Music Theory for Musicians and Normal People · 2015. 9. 11. · music theory for musicians and...

MUSIC THEORYfor

MUSICIANSNORMALPEOPLE

and

by Toby W. Rush

this file is a collection of individual sheetscovering a bunch of lessons on music theory.

it’s not a book... yet. it might be someday!but as of right now, it’s incomplete.

The truth is, they weren’t intended tobe a single volume when I started making them...

they were just review sheets for my owntheory students.

but the more I made,the more I realized

they could be collectedinto a textbook of sorts...

eventually!

I still have a lot of work to do,but I’ve collected the ones I’ve madeso far into a single document to

make it easier for the folkswho wanted them all... but didn’t wantto download every file individually!

I still have a lot of work to do,but I’ve collected the ones I’ve madeso far into a single document to

make it easier for the folkswho wanted them all... but didn’t wantto download every file individually!

so if you’ve been sent this fileby someone, know that theremight be a newer version —

or more pages — at tobyrush.com.

now let’slearn some

music theory!

but if you like this,or find it useful,

great! feel free toshare it, copy it, and use it.

just don’t sell it, change it,or tell others you made it!*

*for more info, see http://creativecommons.org/licenses/by-nc-nd/4.0/

hello!

Rush

music notation is the art ofrecording music in written form.

modern music notation is a productof centuries of transformation...

and it is neither efficient nor intuitive!

b∫

n#‹

Notation: Pitch#¶#g#F#d#DµD#SµS#d#Mf#SµSµg#F œ œ œ œ œ œ œ œ œ œ œ œ œ œ Œ

pitch is the highness orlowness of a sound.

the system of musical notationwe use is essentially a stylizedgraph of pitch versus time.

the five lines on which notesappear is called a staff.

the white notes on the keyboardare labeled with letters from A to G.

notation is based on the piano keyboard;lines and spaces on the staff represent

the white notes on the keyboard.

the clef determines what notes each staffline corresponds to. the four modern

clefs are shown here; the note displayedon each staff corresponds to middle c.

To notate theblack noteson the piano

keyboard, we useaccidentals,which alter thenote by one or

two half steps.

a half step isthe distancebetween two

adjacent keyson the piano

keyboard,regardless

of what colorthe keys are.

these symbols are placed tothe left of the note that theyaffect, and they apply to all the

notes on that line or spacefor the rest of the measure.

two notes which have the samepitch (for example, f sharp and

g flat) are called enharmonics.

middle c is the c that is closest tothe middle of the piano keyboard.

The double sharp raises thenote by two half steps.

The double flat lowersthe note by two half steps.

The sharp raises thenote by one half step.

The natural cancels outany previous accidental.

The flat lowers thenote by one half step.

treble clefalto clef

tenor clefbass clef

for example, a flute hasa high pitch, while a tuba

has a low pitch.

a note is awritten representation

of a particular pitch.

pitch

pitch

F g a b c d e F g a b c d e

& œ œ œ œ œ œ œ œ

& B B ?

time

w wwwto display notes

outside thestaff, we useshortenedstaff lines

calledledger lines.

F g a b c d e F g a b c d e

& œœb œn œ# œœ∫ œn œ‹

liz phair“what makes you happy” [melody from chorus]whitechocolatespaceegg (1998)

music theory for musicians and normal people by toby w. rush

licensed under a creative commons BY-NC-ND license - visit tobyrush.com for more

whole n

ote

double w

hole n

ote

half n

ote

eig

hth n

ote

sixteenth n

ote

thir

ty-s

econd n

ote

sixty-f

ourth n

ote

one-h

undred-

twenty-e

ighth n

ote

quarter n

ote

whole r

est

double w

hole r

est

half r

est

eig

hth r

est

sixteenth r

est

thir

ty-s

econd r

est

sixty-f

ourth r

est

one-h

undred-

twenty-e

ighth r

est

quarter r

est

Notation: Rhythm

W w h

Œ

q

‰

e

≈

x

®

xK

Ù

xKK

Â

xKKK

∑ ∑„

while pitch is pretty clearly notated on avertical axis, note length is indicated using a

somewhat arcane system involvingnoteheads, stems and flags.

in this chart, each successive type of note is half as longas the note to its left. none of these notes has a standardlength; a half note in one piece may be the same length as

an eighth note in a different piece.

note lengths in a pieceare indicated by the tempomarking at the beginning

of a piece or section.

a rest is a period ofsilence that a length

which corresponds to aparticular note.

usually rests areplaced on the staff at a

particular verticalposition as shown here.

the augmentation dot is a dot placed to theright of a notehead. though small, this dot

wields some serious power: it changes thelength of the note by 150%. In other words,

it makes the note half again as long!

multiple dots can also be added,each one adding half of the

previously added value.

q e e= + q. e e e= + + q.. e e e= + + x+ q... e e e= + + x+ +xK

ties are curved marks which connecttwo notes together to createa single, extended sound.

to tie more than two notes together,draw ties between each note; do not

use a single, extended tie.

a tuplet is any non-standard division of anote. these are usually written as a group

of notes delinated with a bracket anda number showing the division being made.

most tuplets are simple divisions, likethe triplets to the left. but anything ispossible! chopin, for example, wouldoften go to town with these things.

œ .œjœ jœ jœ œ œ œ œ œ œ œ œ œ= =

œ œ œ3 for example, these aren’t

exactly quarter notes;they are each a third aslong as a half note.

wha... gah!chopin, no!down, boy!

frederic c

hopin

noctu

rne in b

major, op. 6

2, no. 1 (1846)



34

qE E

q.E E E

Notation: Meter

QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ >>> QQ Q QQ QQ QQ QQ

34 QQ Q Q QQ

a fundamental feature ofmost pieces of music is a

consistent rhythmic pulse. this pulse is called the beat,

and a single pulseis called a beat unit.

there are two types of beat units:those containing two divisions,

called simple beat units...

...and those containingthree divisions,

called compound beat units.

the c

oors

“heaven k

no

ws” [drum intro]

forgiven, not f

orgotten (1996)

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 toperceive the notes as groups of two, three, or four, even if no accents are present!

these groups are called measures,and they are delineated with barlines.

the organizationof beat units

and measures ina piece is calledmeter. Meter isdescribed by twonumbers placedat the beginningof the piece:

the time signature.

by looking at the topnumber of the time signature,you can tell two things aboutthe meter: whether it’s simpleor compound, and how many

beats are in a measure.

beats p

er m

easure

simple compound

2

3

4

the top numberindicates the numberof beats in a measure.

the bottom numberindicates the type ofnote which serves asthe beat unit.

simple TIME SIGNATURES are easy.

measurebarline

the code for the bottom noteis pretty easy: refers to

a quarter note, to an eighthnote, to a sixteenth note,

and so on.

48

16

68

2 63 94 12

2 68 Q. Q. Q. Q.the top number indicates the numberof divisions in a measure. to get thenumber of beats, divide it by three.

in fact, wouldn’t this bean easier way to notate

compound meters?

sorry... the man saysyou have to do itthe other way.

the bottom number indicates the type ofnote which serves as the division.to get the beat unit, use the note thatis equal to three of these notes.in a compound meter, the beat unit isalways a dotted note!

compound TIME SIGNATURES are stupidly complicated.

notes that have flags canbe grouped together by usingbeams in place of flags.

however, beaming is only used to group notes within beats.for the most part, you shouldn’t beam notes between beats,

nor should you tie notes within beats.




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) intogroups that are equal to the beat unit of the current meter.

for complex rhythms, however, things can get complicated... when a rhythm includes thingslike syncopations or other off-beat figures, illustrating the meter may involve dividingnotes across beat units with ties. fortunately, there is a step-by-step system for correctlybeaming these complicated rhythms!

*translation:

step 1:

Hey,

kids!it’s Sparkythe music theory dog!

DOING STUFF THE SPARKY WAY IS ALWAYS FUN!

Q:

A: WOOF!*

Dear Sparky:I understand that we’re supposed to beam rhythms to show the organization ofbeats in the measure, but is there an easy way to beam complex rhythms?

