music theory for musicians and normal people

8/12/2019 Music Theory for Musicians and Normal People

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MUSIC THEORYfor

MUSICIANSNORMALPEOPLE

and

by Toby W. Rush

this file is a collection of individual sheets

covering a bunch of lessons onmusic theory.

its not abook...yet. it might be someday!but as of right now, its incomplete.

The truth is, they werent intended to

be asingle volumewhen I started making them...

they were justreview sheetsfor my own

theory students.

but the more Imade,

the more I realized

they could be collectedinto a textbook of sorts...

eventually!

I still have alot of work to do,

but Ive collected the ones Ive made

so far into asingle documentto

make it easier for the folks

who wanted them all... but didnt want

to download every file individually!

I still have alot of work to do,but Ive collected the ones Ive made

so far into asingle documentto

make it easier for the folks

who wanted them all... but didnt want

to downloadevery file individually!so if youve been sent this file

by someone, know that there

might be anewer version

ormore pages

at tobyrush.com.

now lets

learn some

music theory!

but if youlike this,

or find ituseful,

great! feel free to

share it,copy it, anduse it.

just dontsell it,change it,

or tell others youmade it!*

or more info, seehttp://creativecommons.org/licenses/by-nc-nd/4.0/

hello!

Rush


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music notationis the art ofrecording music in written form.

modern music notation is a productofcenturies of transformation...

and it is neitherefficient nor intuitive!

bn

Notation: Pitch

##g#F#d#DD#SS#d#Mf#SSg#F

pitch is the highness orlowness of a sound.

the system of musical notationwe use is essentially astylizedgraph ofpitch versus time.

thefive lineson which notesappear is called astaff.

the white noteson the keyboardare labeled with letters fromAtoG

otation is based on thepiano keyboard;nes andspaces on the staff represent

the white noteson the keyboard.

heclefdetermines what notes each staffline corresponds to. thefour modern

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

To notate theblack notes

on the pianoeyboard, we use

accidentals,which alter thenote by one orwohalf steps.

ahalf stepisthe distancebetween twodjacent keys

on the pianokeyboard,

regardlessof whatcolorthe keys are.

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

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

twonotes which have the samepitch (for example,f sharpand

g flat) are calledenharmonics

middle cis thecthat is closest tothemiddle of the piano keyboard.

Thedouble sharp raises thenote by two half steps.

Thedouble flat lowersthe note by two half steps.

Thesharp raises thenote by one half step.

Thenatural cancels outany previous accidental.

Theflat lowers thenote by one half step.

treble clef

alto clef tenor clef

bass clef

for example, aflute hasahigh pitch,while a tuba

has alow pitch.

anote is awritten representation

of a particularpitch.

pitch

pitch

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

B B ?

time

w wo display notesoutside thestaff, we useshortenedstaff lines

called

ledger lines.

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

liz phairwhat makesyouhappy[melodyfromchorus]w hitechocolatespaceeg g (1998)

music theory for musicians and normal peopleby toby w. rush

licensed under acreative commons BY-NC-NDlicense - visit tobyrush.comfor more


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whole

note

doubl

e

whole

note

h

alf

note

eighth

note

sixt

eenth

note

thirty-second

note

sixty-

fourth

note

one

-hundred-

twenty

-eighth

note

quarter

note

wholer

est

double

who

le

rest

half

re

st

eighthr

est

sixteenth

rest

thirty-secon

d

rest

sixty-fourt

h

rest

one-hund

red-

twenty-eighth

rest

quarter

rest

Notation: RhythmW w h

q

e

x

x

x

x

whilepitch is pretty clearly notated on a

vertical axis,note lengthis indicated using

somewhat arcane system involving

noteheads, stems and flags.

in this chart, each successive type of note ishalf as long

as the note to its left. none of these notes has astandard

length;a half note in one piece may be the same length as

an eighth note in a different piece.

note lengths in a piece

are indicated by the temp

markingat the beginning

of a piece or section.

arest is a period of

silence that a length

which corresponds to a

particular note.

usually rests are

placed on the staff at a

particular vertical

position as shown here.

theaugmentation dot

is a dot placed to the

right of a notehead. though small, this dot

wields someserious power:it changes the

length of the note by150%.In other words,

it makes the note half again as long!

multiple dots can also be added,

each one adding half of the

previously added value.

