29, 63, 81, 106, 158, 172,211, 2t9, 235, 237,24t, 2+3, 245, 268 Schuller, Gunther, 211, 219, 220, 278 Schuman, lViÌliam, 27, 28, 29,74, 150, 172, 2r0, 228, 213, 278 Scriabine,Alexander, 63, 81, 85,219 Searle,Humphrey, 157 Sessions, Roger, 28, 29, 63, 106,209,210, 219.2+r.268 Shapero,Harold, 85, 268 Shoitakovich,Dmitri, 27,28, 41,62, 222, 241 Sibelius,Jean, 41, 42, t0,225 Skalkottas,Nikos, 172 Stevens,Halsey, 210 Stockhausen, Karlheinz, 172, 279, 278 Strang, Gerald, 180 Stravinsky, lgor, 27, 28, 29, 43, 50, 60, ó2, 81, 85, 10ó,118,1t0, 158,172,209, 210,219,220,225, 228,2+3,268,27I Szymanowski, Karol, 268
(283 Tansman, Alexander, 87, 180 Tcherepnine, Aiexandre, 28 Thompson,Randalì,28,42 Thomson, Yirgil, 42,74, 210 Tippett, Àlichael, 277 Toch, Ernst, 158 Togni, CamiÌlo,126,211,228 Turchi, Guido, 28,81,278 Usmanbas,Ilhan, 211 Valen, Fartein, 2ó8 Varèse,Edgard, 133,172.220,273 Vaughan Williams, Ralph, 59, 209,278 Vererti, Antonio, 1i8, 180 ViÌla-Lobos,Heitor, 27, 87, 1.26 V I a d , R o m a n ,2 1 1 , 2 2 2 , 2 7 72,7 8 'Walton,
lVilliam, 42, 106,243 Weber, Ben, 211 Webern, Anton, 10ó, 172,209, 222, 228, )77 )72
Weill, Kurt, 27 Weisgall, Hugo, 210,235 trViren, Dag,42 Woipe, Stefan, 210 Zimmermann, Bernd Alois, 29
Súject Index
Accents, 220,227, 231, 273 Added-note chords, 109-120,140 Aeoìian mode, 32 Alteration. chromatic. 237-24L Alterations, common, 239 Altered chords, 36-37,77, 239 Atonaliry, 251, 261-262,?75 Augmentation, 235 Augmented sixth chords, 109-111 Bar line, 21Í
Clusters, 126-133, 274 Compound harmony, 102, 163-172,250, 261 Counterchords, 14í CoupÌing, 113, 192, 202, 774 Cross relation, 240 Cycle of 5ths, 3rds, and 2nds, 185 Cyclic relationships, ó6-71, 252
Deceptive cadence.207 Density, 56, 112,139,lg2, 1E7 DeveÌopment, see Transformation 103,147, Diminished octave,79 Diminution, 235 Dismemberment.188.236 Dissonanttone. 12i. 196 Dodecuple scale.ó0 Dorian mode, 31,33,249 Double Harmonic scale,44, 47, 176,238, 249 Doubling, 21,78,96, 113, 123,752,197, 265,272 Dynamics, 26, 212, 22ç228,276
Cadential devices,99, 100,f01, 170,20Ç209,227,250,266 Chordal melodv. 198 Chords bv fouiths. 81-108 Four-nóte chords, 101-104 Multi-note chords, 10ç106 Three-note chords, 95-101 Chords bv rhirds. óó Chord connection, 189 Chords bv seconds. 121-134 Clusteró, t2ç133 Multi-note chords, 125-126 Three-note chords, l2l-124 Chromaticism,&43, 103,185,193,207, Eleventh chords, 82-8Í 251 Elision, 188,236,274 28t
286) Embellishment, 230-2ü Ornamental fi guration, 230-235 Enigmaticscale,4'1,45,2+9,255 Evaporatiorq 196,275 Extension, 235 Fifteenth and seventeenthchords, 8Í-87 Fifths, successive,201-205 Form ideas,275 Fused compound harmonY' 170 Harmonic direction, 745, 166, 182-2ll F{armonic rhythm, 169,212,221 Harmonic synthesis,8I, 234, 27I-279 Hexatonic scaÌes,53-ó0 Hiraloshi scaÌe,50, 53 flunqarian ÌVIa]orscale,44, 47,48,249 Hun[arian Minor scale,44, 47, 176,249, 255 Imitation, 235 Intervallic strands, 22 Intervals, 13-30 Construction, 13-I7 In chords, 19-23 Inversion and spacing,17-18 Medium, effect of,25-27 Overtone influence on, 2l-25 Inversion, 17,75, 79, 82, 95, 122,138' 173' )7) lnverüble scales, r/) Ionian mode, 31 Isomelos,217 Isorhythm, 217