--A.Y., Owatonna, MN

& 43 Jœ Jœ Jœ Jœ Jœ Jœ & 43 œ œ œ œ œ œ

& 44 .Jœ Jœ œ Rœ Rœ Rœ Jœ Rœ Rœfor example, let’s

take this rhythm,which is written

without beaming.

find the smallest note value used, and fill a complete measure with this type ofnote, beamed in groups that are equal to a beat unit in the current meter.

step 2: add ties between individual notes to recreate the original rhythm. make sure thateach tied group corresponds to a note in the rhythm you started with!

step 3: find every group of two or more notes that are both tied together andbeamed together, and replace them with a single note of equivalent value.

a correctly beamed rhythm may include ties, but it willvery clearly show the beats in the measure... which, inturn, makes it easier for the performer to read!

yes, i know itlooks weird...but we’re not

done yet!

if you have notesthat are tied orbeamed, but not

both, then leavethem alone!

=

don’ttouch!

handsoff!

yes...simplify it!

original rhythm:

& 44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

& 44 œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

44 .Jœ Jœ œ Rœ Rœ Rœ Jœ Rœ Rœ

& 44 .œ œ œ .œ œ œ œ œ .œ œ

œ œ œJœ œJ œ œ


The Major Scale& 43 œ œ œ œ

œ œ# œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ .˙

& 43 œœ œ# œ œ œ œ

œ œ œ# œ œ œ œ œœœ#œœœ œ œ

johann s

ebastian b

ach

Min

uet

in G

major

note

book f

or a

nna m

agdale

na b

ach, 1722

one of the reasons that a particular piece ofmusic sounds the way it does has to do with thegroup of notes the composer decided to use.

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 notesin alphabetical order,starting on the notethat the melody soundedlike it was centering on.

what we end up withis the “palette” forthis particular piece...

there are actually manydifferent types of scales,

each with a different patternof whole steps and

half steps.

a half step is thedistance between

two adjacent keyson the piano keyboard,regardless of color.

like the board on which a painter holdsthe bits of paint being used in the painting being created.

in music, this “palette” is called a scale. though we usually write scales from low to high, the order is actually unimportant; it’s the notes contained in the scale that help make a piece sound the way it does.

œ œœ#œœœ œ œ

œ œœ#œœœ œ œ a whole step is theequivalent oftwo half steps.

this particulararrangement, wherehalf steps occur betweensteps 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.

knowing this formula, you can create a major scale on any note!

(this scale, by the way, is called theg major scale, because it starts on g.)

the f major scale

the b major scale

the d flat major scale

the g flat major scale

but remember...with

great powercomes great

responsibility!

wholestep

wholestep

halfstep

halfstep

wholestep

wholestep

wholestep

& œ œ œ œb œ œœ œ

& œ œ# œ# œ œ# œ#œ# œ & œb œb œb œb œb œb

œ œb& œb œb œ œb œb œb

œ œb



if you start writing majorscales and pay attention tothe accidentals that occur,

you are going to startnoticing a pattern...

for example look at the flatkeys, starting with the keythat has one flat, all theway through the key with

seven flats: the flats accruein a specific order.

same with the sharp keys!

so if you look for a key thathas only a d flat, you won’tfind it: if a key has a d flat,it must also have a b flat,an e flat and an a flat!

A

A

b

b

c

c

c

d

d

e

e

f

f

g

g

b

b

b

b

b

#

#

b

Key Signatures

B E A D G C F b

n

f c g #

f c g d a #

f c g d a e b #

f c #

f c g d #

f c g d a e #

f #

B E A D b

B E b

B E A D G b

B E A b

B b

B E A D G C b

since writing an entire piece inc sharp major would havebeen a sure-fire way to getcarpal tunnel syndrome withall the sharps involved,composers pretty quickly cameup with a way to simplify things:key signatures.

a key signature is a group ofaccidentals placed at thebeginning of every line of music,just to the right of the clef,that instructs the performerto apply those accidentals toevery corresponding note inthe piece unless specifiedotherwise.

oh, and another thing: theaccidentals have to be placedin the correct order, andthey need to follow aparticular pattern ofplacement that varies slightlydepending on the clef being used!if you deviate from this, you, asa composer, will be mocked!

for example, this keysignature indicates thatevery f, c, and g in thepiece should be sharped,regardless of octave!

tenor clef sharps! what’syour problem? you need to

conform! ha ha... never!



F

A

E

B

D

GC

theorists find it convenient toorganize all the possible key signaturesinto 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 thekey signatures around the perimeter. we’ll return to this chart

as we continue learning abouthow composers use keys.

as you move clockwise around thecircle, you add sharps to the key signature.

as you move counterclockwise around,you add flats to the key signature.

notice how thatbeadgcf patternpops up all over

the circle offifths?

weird!

so could youcontinue theenharmonicdeal and have

the key off flat major?yes, if you wanta double flat

in yourkey signature:

nooooo!

to determine the keysignature for a key, look to

see which “spoke” of the circleit’s on to determine how manyflats or sharps it has, andadd accidentals to the key

signature appropriately.

the keys down here line upenharmonically... for example,

the key of d flat major will soundjust like the key of c sharp major.

b #

Bb

E b

Ab

DbGb

C bC#

F#

The Circle of Fifths

for example,e flat major

has three flats,so it should

look like this:

0

1b

2b

3b

4b

5b

6b

7b

1#

2#

3#

4#

5#

6#7#

when adding flats toa key signature, add them

in this order:

when adding sharps,use the reverse

of the order above.

beadgcfb

#



b

an interval isthe distance in pitchbetween two notes.

the most basic way which weidentify different intervals is

by counting the steps betweenthe two notes.

specifically, wecount scale degrees,

but the easiest way to do it isto count lines and spaces

on the staff.

when counting,begin with the

bottom note asone and countuntil you reachthe top note.

this intervalis a seventh!

two notes onthe same line orspace is called

a unison.

when we are talking aboutintervals we sometimes discuss

harmonic intervals andmelodic intervals.

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.

it’s helpful to rememberthat seconds always invert

to sevenths, thirds tosixths, and so forth...

the fact that each ofthese pairs add up to nine

is known to theorists as“the rule of nines.”

a harmonic interval is simplytwo notes played simultaneously;

a melodic interval is one noteplayed after the other.

harmonicinterval

melodicinterval

that’s latin for“one sound”!

and that’s latinfor “eight”!

the distance froma note to the nextclosest note with

the same letter nameis called an octave.

second

unison

third

fourth

fifth

sixth

seve

nth

octa

ve

when countingthe lines andspaces, wecan safelyignore any

accidentals.

this intervalis also a

seventh...we’ll discuss

how it’sdifferentvery soon!

12

34

56

7

smallerintervals

Diatonic Intervals& œœ

œœ œœ œœ

largerintervals

& œœ œ œ& œœ

œœ2nd 7th

3rd 6th

4th 5th

5th 4th

6th 3rd

7th 2nd

THE RULE

OF NINES



the distance of an interval is the first part of itsname, but there’s more: every interval has anotherquality to it, which we’ll call its inflection.

are the easiest to label: if thetwo notes are the same (forexample, b flat and b flat),then the inflection is perfect:such an interval is called aperfect unison or aperfect octave.

require a little more explaining.

if you look at all the fourths and fifths youcan create using only the white notes on thepiano keyboard (in other words, using only noteswithout accidentals):

well, if you were to count the half-steps that make upeach interval, you’d notice that all the other ones areequal in size, but the b to f intervals are not: f to b isa half-step larger than a perfect fourth, and b to fis a half-step smaller than a perfect fifth.

an interval that is a half-steplarger than perfect is called

an augmented interval.

you can go further,to doubly augmented and

doubly diminished intervals,but... do you really want to?

and there’sno such thing as adiminished unison...

just like two thingscan’t be negative two feet

away from each other!

A5 A4

d5 d4 d8

A1A8

wait...why are the

b to f intervalsdifferent?

each one isperfect exceptfor those which use f and b!

unisons and octavesfourths and fifths

inflection is a bit harder to understand, partly because it depends on the type of interval.so let’s start by looking at unisons, fourths, fifths and octaves.

which raises the question: if the interval is not perfect, than what is it?