q e e= + q e e e= + + q e e e= + + x+ q e e e= + + x+ +xties are curved marks which connect

two notes together to create

asingle, extended sound.

to tiemore than twonotes together,

draw ties betweeneach note;do not

use a single, extended tie.

a tuplet is any non-standard division of a

note. these are usually written as a group

of notes delinated with abracket and

anumber showing the division being made.

most tuplets are simple divisions, like

the triplets to the left. but anything is

possible!chopin,for example, would

oftengo to townwith these things.

j j = =

3 for example, these arentexactly quarter notes;they are each a third aslong as ahalf note.

wha...gah!chopin,no!

down, boy!

fredericchopin

nocturneinbmajor,op.62,no.

1(1846)




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34q E q E E

Notation: Meter

Q Q Q Q Q Q Q Q Q Q Q> Q Q Q Q Q3 Q Q Q Q

a fundamental feature of

most pieces of music is a

consistent rhythmic pulse.

this pulse is called thebea

and a single pulse

is called abeat unit.

here are two types of beat units:

those containing two divisions,

calledsimplebeat units...

...and those containing

three divisions,

calledcompound beat units.

in music, beats are organized into patterns ofaccented andunaccented beat units.

in fact, if you listen to a sequence of repeated notes, your brain will probably start to

perceive the notes as groups of two, three,orfour,even if no accents are present!

these groups are calledmeasures,

and they are delineated withbarlines.

the organization

of beat units

and measures in

a piece is called

meter.Meter is

described by two

numbers placed

at the beginning

of the piece:

the time signature.

by looking at the top

numberof the time signature,

you can tell two things aboutthe meter: whether itssimple

orcompound,and how many

beats are in ameasure.

be

ats

per

measure

simple compound

2

3

4

the top number

indicates thenumber

of beatsin a measure.

the bottom number

indicates the type of

notewhich serves as

thebeat unit.

simple TIME SIGNATURES areeasy.

measurebarline

the code for the bottom note

is pretty easy: refers to

a quarter note, to an eighth

note, to a sixteenth note,

and so on.

48 6682 63 94 2

2 6 Q Q Q Qthe top number indicates thenumberof divisions in a measure. to get thenumber of beats, divide it by three. in fact, wouldnt this bean easier way to notatecompound meters?sorry... theman says

you have to do it

the other way.

the bottom number indicates the type of

notewhich serves as thedivision.

to get thebeat unit,use the note that

is equal to three of these notes.

in a compound meter, the beat unit is

always adotted note!

compound TIME SIGNATURES arestupidly complicated.

notes that haveflags can

be grouped together by using

beams in place of flags.

however, beaming is only used to group notes within beats.

for the most part, you shouldntbeam notesbetween beats,

nor should you tie notes withinbeats.




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notes should be beamed in groups that illustrate th meter.for simple rhythms, this is pretty easy to do;simply group any notes that can be beamed (eighth notes and smaller) intogroups that areequal to the beat unit of the current meter.

rcomplex rhythms,however, things can get complicated... when a rhythm includes thingsesyncopations or other off-beat figures,illustrating the meter may involvedividing

otesacross beat units with ties.fortunately, there is astep-by-step systemfor correctaming these complicated rhythms!

*translation:

step 1:

y,kids!

itsSparkythemusic theory dog!

DOING STUFF THE SPARKY WAY IS ALWAYS FUN

Q:

A:

WOOF!*

Dear Sparky:

I understand that were supposed to beam rhythms to show the organization o

beats in the measure, but is there an easy way to beam complex rhythms?

--A.Y., Owatonna, MN

4 J J J J J J 4 4 J J R R R J R Ror example, letstake 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:findevery group of two or more notes that areboth tied together and

beamed together,and replace them with asingle noteofequivalent value

acorrectly beamed rhythmmay include ties,but it willvery clearlyshow thebeatsin the measure... which, inturn, makes iteasier for the performer to read!

yes, i know itlooks weird...but were not

done yet!

you have notesthat are tied orbeamed, but not

both,then leavethemalone!

