Notation: Pitch
music notatio notation n is the art of
recording music in written form.
F#d# Dµ DµD Sµ #SµS#d #M f##M Sµ SµSµg F #F #¶ #g# #g# F#d# modern music not notation ation is a product of centuries of transformation... and it is neither efficient nor intuitive!
the system of musical not notation ation we use is essentially a stylized graph of pit pitch ch versus time.
pitch pit ch is the highness or
lowness of a sound. for example, a flute has a high pitch, pitch, while a tuba has a low pitch. pitch.
h c t i p
h c t i p time
the five lines on which notes on appear is called a st staff aff. .
a note is a written representation of a partic particular ular pit pitch. ch.
notation is based on the piano keyboard; keyboard; lines and sp spaces aces on the staff represent the white notes on on the keyboard.
to display notes outside the staff, we use shortened staff lines called
F g a b c d e F g a b c d e the white notes on on the keyboard are labeled with letters from A to G.
treble clef
ledger lines.
alt al to clef
tenor clef bass clef
the clef determines determines what notes each st staff aff line corresponds to. the four modern modern displayed yed clefs are shown here; the note displa on each staff corresponds to middle c.
To notate the black notes notes
The double sharp sharp raises the note by two half steps.
on the piano keyboard, we use accidentals, accident als,
which alter the note by one or two half steps. a half step is is the distance between two adjacent ad jacent keys
on the piano keyboard, regardless of what color the keys are.
is the c that is that is closest to middle c the middle of the piano keyboard.
The sharp raises the note by one half step.
these symbols are placed to the left of the note that they affect, and they apply to all the notes on that line or space for the rest of the measure.
. d e v r e s e r s t h
The na natural tural cancels out any previous accident accidental. al.
g i r l l a . h s u r . w y b o t
The fla flat t lowers the note by one half step.
9 0 0 2
F g a b c d e F g a b c d e The double flat flat lowers the note by two half steps.
two notes which have the same and and pitch pit ch (for example, f sharp ) are called enharmon g flat flat enharmonics. ics.
© t h g i r y p o c . m o c . t o p s g o l b . h s u r y b
Notation: Rhythm e t o n e l o h w e l b u o d
e t o n e l o h w
e t o n r e t r a u q
e t o n f l a h
while pit pitch ch is pretty clearly notated on a vertical axis, note length is indicated using a somewhat arcane system involving
noteheads, stems stems and flags. e t o n d n o c e s y t r i h t
e t o n h t n e e t x i s
e t o n h t h g i e
e t - o d n e h r t d h n g u i h e - y e t n n o e w t
e t o n h t r u o f y t x i s
in this chart, each successive type of note is half as long
note lengths in a piece
as the note to its left. left. none of these notes has a st standard andard
are indicated by the tempo
a half note in one piece may a may be the same length as length;
at the beginning at marking
an eighth note in a different piece.
t s e r e l o h w e l b u o d
t s e r e l o h w
t s e r r e t r a u q
t s e r f l a h
of a piece or section.
t s e r d n o c e s y t r i h t
t s e r h t n e e t x i s
t s e r h t h g i e
t s - e d r e h r t d h n g i u e h - y e t n n o e w t
t s e r h t r u o f y t x i s
a rest is a period of
usually rests are
silence that a length
placed on the staff at a
which corresponds to a
particular vertical
particular note.
position as shown here.
the augment is a dot placed to the augmentation ation dot is right of a notehead not ehead. . though small, sma ll, this dot
multiple dots can ca n also be added adde d,
wields some serious power: it changes the
each one adding half of the
length of the note by 150%. In other words,
previously added value.
it makes the note half again as long!
=
=
+
+
+
=
+
+
+
=
+
+
+
+
ties are curved marks which connect
to tie more than two notes together,
two notes together to create
draw ties between each note; do not do
a single, extended extended sound.
=
use a single, extended tie.
=
a tuplet is any non-standard division of a
most tuplets are simple divisions, like
note. these are usually written as a group
the triplets to the left. but anything is
of notes delinated with a bracket and
possible! chopin, for example, would
a number showing the division being made.
3
to town town with these things. often go to
for example, these aren’t exactly quarter notes;
wha... gah!
they are each a third as
chopin, no!
note. long as a half note.
down, boy!