Perfect Intervals

& œ œ œ œ œ œœ œ

œ œ œ œ œ œ œ œ

& œ œ œ œ œ œœ

œ œ œ œ œ œœ

& œ œ œ œ œ œœ

œ œ œ œ œ œœ

Pd

A

an interval that is a half-stepsmaller than perfect is called

a diminished interval.

p e r f e c t

a u g m e n t e d

d i m i n i s h e d

& œœb &œ#œ

& œ#œ & œ œb

& œœ# & œ∫œ &œbœ



d6m6M6

We’ve talked about unisons, fourths, fifthsand octaves, but what about the rest? arethese other intervals somehow imperfect?

well, yes, but not because they are somehow inferior to perfect intervals...seconds, thirds, sixths and sevenths just work a little differently!

for one thing, the inflection for these intervals is never perfect;it will be either major or minor. minor intervals are a half-step smallerthan major intervals. like perfect intervals, though, they can also beaugmented or diminished; augmented intervals are a half-step largerthan major, and diminished intervals are a half-step smaller than minor.

Imperfect Intervals& œ œ œ œ œ œ

œ œœ œ œ œ œ œ œ œ

Mm

Am a j o r

a u g m e n t e d

m i n o r

dd i m i n i s h e d


œ œ œ œ œ œ œ œ

& œ œ œ œ œ œ œ œœ œ œ œ œ œ œ œ

how do we know if an interval is major or minor? we can actuallyuse the major scale to find out. notice that, in the major scale,intervals from the tonic up to another scale degree are major.

likewise, intervals from the tonic down to another scale degreeare minor.

knowing this, when you are confronted with a second, third, sixth or seventh, you canfind its inflection by thinking about the key signature of the top and/or bottom note.

when the notes of the interval have accidentals, the associated key signatures canbe more complicated... so it’s easiest to temporarily ignore the accidentals,determine the interval, and then add the accidentals back one at a time and

track how the interval changes!

ack! what isthat? let’s

first hide theaccidentals...

if the top note is in the major key of the bottom note, the interval is major.if the bottom note is in the major key of the top note, the interval is minor.

we know this is a major sixthbecause d, the top note, is in

the key of f major(the bottom note).

and this is a minor seventhbecause b, bottom note, is inthe key of a major(the top note).

majorsecond

majorthird

majorsixth

majorseventh

minorsecond

minorthird

minorsixth

minorseventh

& œœ &œœ

& œbœ#adding backthe sharp

makes it evensmaller...

a diminishedsixth!

& œbœ#adding back

the flat makesthe intervalsmaller, so

it’s now aminor sixth...

& œbœe is in the

key of g, sowe knowthis is a

major sixth.

& œœpoof!

poof!




the following chart shows an approach for identifying any interval. a similar approach can be used when youneed to write a particular interval above or below a given note: first, adda note above or below the given note at the correct distance, then followsteps 2 through 4 of this chart to identify it. Then, if necessary, alter thenote you added with an accidental to create the interval called for.

determine the distance of the intervalby counting lines and spaces.

count the bottomnote as one, andcontinue until you

reach the top note.

*translation:

STEP 1:cover up all accidentals.STEP 2:determine the inflection of the intervalcurrently shown as follows:

if it is aunison or octave:

the interval shownis a

perfect unisonor

perfect octave.

if the interval usesthe notes f and b,

it is either an

augmented fourthor a

diminished fifth.

if the top note isin the major key ofthe bottom note,

the interval is

major.

if the bottom note isin the major key of

the top note,the interval is

minor.

otherwise, theinterval is

perfect.

really.it just is.

if it is afourth or fifth:

if it is asecond, third,

sixth or seventh:

STEP 3:

add the original accidentals back,one at a time, and track how theinterval changes inflection.

remember: accidentals can never affectthe distance of an interval... distance is

determined solely by the number oflines and spaces between the two notes!

This method may seem complicated at first,but as you use it, you’ll internalize it andbecome faster... so get out there and

identify some intervals!

STEP 4:

Hey,



Q:

A: WOOF!*

Dear Sparky:Since we are supposed to use different approaches for identifying perfect andimperfect intervals, can you summarize them all into one system?

--I.M., Staten Island, NY

& œbœ# & œœpoof!

poof!

& œbœ#& œœ


There are actually two things that define a key:the key signature is the most obvious one, butanother important part of a key is the tonic...the note around which the key centers.

The Minor Scales

& œ œ œ œ œœ œ# œ

& œ œ œ œ œœ# œ# œ

&œ œN œN œ œ œ œ œ

this key is definedby a key signatureof no sharps andflats, but also bythe fact that itcenters around c.

the

natu

ral

minor

scal

e

the

harm

onic

minor

scal

e

the

melo

dic

minor

scal

e

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?

the thing is, common practice period composersweren’t all that crazy about this scale, because

it lacks something the major scale has:a half-step from seven to one.

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:they added another accidental to raisethe sixth scale degree by a half-step.

now, remember... the reason we raised the leading tone in the first place was to createtension from the seventh scale degree to tonic. but in a melody, if the seventh scaledegree is followed by the sixth scale degree, we don’t need that tension, so we don’tneed to raise the leading-tone at all.

the way we illustrate this is by differentiating between ascending melodic minor anddescending melodic minor; for descending melodic minor, we don’t raise anything!

now we onlyhave whole stepsand half-steps!

the whole stephere didn’t have

the tensionthey liked goinginto the tonic!

& œ œ œ œ œœ œ œ


if we center the key around the sixth scale degree of the major scale, we get a new scale: the minor scale.

so here’s what they did: they raised the leading-tone by a half-step withan accidental. This gave them the tension they were looking for!

half-

step!



C+Cc° c

although a chord is technically any combination of notesplayed simultaneously, in music theory we usually definechords as the combination of three or more notes.

Triadssecundalharmonyœœœœœœœ

chords built fromseconds formtone clusters,which are not

harmonic so muchas timbral.

tertialharmony

œœœ

quartalharmonyœœœ

chords built fromperfect fourthscreate a different

sound, used incompositions fromthe early 1900s

and onward.

quintalharmonyœœœ

chords built fromperfect fifths

can be respelled asquartal chords,and as such theydo not create a

separate system ofharmony.

sexta

l h

armony? s

epta

l h

armony?

as w

ith q

uin

tal h

armony, t

hese

are t

he s

ame a

s t

ertia

l a

nd

secundal h

armony, r

espectively.

chords built fromthirds (MORE

SPECifically, frommajor thirds and

minor thirds)form the basis ofmost harmony in

the commonpractice period.

is the chord still tertialif it is built from diminished

thirds or augmented thirds?

well, diminished thirds soundjust like major seconds, andaugmented thirds sound justlike perfect fourths, so...

the lowest note in the chordwhen the chord is in simpleform is calledthe root. thenames of theother notesare based ontheir intervalabove the root.

when we stackthe chord in

thirds within one octave,we get what is called the

simple form of the chord.

no.

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œœœœ& œœœ œœœ rootthirdfifth

let’s get startedon tertial harmonywith the smallestchord possible:

the triad.

there are four ways to create a triadusing major and minor thirds:

& œœœbb & œœœb & œœœ & œœœ#

the

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the

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the

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r

triad

the

augm

ente

d

triad

a triad is defined as a three-note chord,but in practice it is almost always used

to refer to tertial three-note chords.

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.

two minor thirdsstacked together

a major third on topa minor third on bottom

a minor third on topa major third on bottom

two major thirdsstacked together

min 3rd

min 3rd

maj 3rd

min 3rd

min 3rd

maj 3rd

maj 3rd

maj 3rd



Triads in Inversion

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ladies and gentlemen, it’sfranz joseph haydn!

thank you for having me.in this piece I use quite a

few triads.

here’s one: it has the notesc, e and g. it’s a c major

triad! very nice.

thank you. see how the notesare spread out, and not juststacked in thirds? it’s still

a triad, though.

that’s because the third of thechord is in the bass... when that happens,we say the chord is in first inversion.

ooh! let’ssee ‘em!

and he’s brought amovement from his 1767sonata in g major.

this one is g, b, and d...a g major triad! but it sounds

different, somehow.

so the thing that makes atriad root position, first inversion

or second inversion is simplywhich note is in the bass?

it’s hard to believe that thesound of the chord can change so

much just because of thebass note.

so this one with d, f, and ais a d minor triad... insecond inversion!

first inversion? what is it called when the root is in the

bass, like the first chordwe looked at?

haydn

that’s calledroot position.

exactly! because thefifth is in the bass.

that’s right!and each onehas its owncharacter.

I know, right?it’s awesome.



