peopleacademic.udayton.edu/tobyrush/theorypages/pdf/complete.en-uk.pdf · beats are in a bar. beats...

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!

so understand it’s a work inprogress... the progress is slow

sometimes, because I teach music theoryand aural skills during the day at theuniversity of dayton in dayton, ohio,and then head home to spend time with

my wife and six kids!

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!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

but if you like this,or find it useful,

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

“My Dad”Sofia Rush, Age 5Pen and crayon on printer paper

by the way,this version islocalised forbritish andaustralianmusicians!

the originalamerican edition

is availableat tobyrush.com.

big thanks toMatthew Hindsonfor his help withthe localisation!

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 ortwo semitones.

a semitone 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 semitones.

The double flat lowersthe note by two semitones.

The sharp raises thenote by one semitone.

The natural cancels outany previous accidental.

The flat lowers thenote by one semitone.

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 - british adaptation by matthew hindson - visit tobyrush.com for more

semib

reve

breve

min

im

quave

r

semiq

uave

r

demis

emiq

uave

r

hemid

emis

emiq

uave

r

semih

emid

emi-

semiq

uave

r

crotc

het

semibreve

rest

breve

rest

min

im r

est

quave

r r

est

semiq

uave

r r

est

demis

emiq

uave

rrest

hemid

emis

emiq

uave

rrest

semih

emid

emi-

semiq

uave

r r

est

crotc

het 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 standard

length; a minim in one piece may be the same length asa quaver 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 dotwields some serious power: it adds half

of the original note’s length!

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

previously added value.

q. q e= + q.. q e= + x+ q e= + x+q... +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 .œ

.

jœ jœ jœ œ œ œ œ œ œ œ œ œ= =

œ œ œ3 for example, these aren’t

exactly crotchets;they are each a third as

long as a minim.

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

frederic c

hopin

noctu

rne in b

major, op. 6

2, no. 1 (1846)



ack!Get it off!GEt it off!

34

qE E

q.E E E

Notation: Metre

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 bars,and they are delineated with barlines.

the organizationof beat unitsand bars in

a piece is calledmetre. Metre 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 metre: whether it’s simpleor compound, and how many

beats are in a bar.

beats p

er b

ar

simple compound

2

3

4

the top numberindicates the numberof beats in a bar.

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

simple TIME SIGNATURES are easy.

barbarline

the code for the bottom noteis pretty easy: refers toa crotchet, to an quaver,

to a semiquaver,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 bar. to get thenumber of beats, divide it by three.

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

compound metres?

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 notesin a compound metre, the beat unit isalways a dotted note!

compound TIME SIGNATURES are kind of lying to you.

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 (quavers 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., Minnesota, USA

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

& 44 .Jœ Jœ œ Rœ Rœ Rœ Jœ Rœ Rœ

for example, let’stake 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 œ œ œ# œ œ œ œ

œ œ œ# œ œ œ œ œ œœ#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 centring on.

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

there are actually manydifferent types of scales,

each with a different patternof tones andsemitones.

a semitone 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 œa tone is theequivalent of

two semitones.

this particulararrangement, wheresemitones 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!

tonetone

semi-tone

semi-tone

tonetone tone

& œ œ œ œb œ œ œ 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!


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

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& œ

œœœ œœ œœ

largerintervals

& œœ œ œ & œœœœ

2nd 7th

3rd 6th

4th 5th

5th 4th

6th 3rd

7th 2nd

THE RULE

OF NINES



the distance of an interval is one part of itsname, but there’s more: every interval has anotherquality to it, which we’ll call 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 semitones 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 semitone larger than a perfect fourth, and b to fis a semitone smaller than a perfect fifth.

an interval that is a semitonelarger 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 becauseit depends on the type of interval. so let’s start bylooking 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 œ œ œœ œ œ œ œ œ œ œ

& œ œ œ œ œ œ œœ œ œ œ œ œ œ

& œ œ œ œ œ œ œœ œ œ œ œ œ œ

Pd

A

an interval that is a semitonesmaller 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



some theorists usethe term quality forthis... that’s cool too.

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 semitone smallerthan major intervals. like perfect intervals, though, they can also beaugmented or diminished; augmented intervals are a semitone largerthan major, and diminished intervals are a semitone smaller than minor.

Imperfect Intervals& œ œ œ œ œ œ œ œ

œ 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



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 interval in front of you(the one without accidentals!) 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 howthe interval changes inflection.

remember: accidentals can never affectthe distance of an interval... all they can

ever do is change the inflection!

This method may seem complicated at first,but it becomes easier and faster with

practice... and it gives you the correctanswer every time!

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., New York, USA

& œbœ# & œœpoof

!

poof!

& œbœ#& œbœ& œœ


12

34

56

7

STEP 4:dd i m i n i s h e d mm i n o r Mm a j o r Aa u g m e n t e ddd i m i n i s h e d Pp e r f e c t Aa u g m e n t e d

M6 m6 d6pe

rfec

t

inter

vals

impe

rfec

t

inter

vals

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 œ œ œ# œ

& œ œ œ œ œ œ# 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

natural

minor

scal

e

the

harmonic

minor

scal

e

the

melodic

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 semitone 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 semitone.

now, remember... the reason we raised the leading note 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 note 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 tones

and semitones!

the tonehere didn’t have

the tensionthey liked goinginto the tonic!



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 note by a semitone withan accidental. This gave them the tension they were looking for!

semi-

tone!



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.

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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...

when we stackthe chord in

thirds within one octave,we get what is called the

simple form of the chord.

no.

&

?

œœœœ

œœœœ& œœœ let’s get started

on tertial harmonywith the smallestchord possible:

the triad.

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

& œœœbb & œœœb & œœœ & œœœ#

the

dimini

shed

triad

the

minor

triad

the

major

triad

the

augment

ed

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.

incidentally, four-note chords are technicallycalled tetrads, but we usually call them

seventh chords, since they add a seventh.

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



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

œœœ root

third

fifth

Triads in Inversion

haydn

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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.



what a

re y

ou s

noopin

g a

round h

ere f

or?

he a

lready told y

ou w

hat t

he p

iece w

as.

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 semi-tone 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

&

?

##

##

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 œJœ#

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!