=

ont

uch!

hands

off!

yes...

simplify it!

original rhythm:

4 4 4 J J R R R J R R 4



6/50

he Major Scale4 .4

johannsebastianbach

M i n u e t

i n G m

a j o r

notebookforannamagdalenabach,1722

one of the reasons that a particular piece ofmusicsounds the way it doeshas to do with thgroup of notesthe composer decided to use.

take this melody,for example...lets first remove all theduplicate notes, regardless of which octave theyre in.

next, lets put the notesinalphabetical order,starting on the notethat the melody soundedlike it wascenteringon.

what we end up withis the paletteforthis particular piece...

there are actually manydifferent types of scales,

each with a different pattern

of whole stepsandhalf steps.

ahalf stepis thedistance between

two adjacent keys

on thepiano keyboard,regardless ofcolor.

like theboardon which a painter holdsthebits of paintbeing used in the painting being created.

in music, this palette is calledascale.though we usually write

scales fromlow tohigh,the order is actually unimportant;its thenotescontained in the scale that help make a piece sound the way it does.

a whole step is theequivalent oftwo half steps.thisparticulararrangement, wherehalf steps occur betweensteps three and fourand between stepsseven 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 onany note!

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

thef majorscale

theb majorscale

thed flat majorscale

theg flat majorscale

but remember..with

great power

comesgreat

responsibility

wholestep

wholestep

halfstep

halfstep

wholestep

wholestep

wholestep




7/50

f you start writingmajor

calesand pay attention to

eaccidentals that occur,

you are going to start

noticing apattern...

for example look at the flatkeys, starting with the key

that has one flat,all the

way through the key with

seven flats:the flats accrue

in aspecific order.

same with thesharp keys!

so if you look for a key that

has only ad flat,you wont

find it: if a key has ad flat,

it must also have ab flat,an e flatand ana flat!

A

A

b

b

c

c

c

d

d

e

e

f

f

g

g

Key Signatures

B E A D G C F

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 E

B E A D G

B E A

B

B E A D G C

nce writing an entire piece in

sharp majorwould have

een a sure-fire way to get

arpal tunnel syndromewith

l the sharps involved,

omposers pretty quickly came

p with a way to simplify things:

ey signatures.

key signatureis a group of

ccidentals placed at the

eginning of every line of music,

ust to the right of the clef,

at instructs the performer

o apply those accidentals to

very corresponding notein

e piece unless specified

therwise.

h, andanother thing:the

ccidentals have to be placed

thecorrect order,and

ey need to follow a

articular patternof

lacement that variesslightly

epending on theclef being used!

you deviate from this, you, as

composer, will bemocked!

for example, this key

signature indicates that

everyf, c,andgin the

piece should besharped,regardless of octave!

enor clef sharps!whatsourproblem?you need to

conform! ha ha...never!




8/50

F

A

E

B

D

G

C

theorists find itconvenient to

organize all the possiblekey signatures

into achart that shows their relationship

to one another.this chart, called the circle of fifths,

displays each key as aspoke on the circle,

beginning withc majorat the top and

adding accidentals,one at a time, to the

key signatures around the perimeter. wellreturn to this chart

as we continue learning about

how composers usekeys.

as you moveclockwise around the

circle, you addsharps to the key signature.

as you movecounterclockwise around,you addflats to the key signature.

notice how that

eadgcf pattern

ops upall over

the circle of

fifths?

weird!

so could you

continue the

enharmonic

deal and have

the key of

f flat major?

yes, if you want

adouble flat

in your

key signature

nooooo!

to determine thekey

signaturefor a key, look to

see which spokeof the circle

its on to determine how many

flats orsharps it has, and

addaccidentals to the key

signature appropriately.

the keys down here line up

enharmonically...for example,

the key ofd flat majorwill sound

just like the key ofc sharp major.

B

E

A

DG

C C

F

he Circle of Fifths

for example,

e flat major

has three flats,

so it should

look like this:

0

1

2

3

4

56

7

1

2

3

4

56

7

when addingflats to

a key signature, add them

in this order:

when addingsharps,

use thereverse

of the order above.

beadgcf




9/50

an interval isthedistance inpitchbetween two notes.the most basic way which weidentify different intervals isbycounting the stepsbetweenthe two notes.specifically, wecountscale degrees,but theeasiest way to do it isto countlines and spaceson thestaff.when counting,begin with the

bottom noteasone and countuntil you reachthe top note.

this intervalis aseventh!

two notes onhe same line orspace is called

aunison.