6

(5)(3)

6 6 6# 6# 6# ##

Figure 1. �e Basso Continuo

musical works written in the baroque era would ofteninclude a part called the basso continuo which wouldconsist of a single bass clef melodic line with variousnumbers and accidentals printed beneath the notes.

the numbers and symbolsprinted below the bassocontinuo part are calledthe figured bass. So howdo you turn figured bassinto chords?

first of all, it’s important to know that the note given on the bass clef part is alwaysthe bass note of the chord. and remember: the bass is not necessarily the root!

second, the numbersrepresent intervalsabove the bass, eventhough some numbersare usually left out.

lastly, accidentals areapplied to the interval

they appear with. if youhave an accidental by

itself, it applies to thethird above the bass.

by the time the classical period gotgoing, composers stopped including abasso continuo part, and so figured

bass fell out of use... with only oneexception: music theory classes!

wooo!

realizing figured bass (writing chordsgiven a figured bass line) makes for anexcellent exercise for students to learnhow to write in the common practiceperiod style!

don’t overthink these:if the composer wants

a note raised by a half-step and it’s flatted in

the key signature, thefigured bass will have

a natural, not a sharp.

note that the intervalsare always diatonic.don’t worry aboutinflection... just usethe notes from thekey signature!

if there areno numbers,

add a third anda fifth above thebass... you get a

root position triad!

here, the sharpapplies to the

sixth above thebass, so we add asharp to the g.

here, there is nonumber next to thesharp, so we apply

it to the third abovethe bass note.

note that there isa natural, not a flat,

next to the six...if it were a flat, we

would write a c flat.

a six by itselfindicates a sixth

and a third abovethe bass, whichcreates a first

inversion triad!

a six and a fourindicate a sixthand a fourthabove the bass,

giving you a secondinversion triad!

in performances, the bass clef instrument would simply playthe given notes, but the keyboard player would improvise apart based on the notes and the symbols below the part!

no, no, no... there wasn’t an actual instrument calleda basso continuo! the part was played by two

instruments: a bass clef instrument like cello orbassoon, and a keyboard instrument like a harpsichord.

Figured Bass

&

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##

##

jœœœ œœ œœ œœ#œ œ œ# œœ œ œ

œ œ# œ œ œ œ œ œ

œœ œœ œ œ œ œ œœ œ œ# œ œ

œ# œ œ œ œ œ œœ#

œ œœ

Jœ œ Jœ#œ œ œ œ

? ## œ œ# œ œ œ œ œ œ œ# œ œ œ œ œ œœ# œ œ œ œj.S. Bach: brandenberg concerto no. 5, bwv 1050

6 6 9 55

65

65

so this...

could be played as this!

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wwwn



now that we’re familiar with howtriads work, it’s time to put them

into the context of a key.

since writing music in a particular key means using the notes in that key signature,it stands to reason that most of the chords will be built from those same notes!

chords which use notes from a particular key signature are said to be diatonicto that key. diatonic means “from the key.” that means no accidentals!

we can quickly show all the diatonic triads in a particular key by writing a scalein that key and building triads on each note, using only the notes in that key.

Triads Within Tonality

& œœœ œœœœœœ œœœ

œœœ œœœœœœ

I ii iii IV V vi vii°

tonic

Superto

nic

media

nt

subdo

min

ant

do

min

ant

subm

edia

nt

leadin

g-t

one

we refer tothese chords

with romannumerals asshown here.

notice howchord typeis shown by

capitals orlower case?

these chords are alsosometimes referred to by

their official names!

same namesand romannumerals...differentcapitalization!

this pattern ofmajor, minor and diminished

triads is the same in every major key!the subdominant triad is always major,

and the leading-tone triad is alwaysdiminished, whether you’re inc major or f sharp major!

why is the sixth chord called the submediant?well, just as the mediant chord is halfway

between the tonic and dominant chords,the submediant chord is halfway between thetonic... and the subdominant a fifth below!

the diatonic triads in minor work the same way... since we’re dealing with chords, weuse the harmonic minor scale. however, it’s important to note that common practiceperiod composers raised the leading tone only over dominant function harmony:the dominant and leading-tone triads!

because the dominant and leading-tone triads bothhave a strong tendency to resolve to tonic, we say they

have a “dominant function.” the subdominant and supertonic chords both tend toresolve to the dominant, so we say they both have a “subdominant function.”

& œœœ œœœœœœ œœœ

œœœ# œœœœœœ#

i ii° III iv V VI vii°



Introduction to Part-Writingas we look ahead, we’re

confronted with an ugly truth:

there is a lot of musicin the history of the world

that is worth studying...

much more than we canhope to cover in the span

of a few semesters.

since we can’t cover it all, we have to choose a specific musical language to study in depth.

let’s start by narrowing things down to the common practice period.

2000

1900

1800

1700

1600

1500

romantic early 20thcentury

contemporaryclassicalbaroquerenaissance

the common practice period is the music of the baroque,classical and romantic eras in europe and america.the name comes from the fact that most composers used

a common musical language during this time.

it’s especially worthstudying because

most of the piecescommonly performed

in concert arefrom this period...

...and the languageforms the basis forthe most popular

musical styles today.

by analyzing bach’s cantatas, we can construct a set of “rules” for writing infour-voice common practice period musical style, allowing us to study it in depth.

luther j.s. bach

but there is a ton ofcommon practice period music...

more than we can hope to cover. is there arepresentative style we can sink our

academic teeth into?

four-voice chorale writing is a good style to study for several reasons:

chorales have a fastharmonic rhythm, allowing

for a larger number ofchords per exercise.

a large percentage ofcommon practice period music

can be easily reduced tofour-voice counterpoint.

the cantatas of j.s. bachprovide us with a tremendous

amount of consistently-writtenfour-voice chorales.

one of the changes to the catholic churchproposed by martin luther

was to allow members ofthe congregation to

participate in the singingof the liturgy.

more than two hundred years later, j.s. bachwas appointed musicaldirector at the st. thomaschurch in leipzig, germanyand, in the spirit of luther,wrote five years’ worthof liturgical music.

of course, luther wasbranded a heretic for

his proposals, and beganhis own church in whichto implement his ideas.

each of these works,called cantatas, were built

around a hymn melodyharmonized in four partsfor congregational singing.

st. t

ho

mas c

hurch

leip

zig

, germ

any



Part-Writing: The Vertical Rules

&

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to best understand howcommon practice period composers

wrote music, we are going tolearn how to write music using

their musical style.

so the patterns we see in their music,the things they consistently did

or didn’t do, are going to become“rules” for us in our writing.

it’s wrong to think these were“rules” for the composers...they were just writing whatsounded good to them.

nor should we treat these as rulesfor writing music in general...each style of writing has it’s

own set of patterns, and thusit’s own “rulebook.” as a composer,

you get to write your ownrules for your own style!

we’re going to start with thevertical rules... that is, the rulesthat pertain to building a singlechord in four-voice harmony.soprano

soprano

alto

alto

tenor

tenor

bass

bass

first, the distance betweensoprano and alto and betweenalto and tenor must be anoctave or less.

the tenor and bass can be asfar apart as you want!

second, the voices must be kept intheir proper order; for example,the tenor shouldn’t be higherthan the alto. (Bach did this nowand then, but it was only when hewanted to incorporate some specialmelodic shapes.)

third, since we have four voicesand only three notes in a triad,one of the notes should bedoubled. for triads in rootposition, we typically double theroot of the chord unless forced(by other rules) to do otherwise.

lastly, each voice shouldstay in its range. these

are conservative rangesfor modern singers, but

remember that bach’schorales were really

written for amateurs:the common people who

attended church in leipzig!

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Part-Writing: The Horizontal Rules

**

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ta b

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5

“ich a

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ensch, ic

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undenknecht”

..

the supreme goal of part-writing is good voice leading...making each individual voice part easy to sing by avoiding

awkward intervals or large leaps!

before we get to the specific dos and don’ts, let’s take a lookat some important characteristics of four-voice part-writing:

note how each voice movesas little as possible, goingto the nearest chord tonein each subsequent chord!

the bass line, since it providesthe foundation of the harmony

in each chord, tends to includelarger leaps than the otherthree voices, but that’s okay.

there are also a few otherrules that apply to this style:

when you have the leading tonein an outer voice (soprano or

bass) it must resolve to thetonic in the next chord.

you may not move any voiceby an interval of an

augmented secondor an augmented fourth.

it’s common for the bass tomove in the opposite direction

of the upper three voices.this is called contrary motion

and it helps maintainvoice independence.

four-voice harmony is a form of counterpoint,which is the combination of more than onemelody played simultaneously. in counterpoint,each voice is equally important; no voice isgiven a role of accompaniment to another voice.

the good news:you can avoid all three of

these by doing the followingwhenever possible:

1. keep the common tone!2. move to the nearest chord tone!3. use contrary motion!

in counterpoint, it is important for each voice tobe independent; that is, no two voices should be

doing the exact same thing. if two (or more)voices were moving in parallel, the richness

of the texture would be reduced.

as a result, common practice composers werevery consistent in avoiding two or more voicesthat moved in parallel perfect octaves, parallelperfect fifths, or parallel perfect unisons!

paralleloctaves!

parallelfifths!

parallelunisons!

in some cases, the voicecan simply stay on the same

note. This is calledkeeping the common tone,

and it’s always cool!

voice independence?