? ## www ? ## www ? ## www6

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4

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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 œœœ œœœ œœœ œœœ œœœ œœœI ii iii IV V vi vii°

tonic

Superto

nic

media

nt

subdo

min

ant

do

min

ant

subm

edia

nt

leadin

g n

ote

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 note 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 note only over dominant function harmony:the dominant and leading note triads!

because the dominant and leading note 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 œœœ œœœ œœœ œœœ# œœœ œœœ#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

&

?

œœ

œœ

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 itsown set of patterns, and thus

its 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!

&

?

œœ

œœ

œœ

œœ



Part-Writing: The Horizontal Rules

**

J.S

. Bach

canta

ta b

wv 5

5

“ich a

rm

er m

ensch, ic

h s

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 note

in 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 notein 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 note!2. move to the nearest chord note!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 note,

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 note:a note preceded andfollowed by thesame note.

64

the passing chordis a chord placed in

second inversionwhere the bass is

treated like apassing note:

the middle note ofa stepwise line

moving up or down.

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 notes, 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 thesedescending

augmented 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... it makes 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.

a perfect cadence consists of adominant function chord (v or vii)

moving to tonic.

it’s worth mentioning that American theorists call perfect cadences“authentic” cadences, and call imperfect cadences “Half” cadences.

they use the terms perfect and imperfect to referto two different types of authentic cadences:

impe

rfec

t

phry

gian

inte

rrup

ted

“per

fect

auth

entic

”

(USA

)

phry

gian

a plagal cadence consists of asubdominant function chord

(iv or ii) moving to tonic.

an imperfect cadence is any cadence that ends on the dominant chord (v).

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

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

****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

I V

VG:

G: e: e:

vi

iv6 V iv V

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”!

perf

ect

V IG:

plag

al

IV IG:



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

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

V IG:

if the cadencedoesn’t meetall of thosecriteria, theyconsider it to

be animperfectauthenticcadence!

&

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

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,theorists can find a pattern in their choices that we can use to easily rememberwhich chord progressions work and which ones don’t.

one way to understand this pattern is 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.

“Unstylistic” is apolite way of saying

“The composers didn’tdo it so you shouldn’t

do it either”!

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-notetriad must move to tonic.

A to B is down a seventh,but since 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-n

ote

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.

for instance,the I chordin G major

is G-B-D......which isthe V chordin C major!

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

approached and resolved!

Non-Harmonic Notes

passingnote

name

abbr

eviat

ion

appr

oach

reso

lutio

n

note

s

exam

ple

step steppNresolves by continuing inthe same direction as the

approach.

appoggiatura leap stepapp resolves in oppositedirection from approach.

changingnotes

any stepcntwo non-harmonic notes

on either side of thenote of resolution.

suspensioncommon

notestepsus

a note held over froma previous chord and

resolved down.

pedal notecommon

notecommon

noteped

4-3sus

9-8sus

2-3(bass)sus

7-6sus

a chord note whichtemporarily becomesa non-harmonic note.

neighbournote

step stepNnresolves by returning tothe note preceding the

non-harmonic note.

Escape note step leapesc resolves in oppositedirection from approach.

anticipation anycommon

toneant

a chord note playedbefore the rest ofthe chord arrives.

retardationcommon

notestepret

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 note, 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., Michigan, USA

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!


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-note

overdominant-functionharmony!

wwwwthe

major

sevent

hmajor 7thabove root

major triad

wwwwb

wwwwbb

wwwwbbb

wwww∫bb

the

major-m

inor

sevent

h

the

minor

sevent

h

the

half-

dimini

shed

sevent

h

the

full

y dim

inished

sevent

h

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 note.

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 V7 V7 I6

V7 V6V7

V7V7The dominant seventh is the diatonic seventhchord built on the fifth scale degree. we

already discussed diatonic seventh chords...

why give this one all this special attention?

for one thing, the

dominant seventh is,

by far, the most commonseventh chord used by

the composers of the

common practice period.

first, a note on terminology:

the terms “major-minor seventh”

and “dominant seventh” are not

interchangeable! “Major-minor

seventh” is the chord’s type, and

“dominant seventh” is the rolethe chord plays in the contextof a particular key.

the reason these are often

confused is that in popularand jazz theory, the term

“dominant” is used to label

the chord type instead of

the chord’s role.

but another reason

for spending a little extra

time with it is the fact that

there are a few things

that apply to it that don’tapply to the other diatonic

seventh chords.

& wwwwbit’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 practice

period composers would sometimes use some non-standard ways of resolving the seventh!

in this resolution, the seventh is still

resolved down by step, but it takes an

ornamental “detour” before getting there.

Here, the resolution of the seventh is

delayed by moving to some other chord

(usually the subdominant) and having the

seventh of the chord hold out until the

dominant seventh returns.

in this resolution, the seventh of the chord

is still resolved down by step, but the note

it resolves to appears in the bass voice.

the voice that

had the seventh

resolves up,usually by step.

after the V7

returns, the

voice that has

the seventh

should stillresolve it

appropriately!

this is the “hot potato” resolution: instead of

being resolved down by step in the same voice,

the seventh is passed to another voice in

another dominant seventh chord.

the ornament

can be any

shape or

length, but it

must resolve

to the note

down a stepfrom the

seventh of the

seventh chord.

seventh

seventh

ornament

resolution

resolution

transferred

to tenor

ornamental resolutionthe

delayed resolutionthe

bass resolutionthe

transferred resolutionthe

&?