Key centers,2+8-270 41 Key signarures, IluÍÍìor scale, )u Leading Whole-tone scale,44, 239,244 Locrian moóe, ]7,249 Lydian Minor scale,44, 176'249 Lyaian mode, J3, 249, 255 Maior Locrian scale,44, 176,249 Medium, cfiect of, 23,24,25,26 Melodic set, 263 Merer,2l3, 267 Mirror rvritin g, 46, 47, 772-180,26 MixoÌydian mode, 33, 249 ModaÌ intercl-range,40, 256 Modes, 3143, 69 Modulation, 251-255
suBJECr INDEX Neapolitan Major scale,44, 47, 239,240, 249 Neapolitan Minor scale, 44, 249 Ninih chords, 7+81,9 Oblique harmony, 201 Oriental scale,44, 47, 48, 176,238,249 Original scales,43, 46 Oríamental tones, 70, 83,132, 147, 177, 200,221,230,26ó Ostinato, 241-243 Overtones,14,23,25,137,150 Overtone scaÌe,44, 196,249 Overtone series,23,43, 173 Pandiatonicwriting, 223-22t Parallel fifths. 73. 201 Parallel harmony, 128, 198-201,251,265 Partials,23 Passive resolution, 196, 206 Pedaì point, 98, 135,2+l-243 Pelog icale, 50 Pentãtonicscales,50-53,94 Percussion,216,221 Percussive harmonv, 169, 220-222 Phrysian mode, 34, 249,zts Pivóichord. 251,266 Polychords, 84, 103, 135-162,234,25ó' Non-uiadic units, 153-158 Three or more triadic units, 15S-153 Two triadic units. 137-150 Polymeter,214 Polvmodaliw. 39 Polírhvthm, Zt+ Polytonaliry, 39, 233,2t 4, 2t t-261 35,67, 68,76' 115,147,169, Progression, r82,189 PrometheusNeapolitan scale,53, 54 Prometheusscale,53 Pyramidd chordg 165 Quartal harmony, 93-108 Reflective harmony, 172 Reflective keyboard writing, 179 Repetition, 220,223,235,254, 276 Reionance,25, llj, l4l, 1+7,2t8 Rests,i93, 22Ç228 Retrogression,187, 236 Rhvthm, 212-220 Rootless harmony, 9'1, 251 Scalematerials,31-ó5 Secundal harmony, 121-134
(2n
SUBJECTINDEX Sequences, 80, 196,202,235 Serial harmonv. 62. 262-268 Seventh chords. 7+-76. 100 Spacing,17, 22,26, 722,137, 139,752,197, 223. 2t7 Spanishscale,44,249 Static harmonv. 223 Super Locrian scale,,14,249,255 SymmetricaÌ scale, 44, 249 Syncopation, 215 Synthetic scales,43-50, 7O-7l, 239
Timbre, instrumental, 16, 26, 791, 200, 276 Time signarures, 214-216 Timing, 212-220 TonaÌity, 103,147,248-2tI Transformation, 23V217 Extension and imitation, 235-237 Transposition, 141, 18ó Triads, 6óJ4 Tritone, 15, 16, 18,21, 102,256,257 Twelve-note chords, 87-90,105,165 Twelve-tone technique, 2ó2 Two-ociave scales.48-49
Telescoping, 263 Tempo. 212 Tertian harmonv. 74-92 IJndertone series.173 Texture, 109,1lt, 155,197,203, 271-275 Unison, 148,213-2+5,273 Themes, 275-277 Thirteenth chords, 82-85, 100 Whole-tone scale,53-59
ff r ï:r;,:'