when we are talking aboutintervals we sometimes discuss

harmonic intervalsandmelodic intervals.

and when youswap the two notes(move the lower noteup by an octave

so it becomes thehigher note),

that is called inverting the interval.

its helpful to rememberthatseconds always invert

tosevenths, thirdstosixths,and so forth...

the fact that each of

these pairs add up tonineis known to theorists as

the rule of nines.

a harmonic interval is simplytwo notes playedsimultaneously;

a melodic interval isone note

played after the other.

harmonic

interval

melodic

interval

thatslatin forone sound!

and thatslatinfor eight!

the distance froma note to the nextclosest note with

the same letter nameis called an octave.

second

unison

third

fourth

fifth

sixth

seventh

octave

when countinthelines anspaces,wecan safelyignore any

accidentals

this intervalis also a

seventh...

well discushow itsdifferent

verysoon!

1

23

4

5

6

7

smallerintervals

iatonic Intervals

largerintervals

2nd 7th3rd 6th

4th 5th

5th 4th

6th 3rd

7th 2nd

THE RULE

OF NINES




10/50

thedistance of an interval is thefirst part of itsname, but theresmore:every interval has anothequality to it, which well call its inflection.

re the easiest to label: if thewo notes are thesame (forxample,b flatandb flat),hen the inflection isperfect:uch an interval is called aerfect unisonor aerfect octave.

require a little moreexplaining.

if you look at all the fourths and fifths youcan create using only the white noteson thepiano keyboard (in other words, using only notes

without accidentals):

well, if you were to count thehalf-stepsthat make upeach interval, youd notice that all the other ones are

equal in size,but the b to f intervals are not:ftobisa half-steplarger than a perfect fourth, andbtofis a half-stepsmaller than a perfect fifth.

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

anaugmented interval.

you can gofurther,

todoubly augmentedanddoubly diminishedintervals,but... do you really want to?

and theresno such thingas adiminished unison...

just like two thingscant benegative two feet

away from each other!

A5 A4

d5 d4 d8

A1A8

wait...why are the

btofintervalsdifferent?

each one isperfect exceptfor those which usefandb!

unisons and octaves

fourths and fifths

nflection is a bitharder to understand, partly because it depends on the type of intervalso lets start by looking atunisons, fourths, fifthsand octaves.

which raises the question:if the interval is notperfect,than what is it?

erfect Intervals

P

d

A

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

adiminished interval.

p er f e c t

augment ed

d i m i n i sh ed




11/50d6m6M6

Weve talked aboutunisons, fourths, fifthand 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, sixthsandsevenths just work a littledifferently!

for one thing, the inflection for these intervals is neverperfect;it will be eithermajororminor. minor intervals are a half-step smallethan major intervals. like perfect intervals, though, they can also be

augmentedordiminished;augmented intervals are a half-step largerthan major, and diminished intervals are a half-step smaller than minor.

mperfect Intervals

Mm

Ama jor

ugment ed

m i nor

di m i n i sh ed

how do we know if an interval ismajor orminor?we can actuallyuse themajor scaleto find out. notice that, in the major scale,

intervals from the tonic up to another scale degree aremajor.

likewise, intervals from the tonicdown to another scale degreeareminor.

nowing this, when you are confronted with asecond, third, sixthorseventh,you cannd its inflection by thinking about the key signature of the top and/or bottom note.

when the notes of the interval haveaccidentals,the associated key signatures canbe morecomplicated...so its easiest to temporarily ignorethe accidentals,determine the interval, and thenadd the accidentals back one at a timeand

track how the interval changes!

ack! what isthat? lets

first hide theaccidentals...

if the top noteis in the major key of thebottom note,the interval ismajor.if thebottom noteis in the major key of the top note,the interval isminor.

we know this is amajor sixthbecaused,the top note, is in

the key off major

(the bottom note).

and this is a minor seventhbecauseb, bottom note, is inthe key ofa major

(the top note).

major

second

major

third

major

sixth

major

seventh

minor

second

minor

third

minor

sixth

minor

seventh

adding backthesharpmakes it evensmaller...adiminishedsixth! adding backtheflat makesthe intervalsmaller,soits now aminor sixth... eis in thekey ofg,sowe knowthis is amajor sixth. poof!poof!