#

#œ œ œ œ œ ˙˙ ˙˙ ˙˙ ˙

the seventh still

needs to resolve

down by step by

whatever voice is

the 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



V7

& bb wwww

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

eleventh chord

wwwwww####

augmented augmentedaugmented


wwwwww#‹##

augmented augmenteddoubly-augmenteddoubly-augmentedeleventh chord

wwwwww#‹‹#

augmented augmenteddoubly-augmentedtriply-augmentedeleventh chord

#‹#


ninth chord

wwwwwb∫

diminished diminishedminor

ninth chord

wwwwwbb∫b

diminished minor minorninth chord

wwwwwbbbb

diminished minor majorninth chord

wwwwwbbb

minor minor minorninth chord

wwwwwbbb

minor minor majorninth chord

wwwwwbb

minor major majorninth chord

wwwwwbminor majoraugmentedninth chord

wwwwwb#

major minor minorninth chord

wwwwwbb

major minor majorninth chord

wwwwwb

major major majorninth chord

wwwwwmajor majoraugmentedninth chord

wwwww#

augmentedmajor majorninth chord

wwwww#augmented major

augmentedninth chord

wwwww##

augmented augmentedaugmentedninth chord

wwwww###

augmented augmenteddoubly-augmented

ninth chord

‹##

diminished diminishedseventh chord

wwww∫bb

diminished minorseventh chord

wwwwbbb

minor minorseventh chord

wwwwbb

minor majorseventh chord

wwwwbmajor minor

seventh chord

wwwwb

major majorseventh chord

wwwwaugmented major

seventh chord

wwww#augmented augmented

seventh chord

wwww##

diminished triad

wwwbbminor triad

wwwbmajor triad

wwwaugmented triad

www# now, there are four types of triadsand eight types of seventh chords,even though common practice periodcomposers only used five of them.

so that makes for twelve chord types so far... but what if we keep going? what other chordtypes can we make by stacking major and minor thirds? tertial chords with five, six and sevennotes are called ninth chords, eleventh chords and thirteenth chords respectively.

suddenly the possibilities increase from twelve...

...to 124!

the good news: commonpractice period composers

only used these “extendedharmonies” as diatonic

chords on the dominant.

seriously: these are the onlyextended harmonies used by

common practice period composers.in fact, the v

11 and v 13 weren’t used

much before the romantic era.

what about a fifteenth chord?try it: if you add another third

on top of a thirteenth, youare just doubling the root.

so tertial harmony stops at 13!

&# ˙̇̇

˙̇G: V9

&# ˙̇̇

˙̇̇G: V11

&# ˙̇̇

˙̇̇˙

G: V13

&

?

œœ

œœ

now, when we put these chords intofour-part harmony, we’ve got aproblem: they all have more thanfour notes. So we have to makethe tough call: which ones dowe cut from the team?

finally, the ninth, eleventh orthirteenth of the chord is what

defines it as a ninth, eleventhor thirteenth chord.

so how do you put these infour-part harmony?

omit the fifth and use onlythe ninth, eleventh or

thirteenth as necessary.

oh, and if you’re worriedabout inversions: stop.in the common practice

period, extended harmoniesare almost always found

in root position.

root

third

thirteenth

we need to keep the rootbecause it defines the chord.similarly, the third is whatmakes the chord tertial.

the seventh acts as a bridgeto the extended harmony,preventing the chord fromcoming across as two separateharmonies played at the same time.

C: V13

seventh



so far, we’ve talked about twotypes of tertial chords: triads and

seventh chords. remember, tertialchords are chords constructed

by stacking major and minor thirds!


& ‰ 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 œJœ

motive

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:



up to this point, all the chords we’vebeen talking about have been built using

only the notes in the current key.

essentially, this meansno accidentals, with the

exception of the raised sixthand seventh scale degrees

in minor, which weconsider to bepart of the key.

first, every altered chord has tohave at least one accidental...if it doesn’t have any accidentals,

then by definition it’s adiatonic chord!

with few exceptions,altered chords can usethe same basic rootmovements that we’ve

been using.

in general, avoid cross relations.a cross relation occurs when a noteappears with two different accidentalsin two consecutive chords, in twodifferent voices.

lastly, when you use these chordsin part-writing, you should,

whenever possible, resolve thealtered notes in the direction

of their alteration.

so if a note has a flat, try toresolve it down by step or by leap.

and we generally avoid doubling altered notes,since doing so would tend to cause parallel octaves.

second, altered chords can be easily used in place of theirdiatonic counterparts. in other words, you can add some pizazzto a composition by replacing a diatonic chord with analtered chordthat has thesame root.

now that we’ve covered allthe possible diatonic chords intertial harmony, it’s time to open

the door to notes outside the key...

these “altered chords” add acertain richness to the harmony

by using one or more notesthat are not in the key signatureand thus require accidentals.

diatoni

c

alte

red

(chr

omatic)

diatonic triads

diatonic sevenths

extended harmonies

8

15

88

next80

km

Altered Chords

we’ll be coveringseveral categoriesof altered chords,each of which havetheir own uniquerules for use.

however, there area few things thatthey all have incommon!

& bb ˙̇̇n & bb ˙̇̇V/V

ii

altered diatonic

&

?

c

c

œ œ œ œ œ

œ œœ œœ œœ

œ œ œ œ

˙̇ ˙̇˙œ œ œ

˙

˙̇̇bbI IV6 IV V7 vi

bVI

23

5

1

like the diatonic sevenths,however, the common root

should only increase tension...don’t move from an altered chord

to it’s diatonic counterpart.

&

?

b

b

˙ ˙˙ ˙˙b ˙˙ ˙

ii°65 V

&

?

b

b

˙ ˙˙ ˙

˙ ˙˙ ˙n



BorrowedChords

6NEAPOLITAN

SecondaryDominantsA 442

Leipzig

Aug.6SecondarySubdominants

B138

# b

Borrowed Chords

& bbb wwwwwww www www

wwwwwwwn

& wwwbwwwwb wwwbb wwwb

wwwbbwwwwNb

altered chords use notes outsidethe scale as a means of adding adifferent “color” to the chord.

for example, the following chords are diatonic chords in c minor:

“borrowed”?why call them

that when majornever bringsthem back?

but if we use them in a major key, they require accidentals and aretherefore altered chords. we call these borrowed chords because they

are borrowed from the parallel minor.

how does a composer decide whichaltered notes to use? in a major key,

one possibility is using notes and chordsfrom the parallel minor.

ii°c: ii°7 III iv VI vii°7

ii°C: ii°7 III iv VI vii°7b b

hey, minor!I’ll have themback by tuesday

this time, Ipromise!

and, in fact, these six chordsare the six most commonly used

borrowed chords in the commonpractice period. (One of them, the

major triad on the lowered mediant,or “flat three,” was not used much

by composers beforethe romantic era.)

some theoristsrefer to the use

of these chords asmode mixture. two of these chords,

the “flat three” and “flat six,”have altered ntoes as roots.

we place a full-sized flat symbolbefore the roman numeral itselfto indicate this altered root.

all the usual part-writing rules apply to thesechords. for example:

the borrowed supertonic is adiminished triad, and is thereforealways used in first inversion.

it’s usually best to resolve alterednotes in the direction of theiralteration, but doing so in the twoaltered root chords won’t work.

the borrowed seventh chordscan be used in any inversion, but the

seventh must be approachedand resolved properly.

the leading-tone fully diminishedseventh is the king of dominant

function. don’t even think ofresolving it to anything but tonic!

ii°6

vii°7

vii°7ii°7

IIIbVIb

VIb V

VIb V

wait... why? since wedouble the root,moving both rootsthe same directioncan often result inparallel octaves.

it’s more important toavoid parallelism thanto resolve the notesa certain way, so this

use of contrarymotion is better.