Part-Writing: Using Inversionswhen common practice composers used inverted chords infour-voice writing, they followed some general patternsregarding which note of the chord should be doubled.

root position

bass

first inversion second inversion

in rootposition triads,

composers usuallydoubled the root,

which is in the

of the chord.

bass

in secondinversion triads,composers usuallydoubled the fifth,

which is in the

of the chord.

soprano

soprano

in major firstinversion triads,

composersdoubled the

of the chord.

bass

in minor firstinversion triads,

composersdoubled the

the doubling of first inversion triads dependson the type of the chord being written.

here’s another way to think of it: the only time you can’t double the bass isin first inversion major triads, where you should double the soprano instead.

vii°6ii°6

the only “rule” regardingroot position triads

and first inversion triadsis that diminished triads are

always placed in first inversion.

other than that, you can useroot position and first inversionessentially whenever you want!

if you write asecond inversion triad and

it’s not one of these three situations,then you are not writing in the common

practice period style! the composers ofthe style just didn’t use these chords

willy-nilly.

it’s second inversion triads thathave the big restrictions.

of the chord.

or

bass

in diminishedfirst inversion

triads, theydoubled the

of the chord.

the cadential chordis a tonic triad insecond inversionfollowed by aroot-positiondominant chordat a cadence.

64

the pedal chordis a second inversionchord where thebass is treated likea pedal tone.

64

the passing chordis a chord placed in

second inversionwhere the bass is

treated like apassing tone.

64

4I6 V IF: 4V6I6 IF:

4IV6I IF:

okay, we know how to use inversions in four-part writing... but when can we use them?



B

BB

X

X what seems to bethe problem, sir? well, I thought I’d transpose tominor, you know, to surprise thefamily... so I did, and then I raisedall my leading tones, becauseI’m a common practice period

progression, right?

okay, sure. so what’s wrong?

attention! attention!we need assistancewith a new patient

in emergency treatmentroom 3b... stat!

BX

i’ve gotaugmentedseconds!

*gasp*

X myaugmentedseconds...

they’recured!

all in a day’s work,my good man.

now let’s turn tothe unpleasant matter

of the bill.

in the commonpractice period,composers usedharmonic minor

by default. butwhen augmented

seconds occurred,they turned to ahero for help:melodic minor!

cure your augmented seconds with melodic minor today!

BX and for thesedescendingaugmented seconds,we’re going to use

an unraised seventh!

v

and thatmakes aminor vchord!

B

BX

paging... dr. melodic minor!

doctor, whatcan we do? for this case of ascending augmented seconds,

I prescribe a raised sixth scale degree!

ooh... a major iv chord! IV6


Part-Writing: Melodic Minormusic theory for musicians and normal people by toby w. rush

so anyway,after we got

him transposedback to tonic, he

began to modulateagain, and...

The Harmonic CadencesA cadence is generally considered to be thelast two chords of a phrase, section or piece.there are four types of cadences, each withtheir own specific requirements and variations.

an authentic cadence consists of a dominant function chord (v or vii) moving to tonic.

perf

ect

auth

entic

impe

rfec

t

auth

entic

impe

rfec

t

auth

entic

perf

ect

plag

al

half

phry

gian

dece

ptive

phry

gian

impe

rfec

t

plag

al

impe

rfec

t

plag

al

to be considered a perfect authentic cadence,a cadence must meet all of the following criteria:

to be considered a perfect plagal cadence,a cadence must meet all of the following criteria:

if the cadencedoesn’t meetall of thosecriteria, it’sconsidered tobe animperfectauthenticcadence!*

***it must use a v chord(not a vii)

both chords must bein root position

the soprano mustend on the tonic

the soprano mustmove by step

a plagal cadence consists of a subdominant function chord (iv or ii) moving to tonic.

a half cadence is any cadence that ends on the dominant chord (v).

a deceptive cadence is a cadence where the dominant chord (V) resolves to somethingother than tonic... almost always the submediant chord (vi).

a specific type of half cadenceis the phrygian cadence, whichmust meet the following criteria:

if the cadencedoesn’t meetall of thosecriteria, it’sconsidered tobe animperfectauthenticcadence!*

***it must use a iv chord(not a ii)

both chords must bein root position

the soprano mustend on the tonic

the soprano mustkeep the common tone

****it occurs only in minor

it uses a iv chord moving to v

the soprano and bass moveby step in contrary motion

the soprano and bass bothend on the fifth scale degree

V I vii°6 I V64 I

IV I IV6 I ii I6

I V

VG:

G:

G:

G: G: G:

G: G:

e: e:

vi

iv6 V iv V

really, it’s the psych-out cadence, in thatyou expect it to resolve to tonic, but it doesn’t.

and, in fact, it’s more common to see this inthe middle of the phrase rather than the end...

where you might call it a “cadence-like structure”!



ii iii vii°6 V IC:

how did composers of the commonpractice period decide which orderto put chords in? did they just throwthem down on paper haphazardly?

as a matter of fact, there are certain chord progressions that appear morefrequently, and there are others that are avoided pretty consistently. whilethe choices were always based on what sounded good to the composer, astheorists there is a pattern in their choices that we can use to easily rememberwhich chord progressions work and which ones don’t.

to understand this pattern, we need to think in terms of root movements. a root movementis the basic interval between the root of one chord and the root of the next chord. youdon’t have to worry about the interval’s inflection, just its distance and direction.

for example, to determine the root movementhere, we look at the root (not bass) of eachchord and figure the interval between them.

so here’s the pattern: common practiceperiod composers generally used root

movements of up a second, down athird, and down a fifth!

remember... sinceinflection doesn’t

matter, we canignore accidentalswhen we figure the

root movements.

so, for example, a g chord to ane chord is down a third, but so is

g to e flat, and g sharp to e flat!

that’s not say that theynever used other rootmovements, but it didn’thappen very often.

sequences of chords thatdon’t follow this patternare called retrogressions,and they are consideredunstylistic.

there are also four simple exceptions to this pattern:

any chord canmove to tonic,

tonic can moveto any chord,

any chord canmove to dominant,

and the leading-tonetriad must move to tonic.

it’s down a seventh, butsince octaves don’t matter,we invert it to up a second.

Harmonic Progression

2

35

&˙̇̇ ˙̇̇

˙

I I V vii° I

&

?

œ œ œ œ œœ œ œ œ œ

œ œ œ œ œœ œ œ œ œ

let’s try it...say you havea supertonicchord and

you are tryingto decide whatchord to useto follow it.

you c

an m

ove

up a

seco

nd to

a m

edia

nt c

hord...

you c

an m

ove

do

wn a

fif

th to

a d

om

inant c

hord...

or y

ou c

an u

se t

he

fir

st e

xceptio

n a

nd

go to a

to

nic

chord!

you c

an m

ove

do

wn a

thir

d to

a l

eadin

g-t

one

chord...