12/50


the following chart shows an approach for identifyin

any interval.a similar approach can be used when you

need to write a particular interval above or below agiven note:first, ad

a note above or below the given note at the correctdistance,then follo

steps2through 4of this chart to identify it. Then, if necessary,alter th

note you added with anaccidental to create the interval called for.

determine thedistance of the interval

by countinglines andspaces.

count thebottom

note as one, an

continue until yo

reach the top not

*translation:

STEP 1:

cover up allaccidentals.STEP 2:

determine the inflection of the interval

currently shown as follows:

if it is a

unison or octave:

the interval shown

is a

perfect unisonor

perfect octave.

if the interval uses

the notesfandb,

it is either an

augmented fourthor a

diminished fifth.

if the top noteis

in the major key of

thebottom note,

the interval is

major.

if thebottom noteis

in the major key of

the top note,

the interval is

minor.

otherwise, the

interval is

perfect.

really.

itjust is.

if it is a

fourth orfifth:

if it is a

second, third,

sixth orseventh:

STEP 3:

add the original accidentalsback,

one at a time,and track how the

interval changes inflection.

remember:accidentals cannever affect

thedistance of an interval... distance is

determinedsolely by the number of

ines and spacesbetween the two notes!

This method may seemcomplicated at first

but as you use it, youll internalize it and

becomefaster...so get out there and

identify some intervals!

STEP 4:

y,kids!



Q:

A:

WOOF!*

Dear Sparky:

Since we are supposed to use different approaches for identifying perfect and

imperfect intervals, can you summarize them all into one system?

--I.M., Staten Island, N

poof!poof!



13/50

There are actually two things that define akey:

thekey signatureis the most obvious one, but

another important part of a key is the tonic...

thenote around which the keycenters.

he Minor Scales

s key is defined

a key signature

fno sharps and

ats,but also by

e fact that it

nters aroundc.

the

natura

l

minor

scale

the

harm

onic

minor

scale

the

melodi

c

minor

scale

but what if wechange the tonic?what if we use the same notes for the key signature,

but change thenote that the key is centered around?

the thing is,common practice periodcomposers

werent all that crazy about this scale, because

it lacks something themajor scalehas:

a half-step fromsevento one.

his scale is great for buildingchords,so we refer to it as theharmonic minor scale

however, composers didnt use it for writingmelodies,because it had aproblem:

anaugmented secondbetween thesixth andseventh scale degrees.

so, formelodies,they made another change:

they addedanother accidental to raise

thesixth scale degreeby a half-step.

ow, remember... the reason weraised theleading tonein the first place was to create

ension from theseventh scale degreeto tonic.but in a melody, if the seventh scale

degree is followed by thesixth scale degree,we dont need that tension, so we dont

eed to raise the leading-tone at all.

he way we illustrate this is by differentiating betweenascending melodic minorand

descending melodic minor;for descending melodic minor, we dont raiseanything!

now we only

have whole steps

andhalf-steps!

the whole step

here didnt have

the tension

they liked going

into the tonic!

if we center the key around thesixth scale degreeof the major scale,

we get a new scale: theminor scale.

so heres what they did: theyraised the leading-tone by ahalf-stepwit

anaccidental.This gave them the tension they were looking for

half-

step!




14/50

C

+

Cc c

although achord is technicallyany combination of notesplayed simultaneously, inmusic theory we usually definechords as the combination of three or more notes.

riads

secundal

harmonyhords built fromseconds formtone clusters,

which are notarmonic so much

as timbral.

tertial

harmony

quartal

harmonychords built from

perfect fourths

create a differentsound, used in

compositions fromtheearly 1900s

and onward.

quintal

harmonychords built fromperfect fifths

can be respelled asquartal chords,

and as such theydo not create a

separate system ofharmony.

sextalharmony?

septalharmony?

as

with

quintalharmony,

these

are

the

same

as

ter

tialand

chords built fromthirds(MORE

SPECifically, frommajor thirdsand

minor thirds)form the basis ofmost harmony in

thecommonpractice period.

is the chord still tertialif it is built fromdiminished

thirdsoraugmented thirds?

well, diminished thirds soundjust likemajor seconds,andaugmented thirds sound justlikeperfect fourths,so...

thelowest note in the chordwhen the chord is insimple

form is calledtheroot.thenames of the

other notesare based ontheir intervalabove the root.