&

?

˙ ˙˙b ˙

˙b ˙˙b ˙

5

&

?

˙ ˙˙b ˙

˙b ˙˙b ˙8

V7 ii°6i i VI Vg:

&

?

bb

bb

œ œ œ# œ œ œ œ œ œœœ œ#

˙ œ œ œ œ

jœ ‰ jœ ‰ œ œ œ œœ œ œ œ œ œ œ œ œ

wUw

wnUwI

the tierce de picardie is a major tonic chord at the end of a minor piece, so many theorists consider it aborrowed chord. really, though, it’s notadding chromatic variety... it’s a last-minute modulation!

named for24th-century

explorerjean-lucpicard!*

*Nope.



*****The Neapolitan Six

in addition to the altered root borrowed chords,there is another altered root chord that fits well

with the borrowed chords, even though it is notactually borrowed from the parallel minor.

that chord is amajor triadbuilt on the

lowered secondscale degree.

there are a couple of interestingthings about this chord. one is

the fact that it is almostexclusively used in first inversion.

seriously! although thischord is extremely common

in the common practiceperiod, there are very few

examples of it used inroot position.

second inversion iseven rarer.& wwwbb

the second interesting thing aboutthe chord is its name: you might expectit to be called a “flat two,” in keepingwith the other altered root chords.

but, in fact, this is the first of a few chordsthat have special names. This particular oneis called the neapolitan chord.

Naples scarlatti

“neapolitan” means “from naples,”referring to the city of naples,italy. the chord isn’t actuallyfrom naples, though; it wasjust associated with the operaswritten by neapolitan composerslike alessandro scarlatti.

funny thing is, this chord was used prettycommonly before scarlatti’s time, incompositions far from the courts of italy.

it’s also worth noting that although nearlyevery theorist and theory textbook calls thechord a “neapolitan sixth chord,” it is more

properly called a “neapolitan six chord.” that’sbecause in the rare situations where it is used

in root position, it is simply called the neapolitanchord, and when it is found in second inversion,

it’s called the neapolitan six-four.

since we don’t pronounce I6 as “one sixth,”we shouldn’t say “Neapolitan sixth” for N6!

N6C:The Neapolitan six chord, since it isbuilt on a form of the supertonic,has some characteristics of asubdominant function chord in that it often resolves toward adominant function. in fact, it is verycommon to see the neapolitan chordresolve to a dominant seventh inthird inversion, or to a cadentialsix-four chord.

(even though the neapolitan chord has a lot in common with other subdominant function chords, it is most often referred to as part of a larger group of chords called predominants, and the label of “subdominant function” is generally limited to the subdominant and supertonic chords and their variants.)

since it’s not a borrowedchord, this chord can be usedin both major and minor.

&

?

˙b ˙˙b ˙

˙ ˙˙ ˙

˙ ˙˙b ˙

˙b ˙˙ ˙

N6 N6V42 I6

4C:



Secondary Dominants

the answer, of course, is with secondary dominants.

let’s say we wanted toapproach this vi chord.

what if we wanted to usethat dominant-tonic magic?

there is a duality at the heart of commonpractice period harmonic progression.like the ancient conflict of jedi andsith, it consists of forces that,at one level, work against eachother... but at another, higherlevel, work together, creatingenergy that drives all else.

that duality, of course, is the relationshipof dominant function and tonic.dominant harmony typifies tensionin the common practice period, and

the tonic represents release.its simplest form, the authentic

cadence, has been ubiquitousin western music for centuries.

V

Ithe progression of dominantmoving to tonic is so strong, itwould be nice to be able to useit to provide motion to chordsother than tonic.

but that’s crazy talk, though,isn’t it? I mean, how could we

control that magic and make itobey our compositional whim?

vi

& ˙̇̇?vi

vi

& ˙̇̇?we could use one of the usualdiatonic chords, the tonic, thesubdominant, the mediant... butwhat if we’re looking for a bitmore tension and release?

& ˙̇̇# ˙̇̇ & ˙̇̇# ˙̇̇

Va: C:i

& ˙̇̇# ˙̇̇

viVa

aV

if we pretend for a moment that the chord we’re resolving to is a tonic chord, what wouldthe corresponding dominant chord be? altered, yes, but we’re not afraid of those anymore:

while we might have once called this ashort modulation, it is really more likeborrowing another key’s dominant chord.

if we think of the V chord in the keyas the primary dominant, V chords of

related keys are secondary dominants.

in major keys, the “x” above can be anydiatonic chord other than tonic (obviously)or the leading-note triad. why? becausea diminished triad has a hard time acting

like a temporary tonic chord.

in minor keys, the composers generallyonly used secondary dominants

of iv and of V.

these chords often resolve to thechord “under the slash,” but they can

actually be approached and resolvedusing the basic root movements!

yes. yes they do.

now, we’re not just limited to the v chord:there are five chords with a dominant function!

V vii°V7 vii°7 vii°7dominant function chords

the secondary dominants

Vx x x x x

vii°V7 vii°7 vii°7that gives usa huge list ofpossibilities!

23

5

1

the basicroot movements

rock!



Fr.6on 2

I

Augmented Sixth Chords

first, we’ll start withthe doubled root of a

V chord...

V

&˙˙

...and approach thatoctave with a semitonebelow the top note,

...and a semitone abovethe bottom note...

V

&˙# ˙˙b ˙

...and, finally, add thetonic as the third note.