Diatonic Common Chord Modulationmodulation is the process of changing to a different key within a piece of music.

there are several differentways to modulate; perhaps the

simplest is the unpreparedmodulation, where the musicpauses and suddenly changes

key, often up a half-step.

common practice period composers,however, preferred a particular typeof modulation that required a littlemore planning: the diatonic commonchord modulation. as the namesuggests, this uses a chord whichis diatonic in both the outgoing keyand the new key.

let’s say we’re starting off in c major... here is a list of all the keys whichhave chords in common with c major (the specific chords are highlighted):

keys which havechords in commonlike this arecalled related keys.

notice how these keysare all close to one

another on thecircle of fifths.

hey... what is thisportrait doing here?

manilow

i ii° III iv V VI vii°a:

b I ii iii IV V vi vii°B :i ii° III iv V VI vii°b:

I ii iii IV V vi vii°D:i ii° III iv V VI vii°d:

i ii° III iv V VI vii°e:I ii iii IV V vi vii°F:

I ii iii IV V vi vii°G:

I ii V I viC:e: iv V VI iv V i

to use this type ofmodulation, a composer

would pivot the harmonyaround the chord that

fit into both keys.As theorists, we show

this pivot chord byanalyzing the chord in

both keys.

note that the pivotchord is always thelast chord that canbe analyzed in theold key... the firstaccidentals will alwaysoccur in the chordimmediately followingthe pivot chord!



suspensions are typically further identifiedby number. The first number represents theinterval between the note of suspension andthe bass. The second number represents theinterval between the note of resolution andthe bass.

the exception to this rule is the 2-3 orbass suspension, where the numbersrepresent the intervals between the bass(where the suspension occurs) andwhichever voice has the note which is asecond (not counting octaves) abovethe bass.

a non-harmonic tone is a note thatdoesn’t fit into a chord. we classifynon-harmonic tones by how they are

approached and resolved!

Non-Harmonic Tones

passingtone

name

abbr

eviat

ion

appr

oach

reso

lutio

n

note

s

exam

ple

step stepptresolves by continuing inthe same direction as the

approach.

appoggiatura leap stepapp resolves in oppositedirection from approach.

changingtones

any stepcttwo non-harmonic toneson either side of thenote of resolution.

suspensioncommon

tonestepsus

a note held over froma previous chord and

resolved down.

pedal tonecommon

tonecommon

toneped

4-3sus

9-8sus

2-3(bass)sus

7-6sus

a chord tone whichtemporarily becomesa non-harmonic tone.

neighboringtone

step stepNtresolves by returning tothe note preceding the

non-harmonic tone.

Escape tone step leapet resolves in oppositedirection from approach.

anticipation anycommon

toneant

a chord tone playedbefore the rest ofthe chord arrives.

retardationcommon

tonestepret

a note held over froma previous chord and

resolved up.




4 I6 4IV V6C:

vi VC:

this a is thenote of suspension...

it doesn’t belong inthis g major triad.

it resolves tothis g, which doesfit in the chord.it’s the note of

resolution!

when analyzing suspensions, it is important to identify both the note of suspension (the non-harmonic toneitself) and the note of resolution (the note that comes right after thenon-harmonic tone in the same voice).

in almost every case,the suspension isthen labeled usingtwo intervals: theinterval between thenote of suspensionand the bass, and theinterval between thenote of resolutionand the bass.

the only exception to thisis the 2-3 suspension, wherethe suspension occurs in thebass. for this one, we lookat the interval between thenotes of suspension andresolution and the nearestchord tone, whichever voiceit may be in.

when writing an example whichincludes a suspension, it is veryoften useful to begin by writingthe chord that is going to containthe suspension, then adding thesuspension, and finishing by writingthe chord of approach.

*translation:

Hey,



Q:

A: WOOF!*

Dear Sparky:Can you elaborate on why suspensions are identified by numbers? Also, whatshould one watch out for when writing suspensions in four-part harmony?

--S.S., Detroit, MI

IV V6C:

this isa 6th!

this isa 7th!

...so it’s a7-6 suspension!

this isa 2nd!

this isa 3rd!

...so it’s a2-3 suspension!

I6 II6 I6

the real trick, though, is to plan ahead... if you are planning to write a particular typeof suspension, you need to think about the interval that needs to be present in thechord that includes your suspension.

for the 9-8 suspension,the suspension resolvesto an octave above thebass... that’s easy, sinceany chord can include

an octave.

I6 I

for the 4-3 suspensionand 2-3 suspension, you

need a chord with athird above the bass...which means you can

use anything except asecond inversion triad.

for the 7-6 suspension,the suspension resolvesto an sixth above thebass. that means youcan’t use a chord in

root position, becausethey have a fifth and athird above the bass.you need a first or

second inversion triad!



& ‰ œ œ œ ˙b

we’re going to take a little breakfrom the usual stuff and... hey,

it’s ludwig van beethoven!

I’ll tell you what’sgoing on: I’m grumpy!I bet archduke rudolph

20 gulden that Icould write

500 measuresof music this week and

so far I’ve onlycome up with

four stinkin’ notes!

what’s going on, maestro?

repetition

motive repetition

inversion

interval contractioninterval expansion

diminutionaugmentation

rhythmicmetamorphosis

imitation

hey, it’s cool, mr. b...we can use these notesas a motive, and createa ton more music based

on them. watch!

the simplest form of motivicdevelopment: repeating a phrase

immediately gives you twice asmuch music!

Motivic Development

beethoven

woooot!read it andweep, rudy!

you sly fox...506 measures!wait... we are in

4/4 time, right?

so let’s use2/4 time instead!

uh, yeah...

so, heh heh....that gets us to 253

measures...

beethoven

aw, dang!let’s go

double ornothing!

& bbb ‰œ œ œ ˙ Jœ

œ œ œ ˙ Jœ

& bbb ‰œ œ œ

Jœ œn œ œ

Jœ# œ œ œ Jœmotive

motive

augmentation of original motive

metamorphosis of original motive

motive

imitation

int. expansion

sequence

inversion of original motive

sequence

& bbb œ Œ ‰ œ œ œ œ Œ

sequence

& bbb ‰œ œ œ ˙ œ œ œ œ ˙

& bbb Œ œ œ œ .˙

& bbb ‰ œ œ. œ. œ œn œ. œ. œ œ œ. œ. œ œ œ. ‰

&

&

bbb

bbb

Ó ‰ œ œ œ

‰ œ œ œ ˙

jœ œ œ œ œ Œ

.˙ Œ

repeating a motive at a higheror lower level pitch. as withall of these, the intervals

don’t have to match exactly.

flipping the motive upside-down:if the original motive leapsdownward, an inversion will

leap upward.

making the intervals within themotive smaller (contraction) or

larger (expansion).

changing the speed of the motiveso it is played faster (diminution)

or slower (augmentation).

any change of the motive’s rhythm(other than just changing the

tempo, as described above)

an “echo” effect between different voices(between instruments in an ensemble, for

example, or between registers on the piano)

original motive


when we talk about the form of a piece,we are referring to the large-scale layoutof the piece... specifically, the arrangementof sections of music, how and when they

are repeated, and what keys are being used.

Binary Form

baroque dance suites were written for varying instrumentation; many were writtenfor keyboard (usually harpsichord or clavichord), others were written for chamber

groups, and some were even written for full orchestra.

each movement of these suites would be written in the style of a particular baroque dance:allemande, gavotte, bouree, courante, sarabande, louree, gigue, and others,

each of which had a specific character.

because baroque dance form is so common in baroque instrumental music, whentheorists and musicologists are talking about baroque music and say “binary form,”

they are actually referring to baroque dance form.

One of the simplest forms isbinary form, which consists oftwo contrasting sections. werefer to these two sections as

a and b.

the sections might be contrastingin mood, tempo, key, or even in a

combination of these characteristics.

A Bb i n a r y f o r m

another somewhat rare variation ofbinary form is rounded binary form,where the A section returns after theend of the b section. this reprise of

the a section, however, is shortened,so we refer to it as “a prime.”

A ABr o u n d e d b i n a r y f o r m

binary form is used in baroque dancesuites in a very specific way. In thesepieces, both sections are repeated.the A section begins in the primary keyand modulates to the key of thedominant, and the B section begins inthat key and modulates back to theoriginal key. performers of the timewould typically improvise ornamentationwhen repeating each section.