when we stack

the chord inthirds within one octave,

we get what is called thesimple form of the chord.

no.? rootthirdfifthlets get startedon tertial harmonywith the smallestchord possible:the triad.there arefour ways to create a triad

usingmajorandminor thirds:

th

e

diminish

ed

tria

d

the

m

inor

tria

d

the

maj

or

tria

d

the

aug

mented

tria

d

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

to refer to tertial three-note chords.

we label triads using theirroot (ac minor triad). the abbreviations shown above, which useupper case, lower case,andsymbols to show chord type, are calledmacro analysis.

twominor thirdsstacked together

amajor thirdon topaminor thirdon bottom

aminor thirdon topamajor thirdon bottom

twomajor thirdsstacked together

min 3rd

min 3rd

maj 3rd

min 3rd

min 3rd

maj 3rd

maj 3

maj 3




15/50

riads in Inversion

haydn

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ladies and gentlemen, its

franz joseph haydn!

thank you for having me.

in this piece I use quite a

few triads.

heres one: it has the notes

c, eandg.its ac major

triad!very nice.

thank you. see how the notes

arespread out,and not just

stacked in thirds?its still

a triad,though.

thats because the third of the

chord is in thebass...when that happens,

we say the chord is infirst inversion.

ooh!lets

see em!

and hes brought a

movement from his1767

sonata in g major.

this one isg, b,andd...

ag major triad!but it sounds

different,somehow.

so the thing that makes a

triadroot position, first inversion

orsecond inversionis simply

which note is in the bass?

its hard to believe that the

sound of the chord canchange so

muchjust because of thebass note.

so this one withd, f,anda

is ad minor triad... in

second inversion!

first inversion?what is itcalled when theroot is in the

bass, like thefirst chord

we looked at?

haydn

thats called

root position.

exactly!because the

fifthis in the bass.

thats right!

and each one

has its own

character.

I know, right?

itsawesome.




16/50


17/50

now that were familiar with how

triads work, its time to put them

into the context of akey.

since writing music in a particularkey means using the notes in that key signature

it stands to reason that most of thechords will be built from those same notes

chords which use notes from a particular key signature are said to bediatonic

to that key. diatonic means from the key.that meansno accidentals!

we can quickly show all thediatonic triadsin a particular key by writing ascale

in that key and buildingtriads

oneach note,

using only the notesin that key.

riads Within Tonality

I ii iii IV V vi vii

tonic

Supertonic

mediant

subdominant

dominant

submediant

le

ading-tone

we refer to

hese chords

withroman

numerals as

shown here.

notice how

chord type

is shown by

capitalsor

ower case?

these chords are also

sometimes referred to by

their official names!

menames

dromanmerals...

ferent

pitalization!

this pattern of

major, minoranddiminished

triads is thesame inevery major key!

thesubdominant triadis alwaysmajor,

and theleading-tone triadis always

diminished,whether youre in

c majororf sharp major!

why is the sixth chord called thesubmedian

well, just as themediant chord is halfw

between the tonic anddominant chord

thesubmediant chord is halfway between th

tonic... and thesubdominanta fifthbelo

the diatonic triads inminor work the same way... since were dealing withchords,we

use theharmonic minor scale.however, its important to note that common practic

period composersraised the leading toneonly overdominant function harmon

thedominantandleading-tone triads!

because thedominant andleading-tonetriads bot

have a strong tendency to resolve to tonic,we say th

have a dominant function.thesubdominant andsupertonic chords both tend t

resolve to thedominant,so we say they both have a subdominant function

i ii III iv V VI vii




18/50

ntroduction to Part-Writingas we look ahead, were

confronted with anugly truth:

there isa lotof music

in the history of the world

that is worth studying...

much more than we can

hope to cover in the span

of a few semesters.

ce we cant cover it all, we have to choose aspecific musical languageto study in dept

ts start by narrowing things down to thecommon practice period.

20

00

19

00

18

00

1700

1600

1500

romanticearly 20th

centurycontemporaryclassicalbaroquerenaissance

the common practice period is the music of thebaroque,

classical and romantic erasineuropeandamerica.

the name comes from the fact that most composers used

acommon musical languageduring this time.

its especially worth

studying because

most of the pieces

commonly performed

in concert are

from this period...