V

&˙# ˙˙̇b ˙

˙ ˙like that moment of incredible tension justbefore the hero finally kisses the leading

lady, the semitone is the go-to intervalfor creating tension in music of the common

practice period. it drives the entire style!

if one semitone can create such strong tension, howabout two semitones sounding simultaneously? Let’sget creative here for a minute to find a cool new wayto approach a diatonic chord. in this case, we’ll use them to approach the dominant triad.

the result is a new chord, one we call the augmented sixth chord,after the interval created by the top and bottom notes.

augmented sixth chords are predominant chords,meaning they are used to approach dominant chords.they are usually used to approach dominant triads,not dominant sevenths, because of the doubled

roots present in dominant triads.

however, they also oftenapproach tonic chords

in second inversion,which also contain a

doubled fifth scale degree.

rarely, augmented sixth chordsare found transposed downa perfect fifth, analyzed as“on flat two,” and used toapproach a tonic chord inroot position.

&wwww#bIt.6

if we just usethree notes

and double thetonic, we get the

italianaugmented sixth.

&wwww#b

Fr.6

if we add thesecond scale

degree insteadof doubling thetonic, we get the

frenchaugmented sixth.

&wwww#bb

Ger.6

and if wereplace the

second scaledegree with thelowered thirdscale degree,

we get the

germanaugmented sixth.

Ger.6

&

?

˙# ˙˙ ˙

˙b ˙n˙b ˙I6

4

b

&

?

˙ ˙˙ ˙

˙ ˙˙b ˙

Ger.6 V

&

?

˙# ˙˙ ˙˙b ˙˙b ˙5

and, finally, when resolvingthe german augmented sixth

chord to a dominant triad,you might find yourself

writing parallel fifths...but it’s perfectly okay!

mozart did it all the time!




IV6 V7

Ger.6C: V I

I IV VI V I

vii°7 vii°7

E: vii°6G: I

I

D :

F:C:

I IV VVI V I

F:E:

Altered and Enharmonic ModulationAltered common chord modulationis easy: remember diatonic commonchord modulation, where we used a

chord that was diatonic in boththe old and new keys?

altered common chord modulationis the same thing, only using the

pivot chord as an altered chordin either the old key, the new key,

or both.

Now, in both diatonic modulation and altered modulation, we have one chord that plays twodifferent roles, one for each key. But the chord type doesn’t change... if it was a majorchord in the old key, it’s still a major chord in the new key.

& b œœœœœœ œœœ œœœn

www

& b œœœœœœ œœœ œœœ#n#

wwwn#

b

b

b

b

this technique isso — well, odd — that

there are onlytwo specific ways

to do it.

...but what if the chord type did change?...but what if the chord type did change?

in enharmonic modulation, we respell a chordenharmonically so the chord type itself

is different in the old and new keys.

Ger.6C: V7D :b

&wwww#bb

wwwwbbb

ever notice that the germanaugmented sixth chord is just like

a major-minor seventh chordwith the seventh respelled

enharmonically?

fully diminished seventh chords arecool for a lot of reasons, and one of

them is that they are equidistant chords:inverting a fully diminshed seventh

yields another root-position fullydimished seventh chord.

meaning that a fully diminishedleading note seventh chord

can be a pivot chord intothree other possible keys:

note that the pivot chord above isapproached like a dominant seventh,

but resolved like anaugmented sixth chord!

beethovendid!

&

?

bbbbb

bbbbb

œ œ œn œœ œ œn œœ œ œn œnœ œ œn œ

we can take advantage of this and use itas a pivot chord... where it acts like agerman augmented sixth in one key

but like a V7 (or a V7/x secondary dominant)in the other key!

a°7 a°6 c°7

&wwwwbb &

wwwwbb &wwww

∫bb

inve

rt

respell

5

&# œœœ œœœœ

b œœœœ# œœœ#

&# œœœ œœœœ

b œœœœ∫b œœœbbn

&# œœœ œœœœ

b œœœœbœœœnb

5

vii°7 vii°7

D : vii°4G: I

I3

vii°7 vii°7

B : vii°4G: I

I2

which can berespelled as




C:

after learning about secondary dominants,you might wonder if it’s possible to extend theconcept to other chords.

for example, if we can use a dominant function chordfrom a related key, what about a subdominant function

chord from a related key, like IV of V?

well, the answer is yes, and the chords that result are called secondary subdominants.but before we talk about them, you need to understand a few things.

to approach these chords,use any of the basic root

movements.

the most common way to resolvesecondary subdominants is to

the corresponding secondarydominant.which are awesome.

first of all, the very existence ofthese chords is debatable.

what one theorist might calla secondary subdominant:

another might call ashort modulation.

& œœœœbœœœœ#

œœœœœœœœn

V6 Iii°7

VV4

2

V

C:

C:

G:

& œœœœbœœœœ#

œœœœœœœœn

V6I6

Iii°7 V4

2

second, the only placewe find chords that

we can call secondarysubdominants is in the

music of thexromantic era.x

Lastly, since these chords are alreadypushing the limits of tonality, composerswould only use secondary subdominants

from closely related keys. Inother words, secondary subdominants

should only be “of IV” and “of V.”

ivIV iv

Vkeeping these things in mind, let’s look at the possibilities:

what are all the subdominant function chords we’ve encountered?

first, there arethe diatonic triads:

ii IV

next, the diatonicseventh chords:

ii7 IV7

and, lastly, a fewborrowed chords:

ii° ivii°7

so a secondary subdominant canhave any subdominant function

chord above the slash, anda IV or V below the slash.

however, the most commonlyfound secondary subdominantsare those that use the half-

diminished supertonic seventh.

ii°7

IVii°7

VV7

Vii°7

V


Secondary Subdominants


IF: IV V I DM B M

the music of the baroque, classicaland romantic eras share a consistent use

of harmony and counterpoint, enough to causetheorists and historians to group them together

as the “Common Practice Period.”

however, the music of the romanticera employed some interesting

techniques that set it apart fromthe baroque and classical eras...

...and foreshadow some ofthe big changes coming inthe twentieth century!

b

2000

1900

1800

1700

1600

1500

romantic early 20thcentury

contemporaryclassicalbaroquerenaissance

Romantic Era Techniques

we’ve already mentioned a few chordsthat were specific to the romantic era:

dominant eleventh andthirteenth chords,

the “flat three” borrowed chord,and secondary subdominants.