. d e v r e s e r s t h g i r l l a
. h s u r . w y b o t 9 0 0 2 © t h g i r y p o c . m o c . t o p s g o l b . h s u r y
Notation: Rhythm e t o n e l o h w e l b u o d
e t o n e l o h w
e t o n r e t r a u q
e t o n f l a h
while pit pitch ch is pretty clearly notated on a vertical axis, note length is indicated using a somewhat arcane system involving
noteheads, stems stems and flags. e t o n d n o c e s y t r i h t
e t o n h t n e e t x i s
e t o n h t h g i e
e t - o d n e h r t d h n g u i h e - y e t n n o e w t
e t o n h t r u o f y t x i s
in this chart, each successive type of note is half as long
note lengths in a piece
as the note to its left. left. none of these notes has a st standard andard
are indicated by the tempo
a half note in one piece may a may be the same length as length;
at the beginning at marking
an eighth note in a different piece.
t s e r e l o h w e l b u o d
t s e r e l o h w
t s e r r e t r a u q
t s e r f l a h
of a piece or section.
t s e r d n o c e s y t r i h t
t s e r h t n e e t x i s
t s e r h t h g i e
t s - e d r e h r t d h n g i u e h - y e t n n o e w t
t s e r h t r u o f y t x i s
a rest is a period of
usually rests are
silence that a length
placed on the staff at a
which corresponds to a
particular vertical
particular note.
position as shown here.
the augment is a dot placed to the augmentation ation dot is right of a notehead not ehead. . though small, sma ll, this dot
multiple dots can ca n also be added adde d,
wields some serious power: it changes the
each one adding half of the
length of the note by 150%. In other words,
previously added value.
it makes the note half again as long!
=
=
+
+
+
=
+
+
+
=
+
+
+
+
ties are curved marks which connect
to tie more than two notes together,
two notes together to create
draw ties between each note; do not do
a single, extended extended sound.
=
use a single, extended tie.
=
a tuplet is any non-standard division of a
most tuplets are simple divisions, like
note. these are usually written as a group
the triplets to the left. but anything is
of notes delinated with a bracket and
possible! chopin, for example, would
a number showing the division being made.
3
to town town with these things. often go to
for example, these aren’t exactly quarter notes;
wha... gah!
they are each a third as
chopin, no!
note. long as a half note.
down, boy!
. d e v r e s e r s t h g i r l l a
. h s u r . w y b o t 9 0 0 2 © t h g i r y p o c . m o c . t o p s g o l b . h s u r y
Notation: Meter
a fundament fun damental al feat fe ature ure of most pieces of music is a
consistent rhythmic rhythmic pulse. beat t, this pulse is called the bea and a single pulse is called a bea beat t unit.
there are two types of beat units:
...and those cont containing aining
those containing two divisions,
three divisions, called compound beat units.
called simple beat units... beat
in music, beats are organized into patterns of accented and unaccented beat units. in fact, if you listen to a sequence of repeated notes, your brain will probably start to perceive the notes as groups of two, three, or four, even if no accents are present!
these groups are called measures,
measure
barline
and they are delineated with barlines. the organiza organization tion
simple meters meters are easy. are
of beat units and measures in
the top number
a piece is called
indicates the number
meter. Meter is
of beats in a measure. in
described by two the bottom number
numbers placed
indicates the type of
at the beginning
note which serves as which the beat unit.
of the piece: the time signature.
the code for the bottom note is pretty easy: a quarter note, note,
refers to to an eighth
to a sixteenth note, and so on.
compound compou nd meters meters are stupidl are stupidly y complica complicated ted. the top number indicates the number
of divisions in a measure. to get the number of beats, divide it by three. the bottom number indicates the type of
note which serves as the division. which unit, use the note that to get the beat unit, is equal to three of these notes.
in fact, wouldn’t this be an easier way to notate
compound meters?
in a compound meter, the beat unit is always a dotted note !
sorry... the man says you have to do it the other way.
by looking at the top
number of the time signature, of you can tell two things about the meter: whether it’s simple compound,, and how many or compound beats are in a measure. simple
e r u s 2 a e m r 3 e p s t a 4 e b
notes that have flags can be grouped together by using
beams in place of flags.
compound
however, beaming is only used to group notes within beats. for the most part, part, you shouldn’t beam notes between beats, nor should you tie notes within beats.
. d e v r e s e r s t h g i r l l a . h s u r . w y b o t 9 0 0 2
© t h g i r y p o c . m o c . t o p s g o l b . h s u r y
Hey, i t t ’ s ’s Hey, the the Sparky music kids!
theory dog!