A Bb a r o q u e d a n c e f o r m

I V V I

0 1 0 1 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1

0 0 0 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0

0 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 0

1 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0



Ternary Form

in ternary form, the a section appearsboth at the beginning and at the end;

like binary form, the b section iscontrasting in character.

the reprised a section may be an exactrepeat of the first A, or it may be

slightly different, but the length ofthe a sections should be similar.

the minuet and trio is a variation onternary form used for instrumentalmusic. instead of writing out the repriseda section, the score will place theinstruction “da capo al fine” after theb section, which means to return to thebeginning, play through the a section,and end the piece.

it’s worth mentioning thatthere is a common formthat is descended fromminuet and trio form:

the military march formfavored by john philip

sousa and other americanmarch composers.

in the military march form, the a section is split into twosubsections, called the first strain and second strain.the trio adds a flat (or removes a sharp) from the keysignature, modulating to the key of the subdominant.most marches begin with a short fanfare, and repeat thetrio, placing a short, intensely dramatic passage betweenrepetitions called the dogfight or breakstrain.

this is different from rounded binary, where the reprised a section (which wecalled a prime) is significantly shorter than the first a section.

this same form is commonly used in baroque and classical opera, where it is calleda da capo aria. In both minuet & trio and da capo aria, any repeats are ignored

when playing through the reprised a section.

ternary form is a three-part form.rather than using three completelydifferent sections, most pieces in

ternary form consist of two sections,the first of which is reprised.

A ABt e r n a r y f o r m

A Bm i n u e t & t r i o f o r m

minuettrio

Fine Da capoal Fine

m i l i t a r y m a r c h f o r m

A B(d

ogfig

ht)

fanfare

1st & 2ndstrains

trio

I IV

sousa



sonata allegro form is a specific formfirst used by early classical composers in

opening movements of multi-movementworks for solo, chamber or large groups.

it was eventually adopted by other composersof the classical and early romantic eras.

the form itself is based fromternary form, in that the

first large section is reprisedat the end of the form,

one of the most important features of sonata allegro form is the two primary themesthat make up the exposition. THese two themes will be constrasting in character and, atleast in the exposition, will be in different keys. in a major work, the second theme willbe in the key of the dominant; in a minor piece, the second theme will be in the relativemajor. in the recapitulation, however, both themes are played in the tonic!

the diagram above shows the required elements of sonata form; in the diagram below,several other elements, which are optionally included, are also shown.

bear in mind that composers did what they wanted to... some of the greatest pieces writtenin sonata allegro form feature places where the composer artfully broke these “rules”!

Sonata Allegro Form

s o n a t a a l l e g r o f o r m

A ABfirsttheme

majorkeys:

minorkeys:

secondtheme

developmentof main themes

firsttheme

secondtheme

development recapitulationexposition

I V I Ii III i i

s o n a t a a l l e g r o f o r m ( w i t h o p t i o n a l e l e m e n t s )

A AB

introductio

n

transit

ion

codetta

coda

firsttheme

secondtheme

developmentof main themes

addition ofothers

firsttheme

secondtheme

development recapitulationexposition

I V I Ii III i i

majorkeys:

minorkeys:



Diatonic Seventh ChordsWhat are they?

Remember, diatonicmeans “from the key.”

so a diatonic chord is onethat only uses notes in

the key signature.No accidentals!

& wwwwwwww

wwwwwwww

wwwwwwww

wwww

diatonic seventh chords are theseventh chords you can create usingonly the notes in a particular key.

I7 ii7 iii7 IV7 V7 vi7 vii°7

there are eight possible types ofseventh chords in tertial harmony,but the composers of the commonpractice period only used five:

C:

& wwwwwwww

wwwwwwww

wwww#wwww

wwww#i7 ii°7 III7 iv7 V7 VI7 vii°7a:

Here they arein major and

minor.

remember:we only

raise theleading-tone

overdominant-functionharmony!

wwwwthe

majo

r

seve

nth

major 7thabove root

major triad

wwwwb

wwwwbb

wwwwbbb

wwww∫bb

the

majo

r-mi

nor

seve

nth

the

mino

r

seve

nth

the

half

-dim

inish

ed

seve

nth

the

full

y dim

inish

ed

seve

nth

minor 7thabove root

major triad

minor 7thabove root

minor triad

minor 7thabove root

diminished triad

diminished 7thabove root

diminished triad

we use “07” forhalf-diminished sevenths

and “07” forfully diminished sevenths.

in harmonic progressions, diatonic sevenths canbe used anywhere you can use a diatonic triad with thesame root.

& ˙̇̇˙̇̇ ˙̇̇ ˙̇̇ ˙̇̇˙

˙̇̇˙ ˙̇̇˙

˙̇̇˙ ˙̇̇˙V7 I7ii7vi7iiivii°IVIV 7

in fact, these chords canbe approached and resolvedusing any of the same three

root movementsas triads use.

2

35

With the diatonic seventh chords, we add afourth root movement: the common root.However, this root movement can only beused to increase tension, so going froma seventh chord to a triad is avoided.

1

V7VV7 V

respect the seventh!respect the seventh!

when using these chords in four-part writing — infact, when you use any seventh chord in four-partwriting, you must always, always remember to...

ww www wthe seventh of the chordis most often approachedby the common tone.

however, it is okay toapproach the seventhfrom below by a stepor a leap, or from aboveby a step.

You must never approachthe seventh by a leap fromabove!

The seventh of the chordis always resolved downby step. always!

no, i’m serious. don’t everresolve the seventh of aseventh chord any otherway.

doing so will cause youcertain death!

seventh chords have four notes, so doubling in four-partharmony is not an issue... but if you need to use irregular

doubling, double the root and omit the fifth.

the a

dd-a

-seventh-inato

r

pat. p

endin

g



The Dominant Seventh

I

I

I

IVV7 V7V7 I6

V7 V6V7

V7V7The dominant seventh is the diatonic seventhchord built on the fifth scale degree. wealready discussed diatonic seventh chords...why give this one all this special attention?

for one thing, thedominant seventh is,

by far, the most commonseventh chord used bythe composers of the

common practice period.

first, a note on terminology:

the terms “major-minor seventh”and “dominant seventh” are notinterchangeable! “Major-minorseventh” is the chord’s type, and“dominant seventh” is the rolethe chord plays in the contextof a particular key.

the reason these are oftenconfused is that in popularand jazz theory, the term“dominant” is used to labelthe chord type as well asthe chord’s role.

but the primary reasonfor spending a little extratime with it is the fact that

there are a few thingsthat apply to it that don’t

apply to the other diatonicseventh chords.

& wwwwb

& bb wwww

it’s just a major-minor seventh...

until it’s placed in a particular key!

the other important thing to know about the dominant seventh chord is that common practiceperiod composers would sometimes use some non-standard ways of resolving the seventh!

in this resolution, the seventh is stillresolved down by step, but it takes anornamental “detour” before getting there.

Here, the resolution of the seventh isdelayed by moving to some other chord(usually the subdominant) and having theseventh of the chord hold out until thedominant seventh returns.

in this resolution, the seventh of the chordis still resolved down by step, but the noteit resolves to appears in the bass voice.

the voice thathad the seventhresolves up,usually by step.

after the V7

returns, thevoice that hasthe seventhshould stillresolve itappropriately!

this is the “hot potato” resolution: instead ofbeing resolved down by step in the same voice,the seventh is passed to another voice inanother dominant seventh chord.

the ornamentcan be anyshape orlength, but itmust resolveto the notedown a stepfrom theseventh of theseventh chord.

seventh

seventh

ornamentresolution

resolution

transferredto tenor

ornamental resolutionthe

delayed resolutionthe

bass resolutionthe

transferred resolutionthe

&

?

#

#

œ œ œ œ œ ˙˙ ˙˙ ˙˙ ˙

the seventh stillneeds to resolvedown by step bywhatever voice isthe last to have it.

&

?

#

#

œ œ œœ œ œœ œ œœ œ œ

If the bass voice gets it, he resolves it immediately, ending the fun for everyone.

5

&

?

#

#

œ œ œ œœ œ œ œœ œ œ œœ œ œ œ

&

?