V11

V13

IIIb

ii°IV

ii°Viv

IV

V7Ger.6

&

?

˙# ˙n˙ ˙˙b ˙˙b ˙

another technique that is unique to the romantic era isthe resolution of an augmented sixth chord to adominant seventh chord rather than a dominant triad,causing the interval of the augmented sixth to resolveobliquely instead of moving outward to the octave.

finally, romantic era composers would sometimes use a particular type of chordprogression that had the effect of suspending tonality for a portion of thepiece. By temporarily removing the feeling of being in a certain key, the composercould easily modulate to a distant key!

this technique is calledthird relations because it

involves moving by rootmovements of a major or

minor third without respectto key signature.

for example...

here, we’rein F major...

*whump*

...third relations

are like turning

off the gravity

in the room

for a bit...

...and then turningthe gravity backon ... but in adifferentdirection!

if you think oftonality likebeing in aroom...

& b œœœœœœ œœœ œœœ ˙̇̇# ˙̇̇nb

F M E M IB: IV V I# b

& b ˙̇̇### ˙̇̇bb œœœ#n#œœœ# œœœ# œœœ

...here, we’re justmoving down by thirds...

and then we landin b major!

...which obscures anysense of key we had...



right. so the language fux is teaching is reallyan interesting ideal: based partly on hisperceptions of palestrina’s musical languageas delivered to him through italian theorists, andpartly on his own ideas of what he thought thelanguage should be.

anyway, let’s get started! going through fux’s stepsfor learning counterpoint gives us a glimpse of

how the masters learned their craft and afeel for the environment in which theydeveloped their own musical languages.

hurray! Let’s go, giovanni, and bring thebeautiful light of perfect composition

to these eager students!

yeah, Joe, about that... you do realize thatyour idea of perfect composition is just a

no, I mean that it’s

but let’s cut fux some slack here: as theorists, we’re all guilty of this to some degree.

fux

fux

* *

palestrina

palestrina


1900

1950

1850

1800

1750

1700

1650

1600

1550

1500

1450

in 1725, an austrian composer and theorist named johann joseph fuxwrote a theory textbook called gradus ad parnassum, in which heoutlined his method of teaching how to write good counterpoint.

Gradus ad parnassum was a big hit, used (or at least praised) bycomposers like Mozart, beethoven, and haydn. the system thatfux used is referred to as species counterpoint, because itinvolves going through increasing levels of rhythmic complexitywhich are labeled as species I, Species II, and so forth.

interestingly enough, the language fux was advocating was not thecounterpoint of the common practice period to which he belonged,but the more strict rules of counterpoint used by composers ofthe renaissance more than a century earlier.

of course,it’s worth pointing out that

fux didn’t actually have accessto much of my music!

specifically, fux was a starry-eyed admirer of the italianrenaissance composer giovanni pierluigi da palestrina, who heconsidered to represent the peak of compositional artistry...

something he felt was being lost or even squandered by hisbaroque and classical contemporaries.

counterpoint is the combinationof two or more melodies, eachone as important and interesting

as the other.

Gradus ad parnassum means“Steps to parnassus.” Parnassusreferred to the highest peak in

greece, and was used as ametaphor for perfection.

Introduction to Species Counterpoint


it’spronounced“fooks”!

1660-1741

1525-1594

blissfully awesome thing?yes, that’s just what I was thinking!

super fun? yayyyy!!!!!

palestrina


m2 P4

P4

m2 M2P5

P5

before we start combining melodies, we needto understand what constitutes a good melody

in the system of species counterpoint.

oh, and don’t repeat notes like this.contrapuntal melodies need to be

interesting, not boring.

in general, melodies should be primarily stepwise, with a single,definite high point or low point. effective melodies tend to progress slowly towardthe high or low point and then move back toward the starting pitch.

as you can see above, occasional leaps are okay...but they come with a bunch of restrictions.

first, leaps should be no larger than a perfect fifth, with two exceptions: leaping by aperfect octave, and leaping upward by a minor sixth. don’t do these very often, though!

third, leaps of a perfect fourth need to be preceded or followed by stepwise motionin the opposite direction, to counterbalance the leap. and if a leap is larger than aperfect fourth, it needs to be counterbalanced both before and after!

This perfect fourth is counterbalancedby the step that occurs before the leap.

This perfect fifth is counterbalancedby steps on both sides of the leap.

This perfect fourth is surrounded by steps,but they aren’t in the opposite direction.

This perfect fifth has steps on both sides,but the first one isn’t in the opposite direction.

lastly, don’t write three or more leaps in a row. You can writetwo leaps in a row, but they need to outline a major or minortriad. no diminished triads... they have tritones in them!

evil!

second, for heaven’s sake, avoid the tritone! this interval (an augmentedfourth or diminished fifth) was actively avoided so consistently thatFux and his pals called it the diabolus in musica... the “devil in music!”

leaping by a tritone is bad, but it’s alsoimportant to avoid the tritone in otherways... for example, this pattern, where

a tritone is outlined in the melodic line,would be considered inappropriate. tritone

and really, to befair, these aregood guidelines

for any melody...it’s just that fuxis a little morestrict about it.

Species Counterpoint: Melody

& w w w w w w w w w w w whigh point

w w

& w w w w w w

& w w w w & w w w w

& w w w w & w w w w


BUT

why, I

yeah, yeah, Palestrina, we knowyou repeated notes all thetime. But fux was pursuing anideal. Maybe he felt you coulddo... better?

SHHHH. let’s just move on.