Dear Sparky: I understand that we’re supposed to beam rhythms to show the organization of beats in the measure, but is there an easy way to beam complex complex rhythms? --A.Y., Owatonna, MN
Q:
A: WOOF!* *translation: notes should be beamed in groups that illustrate
the
meter. for simple rhythms, this is pretty easy to do; simply group any notes that can be beamed (eighth notes and smaller) simply sm aller) into groups that are equal to to the beat beat unit of the current meter. meter.
for complex rhythms, complicated ted... ... when a rhythm includes things rhythms, however, things can get complica like syncop syncopatio ations ns or other off-beat figures, illustrating the meter may involve dividing notes across beat units with ties. for across fortuna tunatel tely y, there the re is i s a step-by-step system for correctly beaming these complicated rhythms! for example, let’s take ta ke this rhythm, which is written without beaming. find the smallest note value used, used, and fill a complete measure with this type of
step 1: note, beamed in groups that are equal to a beat beat unit in the current meter.
add ties between individual notes to recreate the original rhythm. make sure that
step 2: each tied group corresponds to to a note in the rhythm you started started with! yes, i know it looks weird weird... ... but we’re not done yet! original rhythm:
find every group of two or more notes that are both tied together and and together, and replace them with a single note together, of equiv of equivalent alent value. value.
step 3: beamed if you have notes that are tied or beamed, but not both, then leave them alone!
= don’t touch!
hands off!
yes... simplify it!
a correctl correctly y beamed rhythm rhythm may include ties, but it will very clearl c learly y show the bea show beats ts in the measure... which, in in turn, makes it easier for the performer performer to to read!
DOING STUFF THE SPARKY SPARKY WAY IS ALWAYS FUN!
The Major Scale
one of the reasons that a particular piece of music sounds the way it does has to do with the the composer decided to use. group of notes
take this melody, for example... let’s first remove all the duplicate notes, regardless of which octave they’re in.
next, let’s put the notes in alphabetical order, starting on the note that the melody sounded like it was centering on. what we end up with is the “palette” for this particular piece...
there are actually many different types of scales, each with a different pattern of whole steps and half steps.
a half step is the distance between
like the board on which a painter holds the bits of paint being used in the painting being created.
two adjacent keys
on the piano keyboard, regardless of color.
in music, this “palette” is called a scale. though we usually write scales from low to high, the order is actually it’s the notes contained in the unimportant; scale that help make a piece sound the way it does. particular this arrangement, where half steps occur between steps three and four and between steps seven and eight (or between seven and one , since eight and one are the same note), is called the major scale.
whole step
whole step
half step
whole step
whole step
whole step
half step
a whole step is the equivalent of two half steps.
(this scale, by the way, is called the g major scale, because it starts on g.)
knowing this formula, you can create a major scale on any note! the f major scale
the d flat major scale
but remember... with the b major scale
the g flat major scale
great power comes great responsibility!
. d e v r e s e r s t h g i r l l a . h s u r . w y b o t 9 0 0 2 © t h g i r y p o c . m o c . t o p s g o l b . h s u r y
Key Signatures if you start writing major and pay attention to scales the accidentals that occur,
A
B E A D
A
f c g
b
B E
b
f c g d a
c
B E A D G C F
you are going to start noticing a pattern...
for example look at the flat keys, starting with the key that has one flat, all the way through the key with
seven flats: the flats accrue in a specific order. same with the sharp keys!
c so if you look for a key that has only a d flat, you won’t find it: if a key has a d flat,
c
f c g d a e b
d
B E A D G
d
f c
e
B E A
e
f c g d
f
B
f
f c g d a e
g
B E A D G C
g
f
it must also have a b flat, and an a flat! an e flat
since writing an entire piece in would have c sharp major been a sure-fire way to get with carpal tunnel syndrome all the sharps involved, composers pretty quickly came up with a way to simplify things:
key signatures. a key signature is a group of
accidentals placed at the beginning of every line of music, just to the right of the clef, that instructs the performer to apply those accidentals to in every corresponding note the piece unless specified otherwise. for example, this key signature indicates that every f, c, and g in the piece should be sharped, regardless of octave!
oh, and another thing: the accidentals have to be placed in the correct order, and they need to follow a
particular pattern of placement that varies slightly depending on the clef being used! if you deviate from this, you, as
© t h g i r y p
a composer, will be mocked! what’s tenor clef sharps! your problem? you need to conform!