#

#

œ œœ œœ œœ œ

resolutionseventh



Extended Harmonies

diminished diminisheddiminished

doubly-diminisheddoubly-diminishedthirteenth chord

wwwwwww∫∫b


doubly-diminisheddiminished

thirteenth chord

wwwwwww∫∫b∫b∫

diminished diminisheddiminished diminished

diminishedthirteenth chord

wwwwwww∫∫bbb∫


minorthirteenth chord

wwwwwww∫b

bbb∫

diminished diminishedminor diminished

diminishedthirteenth chord

wwwwwww∫∫bbbb

diminished diminishedminor diminished minor

thirteenth chord

wwwwwww∫b

bbbb

diminished diminishedminor perfect minor

thirteenth chord

wwwwwww∫b

bbb

diminished diminishedminor perfect MAJOR

thirteenth chord

wwwwwwwbb∫b

diminished MINOR MINORDIMINISHED DIMINISHED

thirteenth chord

wwwwwwwb∫bbbb

diminished MINOR MINORDIMINISHED MINORthirteenth chord

wwwwwwwbbbbbb

diminished MINOR MINORPERFECT MINOR

thirteenth chord

wwwwwwwbbbbb

diminished MINOR MINORPERFECT MAJOR

thirteenth chord

wwwwwwwbbbb

diminished MINOR MAJORPERFECT MINOR

thirteenth chord

wwwwwwwbbbb

diminished MINOR MAJORPERFECT MAJOR

thirteenth chord

wwwwwwwbbb

diminished MINOR MAJORAUGMENTED MAJORthirteenth chord

wwwwwwwb#bb

diminished MINOR MAJORAUGMENTED AUGMENTED

thirteenth chord

b#b#b

MINOR MINOR MINORDIMINISHED DIMINISHED

thirteenth chord

wwwwwwwb∫

MINOR MINOR MINORDIMINISHED MINORthirteenth chord

wwwwwwwbbbbb

MINOR MINOR MINORPERFECT MINOR

thirteenth chord

wwwwwwwbbbb

MINOR MINOR MINORPERFECT MAJOR

thirteenth chord

wwwwwwwbbb

MINOR MINOR MAJORPERFECT MINOR

thirteenth chord

wwwwwwwbbb

MINOR MINOR MAJORPERFECT MAJOR

thirteenth chord

wwwwwwwbb

MINOR MINOR MAJORAUGMENTED MAJORthirteenth chord

wwwwwwwb#b

MINOR MINOR MAJORAUGMENTED AUGMENTED

thirteenth chord

wwwwwwwb#b#

MINOR MAJOR MINORPERFECT MINOR

thirteenth chord

wwwwwwwbb

MINOR MAJOR MAJORPERFECT MAJOR

THIRTEENTH CHORD

wwwwwwwbMINOR MAJOR MAJORAUGMENTED MAJORthirteenth chord

wwwwwwwb#

MINOR MAJOR MAJORAUGMENTED AUGMENTED

thirteenth chord

wwwwwwwb##

MINOR MAJOR AUGMENTEDAUGMENTED MAJORthirteenth chord

wwwwwwwb##

MINOR MAJOR AUGMENTEDAUGMENTED AUGMENTED

thirteenth chord

wwwwwwwb###

MINOR MAJOR AUGMENTEDDOUBLY-AUGMENTED

AUGMENTEDthirteenth chord

wwwwwwwb#‹#

MINOR MAJOR AUGMENTEDDOUBLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord

b‹‹#

MAJOR MINOR MINORDIMINISHED DIMINISHED

thirteenth chord

wwwwwwwb∫

MAJOR MINOR MINORDIMINISHED MINORTHIRTEENTH CHORD

wwwwwwwbbbb

MAJOR MINOR MINORPERFECT MINOR

thirteenth chord

wwwwwwwbbb

MAJOR MINOR MINORPERFECT MAJOR

thirteenth chord

wwwwwwwbb

MAJOR MINOR MAJORPERFECT MINOR

thirteenth chord

wwwwwwwbb

MAJOR MINOR MAJORPERFECT MAJOR

thirteenth chord

wwwwwwwb

MAJOR MINOR MAJORAUGMENTED MAJORthirteenth chord

wwwwwww#b

MAJOR MINOR MAJORAUGMENTED AUGMENTED

thirteenth chord

wwwwwwwb##

MAJOR MAJOR MAJORPERFECT MINOR

thirteenth chord

wwwwwwwb

MAJOR MAJOR MAJORPERFECT MAJOR

THIRTEENTH CHORD

wwwwwwwMAJOR MAJOR MAJORAUGMENTED MAJORthirteenth chord

wwwwwww#

MAJOR MAJOR MAJORAUGMENTED AUGMENTED

thirteenth chord

wwwwwww##

MAJOR MAJOR AUGMENTEDAUGMENTED MAJORthirteenth chord

wwwwwww##

MAJOR MAJOR AUGMENTEDAUGMENTED AUGMENTED

thirteenth chord

wwwwwww###

MAJOR MAJOR AUGMENTEDDOUBLY-AUGMENTED


wwwwwww##‹

MAJOR MAJOR AUGMENTEDDOUBLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord

‹#‹

AUGMENTED MAJOR MAJORPERFECT MINOR

thirteenth chord

wwwwwwwAUGMENTED MAJOR MAJOR

PERFECT MAJORTHIRTEENTH CHORD

wwwwwww#AUGMENTED MAJOR MAJOR

AUGMENTED MAJORthirteenth chord

wwwwwww##

AUGMENTED MAJOR MAJORAUGMENTED AUGMENTED

thirteenth chord

wwwwwww###

AUGMENTED MAJORAUGMENTED AUGMENTED

MAJORthirteenth chord

wwwwwww###

AUGMENTED MAJOR MAJORAUGMENTED AUGMENTED


wwwwwww####

AUGMENTED MAJORAUGMENTED

DOUBLY-AUGMENTEDAUGMENTED

thirteenth chord

wwwwwww##‹#

AUGMENTED MAJORAUGMENTED

DOUBLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord

wwwwwww#‹‹#

AUGMENTED AUGMENTEDAUGMENTED AUGMENTED

MAJORthirteenth chord

wwwwwww####

AUGMENTED AUGMENTEDAUGMENTED AUGMENTED

AUGMENTEDTHIRTEENTH CHORD

wwwwwww#####

AUGMENTED AUGMENTEDAUGMENTED

DOUBLY-AUGMENTEDAUGMENTED

thirteenth chord

wwwwwww###‹#

AUGMENTED AUGMENTEDAUGMENTED

DOUBLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord

wwwwwww#‹#‹#

AUGMENTED AUGMENTEDDOUBLY-AUGMENTEDDOUBLY-AUGMENTED


wwwwwww###‹‹

AUGMENTED AUGMENTEDDOUBLY-AUGMENTEDDOUBLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord

wwwwwww#‹#‹‹

AUGMENTED AUGMENTEDDOUBLY-AUGMENTEDTRIPLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord

wwwwwww#‹#‹#‹

AUGMENTED AUGMENTEDDOUBLY-AUGMENTEDTRIPLY-AUGMENTEDTRIPLY-AUGMENTEDthirteenth chord

##‹#‹


doubly-diminishedeleventh chord

wwwwwwb∫b∫


eleventh chord

wwwwwwbbb∫∫

diminished diminishedminor diminishedeleventh chord

wwwwwwbbbb∫

diminished diminishedminor perfecteleventh chord

wwwwwwbb∫b

diminished minorminor diminishedeleventh chord

wwwwwwbbbbb

diminished minorminor perfecteleventh chord

wwwwwwbbbb

diminished minormajor perfecteleventh chord

wwwwwwbbb

diminished minormajor augmentedeleventh chord

wwwwwwb#bb

minor minor minordiminished

eleventh chord

wwwwwwbbbb

minor minor minorperfect

eleventh chord

wwwwwwbbb

minor minor majorperfect

eleventh chord

wwwwwwbb

minor minor majoraugmented

eleventh chord

wwwwwwb#b

minor major majorperfect

eleventh chord

wwwwwwbminor major major

augmentedeleventh chord

wwwwwwb#

minor majoraugmented augmented

eleventh chord

wwwwwwb##

minor majoraugmented

doubly-augmentedeleventh chord

wwwwwwb‹#

major minor minordiminished

eleventh chord

wwwwwwb

major minor minorperfect

eleventh chord

wwwwwwbb

major minor majorperfect

eleventh chord

wwwwwwb

major minor majoraugmented

eleventh chord

wwwwww#b

major major majorperfect

eleventh chord

wwwwwwmajor major major

augmentedeleventh chord

wwwwww#

major majoraugmented augmented

eleventh chord

wwwwww##

major majoraugmented


wwwwww‹#

augmented majormajor perfecteleventh chord

wwwwww#augmented majormajor augmentedeleventh chord

wwwwww##

augmented majoraugmented augmented

eleventh chord

wwwwww###

augmented majoraugmented


wwwwww#‹#

augmented augmentedaugmented augmented

ele

Music Theory for Musicians and Normal People · 2015. 9. 11. · music theory for musicians and...

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Transcript of Music Theory for Musicians and Normal People · 2015. 9. 11. · music theory for musicians and...