“first species” counterpoint is the most rhythmically simple type of counterpoint:both voices have the exact same rhythm. as a result, it’s all about the intervals!

and that takes us to the first rule:only use consonant intervals.

next rule: voices can’t cross or overlap.

the next rules have to do with perfect intervals (P1, P5, and P8... remember, P4 isdissonant!), which play important roles and require some special treatment.

because they are such a strong sonority which can stop the counterpoint in its tracks,unisons can only be used on the first or last notes of an exercise.

in fact, each exercise must beginand end with a perfect intervalwith the tonic in the lower voice.

for these exercises, you’ll bewriting a melody above or belowan already-written melody, calleda cantus firmus.

wait... why is thatlast bit important?

the cantus firmus will always startand end on the tonic note...so if you are writing counterpointbelow the cantus firmus, you can’tstart with a perfect fifth, because you’re lower voice won’tbe the tonic. You’ll have to startwith a unison or octave instead!

all perfect intervals must be approached withcare in order to preserve voice independence.first of all, never repeat a perfect interval!

in fact, approaching perfect intervals with bothvoices moving in the same direction is bad, evenif it’s from an imperfect interval.

so it’s easiest to remember what you can do:approach perfect intervals using contrary motion,with at least one voice moving by step.

plus, it’s also not okay to approach a perfectinterval with leaps in both voices!

these are calledparallel fifths...

and they’rejust awful!

and then: thirds and sixths are fine, but no more than three in a row.

to much consonance, andthe natives get restless.

wooooooooooo

and it’simportantto know

that to thesixteenth-centuryear, theperfectfourthwas alsodissonant!

see how thenumber of the

interval is writtenin between the twovoices? you should

do that too.

it’s howrock stars

do it!no seconds! no sevenths! no fourths!

Species Counterpoint: Species I

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voice crossing:top note is lowerthan bottom note

voice overlap:top note is lowerthan the previous

bottom note

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w w w w w

3-3? 66 6 6 6 6

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w w w w ww w w w w1 3 3 1 3

first note:no problem

in the middle:no way

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second speciescounterpoint adds a

touch morecomplexity:

there are two notesagainst every one inthe cantus firmus.

fortunately, that doesn’t make it twice as difficult: in fact, most of the previous rulesstill apply without any changes.

there are only a few exceptions:

species irule:

species iirule:

only useconsonantintervals.

unisonscan onlybe usedon the

first andlast notes.

approachperfectintervals

usingcontrarymotion

with at leastone voice

movingby step.

no leapslarger thana perfect

fifth*

leaps are still fine, but don’t leap to a new high point on a downbeat.

the a in the third measure is anew high point for the line,so leaping to it on thedownbeat puts a lot of weighton that one note, making itstick out of the texture.

still true... for downbeats. for theunaccented beats, dissonant intervalsare fine, as long as they happen aspassing notes: notes that fill in athird created by surrounding notes.

oh, and notice how dissonant intervalshave their numbers circled? nice, huh. You should do it too.

unisons can be used on unaccentednotes... just be careful aboutcrossing or overlapping voices!

this rule still applies: if you use a perfect interval on a downbeat,you need to use contrary motion from the immediately precedingnotes, and at least one voice must move by step.

(in fact, it’s also not okay to have parallel perfect intervals from the unaccented beat to the downbeat, but if you are approaching with contrary motion, that wouldn’t happen anyway.)

however, you must also be careful notto have the same perfect interval ontwo successive downbeats. This iscalled parallel perfect intervalsand it’s going to be a no-no for agood long time.

Species Counterpoint: Species II

6 7 10 8

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8 7

8 10 8 6

3 1

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*excepting, of course, ascending minor sixths and perfect octaves, but you already knew that.


not too bad, is it? yeah! bring on third species!

Species Counterpoint: Species III

8 9 8 9

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third species, as you might have guessed,involves four notes against one.

and, compared to the otherspecies, it’s easy peasy!

in fact, the differences can besummed up into four rules.

As usual, the first note in each measure must be consonant. The third note inthe measure is also usually consonant, but it can be dissonant... as long as it’sthe only dissonant note in the measure.

there are two special figures which act as exceptions to the rules above.

well, they’re kind of similar...Hey, that makes five rules! no fair!

the double neighbor noteinvolves an upper neighbor

and a lower neighbor playedone after another, then

returning to the note thatapproached it.

this figure can be inverted,so the upper and lowerneighbors switch places.

the nota cambiata (orchanging note) follows

the pattern of a step down,a third down, then

two steps up. the middle noteof this five-note figure

must be consonant.

don’t leap more than oncein the same direction.

as for the second and fourth notes, they can be dissonant, as longas they are passing notes or neighbor notes.

a neighbor note is a note approached by step,which resolves back to the note it came from.

third:

fourth:

first: all intervals larger than a third,including perfect fourths, must becounterbalanced by steps onboth sides.

SECOND:

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w3 2 4 3

8 7 5 6 6can be

dissonant!

must beconsonant!

can bedissonant!



wait, dissonanceson beat two?

but i never

quiet,Palestrina.

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Species Counterpoint: Species IV

5 3 6 7 6 7 6 3 6 7 6 4 3

with the fourth species, we stop using smaller note values and back up a bit tospecies I. But instead of having the notes move at the same time, species IV involvesthe voices being offset from one another.

The biggest differencewith species IV is thefact that dissonancesare permitted on thedownbeat. but as youmight expect, they haveto follow certainspecific rules.

oh youdon’t say.



dissonances in species IV must be in the form of suspensions.A suspension is a dissonant note that is approached by beingheld over — suspended — from the previous note.

7-6

4-3 2-3in species IV, you’re dealing with a lot of limitations with melody and counterpoint, soyou will sometimes get trapped in a situation where nothing will work. when this happens,you are allowed to “break species”: forget the tie and slip into species II for a coupleof notes.

don’t go crazy with this, though... species IV counterpoint should embrace suspensions,not avoid them. it’s best to break species only rarely. unfortunately, sometimes that means

backing way up and choosing a different starting pitch for your counterpoint!

for example, here webreak species so wecan avoid writing afux-enraging four4-3 suspensionsin a row!

we label suspensions by the intervals of thesuspension and resolution, so this one

would be called a 7-6 suspension.

another important definingcharacteristic is that the

suspension resolves downby step. if it doesn’t resolve

down by step, it’s not asuspension!