. d e v r e s e r s t h g i r l l a . h s u r . w y b o t 0 1 0 2
ha ha... never!
o c . m o c . t o p s g o l b . h s u r y
The Circle of Fifths
theorists find it convenient to organize all the possible key signatures into a chart that shows their relationship to one another.
this chart, called the circle of fifths, displays each key as a spoke on the circle, beginning with c major at the top and adding accidentals, one at a time, to the we’ll return to this chart
key signatures around the perimeter.
as we continue learning about how composers use keys.
C 0
F
G 1
1
as you move clockwise around the
B
circle, you add sharps to the key signature. as you move counterclockwise around, you add flats to the key signature.
2
to determine the key for a key, look to signature see which “spoke” of the circle
when adding flats to in this order:
flats or sharps it has, and add accidentals to the key
3
D
a key signature, add them
it’s on to determine how many
E
2
signature appropriately.
3
beadgcf
for example,
A
when adding sharps,
e flat major has three flats,
use the reverse of the order above.
so it should look like this:
A
4
4
E
the keys down here line up
enharmonically... for example, the key of d flat major will sound just like the key of c sharp major.
7 5
notice how that
beadgcf pattern pops up all over the circle of fifths?
weird!
C D
so could you
5 6 6
F G
7
B C
continue the enharmonic deal and have the key of
f flat major? yes, if you want a double flat in your
key signature: nooooo!
. d e v r e s e r s t h g i r l l a . h s u r . w y b o t 0 1 0 2 © t h g i r y p o c . m o c . t o p s g o l b . h s u r y
Diatonic Intervals
an interval is the distance in pitch between two notes.
the most basic way which we identify different intervals is by counting the steps between the two notes.
smaller intervals
larger intervals
specifically, we count scale degrees, but the easiest way to do it is to count lines and spaces on the staff. 7
when counting the lines and spaces, we can safely ignore any
when counting, begin with the as bottom note one and count until you reach the top note.
6 5 4 3 2 1
accidentals.
this interval is also a seventh...
we’ll discuss how it’s
this interval is a seventh!
n o i s n u
two notes on the same line or space is called a unison.
d n o c e s
d i r t h
that’s latin for “one sound”!
when we are talking about intervals we sometimes discuss harmonic intervals and
different very soon!
t h r u o f
t h f i f
t h x i s
and that’s latin for “eight”!
t h n e v e s
v e a t c o
the distance from a note to the next closest note with the same letter name is called an octave.
and when you swap the two notes (move the lower note up by an octave so it becomes the higher note), that is called inverting the interval.
melodic intervals.
THE RULE
harmonic interval
melodic interval
a harmonic interval is simply two notes played simultaneously ; a melodic interval is one note played after the other.
it’s helpful to remember that seconds always invert to sevenths, thirds to sixths, and so forth... the fact that each of these pairs add up to nine is known to theorists as “the rule of nines.”
2nd
7th
3rd
6th
4th
5th
5th
4th
6th
3rd
7th
2nd
OF NINES
. d e v r e s e r s t h g i r l l a . h s u r . w y b o t 0 1 0 2
© t h g i r y p o c . m o c . t o p s g o l b . h s u r y
Hey, i t ’s the Sparky music kids! Q:
theory dog!
Dear Sparky: Since we are supposed to use different approaches for identifying perfect and imperfect intervals, can you summarize them all into one system? --I.M., Staten Island, NY
A: WOOF!* *translation:
the following chart shows an approach for identifying
any interval. a similar approach can be used when you
need to write a particular interval above or below a given note: first, add a note above or below the given note at the correct distance, then follow steps 2 through 4 of this chart to identify it. Then, if necessary, alter the note you added with an accidental to create the interval called for.
STEP 1: STEP 2: STEP 3:
determine the distance of the interval by counting lines and spaces.
continue until you reach the top note.
! f o o p
cover up all accidentals.
p o o f !
determine the inflection of the interval currently shown as follows: if it is a
if it is a
if it is a
unison or octave:
fourth or fifth:
second, third, sixth or seventh:
if the top note is
if the interval uses the interval shown
the notes f and b,
is a
it is either an
perfect unison
in the major key of the bottom note,
augmented fourth
or
perfect octave.
count the bottom , and note as one
or a
the interval is
major.
diminished fifth. if the bottom note is in the major key of
really.
otherwise, the
the top note,
it just is.
interval is
the interval is
perfect.