...and the language

forms the basis for

the mostpopular

musical styles today.

by analyzing bachs cantatas, we can construct aset of rulesfor writing in

four-voice common practice period musical style, allowing us to study it in depth.

luther j.s.bach

but there is a ton of

common practice period music...

more than we can hope to cover. is there a

representative stylewe can sink ouracademic teeth into?

four-voice chorale writingis a good style to study forseveral reasons:

chorales have a fast

armonic rhythm,allowing

for a larger number of

chords per exercise.

a large percentage of

common practice period music

can be easily reduced to

four-voice counterpoint.

thecantatas of j.s. bach

provide us with a tremendous

amount of consistently-writte

four-voice chorales.

ne of the changes to the catholic church

proposed bymartin luther

was to allow members of

thecongregation to

participate in thesinging

of the liturgy.

more than two hundred years later,j.s. bach

was appointed musical

director at thest. thomas

churchinleipzig, germany

and, in the spirit of luther,

wrotefive years worth

ofliturgical music.

of course, luther was

branded aheretic for

his proposals, and began

his own church in which

to implement his ideas.

each of these works,

calledcantatas,were built

around ahymn melody

harmonized infour parts

for congregational singing.

s t . t h o m a s c h u r

c h

l e

i p z i g

, g e r m a n y




19/50

art-Writing: The Vertical Rules to best understand how

common practice period composerswrote music, we are going to

learn how to write musicusingtheir musical style.

so the patterns we see in their music,

the things they consistentlydidordidnt do,are going to become

rulesfor us in our writing.

its wrong to think these wererules for the composers...they were just writing whatsounded goodto them.

nor should we treat these as rulesfor writing music ingeneral...

each style of writing has itsown set of patterns, and thus

its own rulebook.as a composer,you get to write your own

rulesfor your own style!

were going to start with thevertical rules...that is, the rulethat pertain to building asingle

chordinfour-voice harmony.soprano

soprano

alto

alto

tenor

tenor

bass

bass

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

the tenor and bass can be asfar apartas you want!

second, the voices must be kept intheirproper order;for examplethe tenor shouldnt behigherthan thealto.(Bach did this nowand then, but it was only when hewanted to incorporate somespecia

melodic shapes.)

third, since we havefour voicesand only three notesin a triad,one of the notes should be

doubled.for triads inrootposition,we typically double the

root of the chord unless forced(by other rules) to do otherwise.

lastly, each voice shouldstay in itsrange.these

areconservative rangesformodern singers,but

remember that bachschorales were really

written foramateurs:thecommon peoplewho

ttendedchurch inleipzig!




20/50

art-Writing: The Horizontal Rules

**

thesupreme goalof part-writing isgood voice leading...making each individual voice parteasy to singby avoiding

awkward intervalsorlarge leaps!

before we get to the specificdosanddonts,lets take a lookat some important characteristicsof four-voice part-writing:

note how each voice movesaslittle aspossible,goingto thenearest chord tonein each subsequent chord!

the bass line, since it providesthefoundation of theharmony

in each chord, tends to includelarger leapsthan the other

three voices, but thats okay.

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

when you have theleading tonein an outer voice(soprano or

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

you may not moveany voiceby an interval of anaugmented second

or anaugmented fourth.

its common for the bass tomove in the opposite direction

of theupper three voices.this is calledcontrary motion

and it helps maintainvoice independence.

four-voice harmony is a form ofcounterpoint,which is the combination ofmore than onemelodyplayed simultaneously. in counterpoint,each voice isequally important;no voice isgiven a role of accompaniment to another voice.

thegood news:you can avoid all three of

these by doing the followingwhenever possible:

1. keep the common tone!

2. move to the nearest chord tone

3. use contrary motion!

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

doing theexact same thing. if two (or more)voices were moving inparallel,therichness

of the texture would bereduced.

as a result, common practice composers werevery consistentin avoiding two or more voicesthat moved inparallel perfect octaves, parallelperfect fifths, orparallel perfect unisons!

paralleloctaves!

parallelfifths!

parallelunisons!

in some cases, the voicecan simply stay on thesame

note.This is calledkeeping the common tone,

and itsalways cool!

voice independence?