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in this case, the suspensionis the F on the downbeat ofthe second measure. it’sprepared by the F in theprevious measure, and resolvesdown to the E.

suspensions are great, by the way,but don’t use the same one morethan three times in a row, orfux will release the hounds.

similarly, inthis example,the suspendednote is the D,which forms afourth withthe A. it moves to a C, a third above thebass, making it a 4-3 suspension.

the only suspension fux allows when writingcounterpoint below the cantus firmus is the2-3 suspension, in which the suspended noteforms a second with the cantus firmus, thenresolves down to a third. (when this suspensionis written an octave lower, it is sometimes calleda 9-10 suspension.)

see how we resolve toa larger interval, unlikethe 7-6 or 4-3? we’rebelow the cantus firmus,so we move away from it.because suspensionsalways resolve down!

the 7-6 and 4-3 suspensionsare the only ones fux allows

when writing counterpointabove the cantus firmus.

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species breaker!

Species Counterpoint: Species V



fifth species counterpoint is the culmination of all the other species,and it’s the closest fux gets to palestrina’s style of florid counterpoint

that fux thought was so amazingly awesome.

there aren’t a lot ofnew rules for this

species, and they mainlydeal with combiningthe other species.

First, aim for a goodmix of differentspecies. don’t staytoo long with anyparticular note valuebefore switching tosomething else, soyour counterpointremains rhythmicallyinteresting.

when you’re using a particular note value,follow the rules of the correspondingspecies. so when you are using minims,make sure you’re obeying the rules ofspecies II. If you tie two minims together,keep the laws of fourth species.

Leave the semibreves out, though, untilyou get to the end of your exercise. if yougo all species I in the middle, things getreal boring real fast.

next, species III and IV can be combinedby using dotted minims, which alwayshave to start on a strong beat.

lastly, you can include quavers to addmore rhythmic interest, as long as youfollow a few restrictions:

any dissonances involved with this kind offigure have to follow the rules of fourthspecies counterpoint: that is, they needto be suspensions prepared and executedby the dotted minim and resolvedimmediately afterward.

and they’re allabout rhythm!

Species V Casserole2 cups second species

Combine all ingredients in a grand staff and mix well.

Heat through to prevent unjustified dissonances from

forming. Let cool and serve on period instruments.

½ cup first species

2 cups third species 3 tsp ties (fresh or frozen)

dash eighth notes (optional)

1-½ cups fourth species

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ohyeah!

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6 5 6 8 7 6 5

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*they have to occurin pairs on weak

beats,

both notes mustbe approached andresolved by step,

only one pairshould be used

in any givenmeasure!

quavers?I love those

guys!

relax...it actually helps us see

how this all relates to thefour-voice chorale style

of our man Bach...

Let’s head back to species Iagain, but add a third voice!

...and even with adding a whole new set of intervals to look at, it’s really not that bad!

uh... do we have to?

Species Counterpoint: Three Voices



j.s

. bach

j.s. bach

woo!

we still need to useonly consonantintervals betweeneach upper voiceand the bass...

in general, the rules formelodies and counterpointare the same for species I

in two voices.

but the intervalbetween the uppertwo voices can bedissonant... it caneven be a tritone!

and perfect intervalsstill need to be

approached with care:you still can’t go wrong

with contrary,stepwise motion!

However, in three voices,perfect intervals can alsobe approached with both

voices moving in the samedirection if the top voicemoves by step, and if the

third voice moves incontrary motion with

the others.

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a4

THe chords created should be triads.You can form incomplete triads

occasionally by having a doubled rootand a third, but avoid having open fifths

except on the first or last chord.

technically, the triads must bemajor and minor in root positionand first inversion, and diminished

triads in first inversion only.

but if you follow the rules aboveabout consonant and dissonantintervals, it prevents you from

using the wrong inversion!

ooh!becausesecond-inversiontriads and

root-positiondiminishedtriads all

have fourthsabove the

bass!

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www

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5

As with two-voicecounterpoint,

Parallel perfectintervals are forbidden

between any voices!

avoiding parallel perfect intervalsand second inversion triads?

keeping diminished triads in first inversion?these are all fantastic ideas!

C (d) C6 a6 b°6 (C)

palestrina

use them, Bach!use them

like the wind!

The Modern Modes

v. williams aristoxenusplatohildegard

and, to make matters worse, each of these things use the names to represent differentconcepts! fortunately, right now, we’re only worried about the modern modes.

these modes are used a lot...especially in folk music. as for

standard western repertoire,they are first prominently featured

in the post-romantic musicof the early twentieth century

british isles.

well, remember when we created the natural minor scale by starting with a major scale,but using the sixth note of the scale as the tonic? it gave us a new pattern of tones andsemitones... a new scale.

by starting on the other notes of the major scale, we get the other five modes.

a more effectivemethod of keepingthe modes straightinvolves memorizing

each mode’scolor note:

the scale degreethat makes it

unique from themajor or minor

scale with thesame tonic.

major + lowered 7th

minor + raised 6th

minor + lowered 2nd

major + raised 4th

in fact, these are two of the seven modern modes:major is the ionian mode, and natural minor is the aeolian mode.

minor

keeping the same key signature,we use this note as our new tonic!

one of the primary characteristics ofthese english modalists is that theytended to avoid the strong tensionsof the common practice period...for example, they avoided chordsthat used a tritone... and avoided

raising the leading note in minor keys!

the modernmodes’ namescame from thevarious “keys”used in medievalchurch music

which were, inturn, named inhonor of thelute ranges usedin later ancientgreek music

and thoseused the samenames as scaletunings discussedby plato in380 bc!

brita

in!

so what are they?

major

c ionian

c mixolydian

c lydian

a aeolian

a dorian

a phrygian

& œ œ œ œ œ œ œ œ & œ œ œ œ œ œ œ œ

D to D: the dorian mode

E to E: the phrygian mode

F to F: the lydian mode

G to G: the mixolydian mode

B to B: the locrian modebecause it hasa diminished tonic,

locrian is a theoreticalmode... it’s not usedin actual practice.

the modes here all sharethe same key signature...

they are related, likec major and a minor!

modern?wait, isn’t this stuff, like,

100 years old?

& œ œ œ œ œ œ œ œ œ œ œ œ œ œ


& œ œ œ œ œ œ œb 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 œb œ œ œ œ œ œ

yes, but we only call them “modern” because we need to differentiate between a bunch ofunrelated things across music history that, ever so inconveniently, use the same names!



peopleacademic.udayton.edu/tobyrush/theorypages/pdf/complete.en-uk.pdf · beats are in a bar. beats...

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