STEP 4:
minor.
add the original accidentals back,
one at a time, and track how the interval changes inflection.
remember: accidentals can never affect the distance of an interval... distance is determined solely by the number of lines and spaces between the two notes!
This method may seem complicated at first, but as you use it, you’ll internalize it and become faster... so get out there and
identify some intervals!
DOING STUFF THE SPARKY WAY IS ALWAYS FUN!
The Minor Scales
There are actually two things that define a key: the key signature is the most obvious one, but another important part of a key is the tonic... the note around which the key centers.
this key is defined by a key signature of no sharps and flats, but also by the fact that it centers around c. but what if we change the tonic? what if we use the same notes for the key signature, but change the note that the key is centered around? if we center the key around the sixth scale degree of the major scale, we get a new scale: the minor scale.
a l r t u o r a n i n e m a l e t h
s c
the thing is, common practice period composers
the whole step here didn’t have
weren’t all that crazy about this scale, because it lacks something the major scale has: a half-step from seven to one.
the tension they liked going into the tonic!
so here’s what they did: they raised the leading-tone by a half-step with an accidental. This gave them the tension they were looking for!
i c n m o r r h a m i n o e a l c s e t h
h a l f ! p e t s
this scale is great for building chords, so we refer to it as the harmonic minor scale. however, composers didn’t use it for writing melodies, because it had a problem: an augmented second between the sixth and seventh scale degrees. so, for melodies, they made another change:
now we only
they added another accidental to raise
have whole steps
the sixth scale degree by a half-step.
and half-steps!
i c d l o r e m i n o e m l e t h
a s c
now, remember... the reason we raised the leading tone in the first place was to create tension from the seventh scale degree to tonic. but in a melody, if the seventh scale degree is followed by the sixth scale degree, we don’t need that tension, so we don’t need to raise the leading-tone at all. the way we illustrate this is by differentiating between ascending melodic minor and for descending melodic minor, we don’t raise anything! descending melodic minor;
. d e v r e s e r s t h g i r l l a . h s u r . w y b o t 0 1 0 2 © t h g i r y p o c . m o c . t o p s g o l b . h s u r y
Triads
although a chord is technically any combination of notes played simultaneously, in music theory we usually define chords as the combination of three or more notes.
secundal harmony
tertial harmony
quartal harmony
quintal harmony
chords built from seconds form
chords built from (MORE thirds SPECifically, from major thirds and minor thirds ) form the basis of most harmony in the common
chords built from
chords built from
perfect fourths
perfect fifths
create a different sound, used in compositions from the early 1900 s and onward.
can be respelled as
tone clusters,
which are not harmonic so much as timbral.
quartal chords,
and as such they do not create a separate system of harmony.
e s
practice period.
is the chord still tertial if it is built from diminished thirds or augmented thirds?
well, diminished thirds sound just like major seconds, and augmented thirds sound just like perfect fourths, so...
let’s get started on tertial harmony with the smallest chord possible: the triad.
when we stack the chord in thirds within one octave, we get what is called the simple form of the chord. a triad is defined as a three-note chord, but in practice it is almost always used to refer to tertial three-note chords.
e d h n i s a d i i d i m t r e t h
c°
t
a major third on top a minor third on bottom
e e d t h n t e d m g r i a u a t
a minor third on top a major third on bottom
maj 3rd min 3rd
c
no.
the lowest note in the chord when the chord is in simple form is called the root. the fifth names of the third other notes are based on root their interval above the root.
e t h o r j d a m r i a t
r o n m i r i a d
min 3rd min 3rd
s
there are four ways to create a triad using major and minor thirds:
e t h
two minor thirds stacked together
? y . y n e l o e d s v n i m e a r h t a t l c e , a h p y i l n t s e a r t o r m e p , t y r e a s n s h a o ? l m y a e r t m n a n o i a h s u m l r q a a e h h d h t t i n l w e a r u t s a c x a e
two major thirds stacked together
min 3rd maj 3rd
C
maj 3rd maj 3rd
+
C
we label triads using their root (”a c minor triad ”). the abbreviations shown above, which use upper case, lower case, and symbols to show chord type, are called macro analysis.
. d e v r e s e r s t h g i r l l a . h s u r . w y b o t 0 1 0 2 © t h g i r y p o c . m o c . t o p s g o l b . h s u r y