21/50

art-Writing: Using Inversionswhen common practice composers used inverted chordsin

four-voice writing, they followed somegeneral patterns

regarding which note of the chord should bedoubled.

root position

bass

first inversion second inversion

inroot

position triads,

omposers usually

doubled the root,

which is in the

of the chord.

bass

insecond

inversion triads,

composers usually

doubled the fifth,

which is in the

of the chord.

soprano

soprano

inmajor first

inversion triads,

composers

doubled the

of the chord.

bass

inminor first

inversion triads,

composers

doubled the

the doubling offirst inversion triadsdepends

on the type of the chord being written.

heresanother way to think of it: the only time you cant double thebass is

infirst inversion major triads,where you should double thesoprano instead.

vii6

ii6

the only rule regarding

root position triads

andfirst inversion triads

is thatdiminished triadsare

always placed infirst inversion.

other than that, you can use

root position and first inversion

essentially whenever you want!

if you write a

second inversion triadand

its not one of these three situations,

then you arenot writing in thecommon

practice period style!the composers of

the style just didnt use these chords

willy-nilly.

itssecond inversion triadsthat

have thebig restrictions.

of the chord.

or

bass

indiminished

first inversion

triads, they

doubled the

of the chord.

thecadential chord

s a tonic triad in

second inversion

followed by a

root-position

dominant chord

at a cadence.

64

thepedal chord

s a second inversion

chord where the

bass is treated like

apedal tone.

64

thepassing chord

is a chord placed in

second inversion

where the bass is

treated like a

passing tone.

64

4I6

V IF: 4V6

I6

IF:

4IV6

I IF:

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




22/50

what seems to be

theproblem, sir?well, I thought Id transpose to

minor,you know, to surprise the

family... so I did, and then I raised

all myleading tones, because

Im a common practice period

progression, right?

okay, sure. so whats wrong?

attention! attention!

we need assistance

with anew patient

in emergency treatment

room3b...stat!

ive got

augmented

seconds!

*gasp*

my

augmented

seconds...

theyre

cured!

all in adays work,

my good man.

now lets turn to

the unpleasant matter

of thebill.

in thecommon

practice period,

composers used

harmonic minor

by default. but

whenaugmented

secondsoccurred

they turned to a

hero for help:

melodic minor!

cure your augmented seconds withmelodic minor today!

and for thesedescendingaugmented seconds,were going to useanunraised seventh!v

and that

makes a

minor v

chord!

paging... dr. melodic minor!

doctor, what

can wedo? for this case ofascendingaugmented seconds,

I prescribe araised sixth scale degree!

ooh... amajor iv chord! IV6


art-Writing: Melodic Minormusic theory for musicians and normal peopleby toby w. rush

so anyway,

after we got

him transposed

back to tonic, he

began to modulate

again, and...


23/50

he Harmonic CadencesAcadence is generally considered to be the

last two chordsof aphrase, section or piece.there arefour types of cadences, each withtheir own specificrequirements and variations.

authentic cadenceconsists of adominant function chord (vor vii) moving to tonic.

perf

ect

auth

entic

impe

rfec

t

auth

entic

impe

rfec

t

auth

entic

perf

ect

plag

al

half

phry

gian

decept

ive

phry

gian

impe

rfec

t

plag

al

impe

rfec

t

plag

al

be considered aperfect authentic cadence,

cadence must meetall of the following criteria:

be considered aperfect plagal cadence,cadence must meetall of the following criteria:

if the cadencedoesnt meet

all of thosecriteria, itsconsidered tobe animperfect

authenticcadence!*

***

must use a vchordot a vii)

th chords must beroot position

e soprano mustd on the tonic

e soprano mustveby step

plagal cadenceconsists of asubdominant function chord (ivor ii) moving to tonic.

half cadenceisany cadence that ends on thedominant chord (v).

deceptive cadenceis a cadence where thedominant chord (V)resolves to somethingther than tonic...almost always thesubmediant chord (vi).

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

if the cadencedoesnt meet

all of thosecriteria, itsconsidered tobe animperfect

authenticcadence!*

***

must use a iv chordot a ii)

th chords must beroot position

e soprano mustd on the tonic

e soprano mustep thecommon tone

*

***it occurs only inminor

it uses a iv chord moving to v

the soprano and bass moveby stepincontrary motion

the soprano and bass bothend on thefifth scale degree

V I vii6

I V64 I

IV I IV6

I ii I6

I V

VG:

G:

G:

G: G: G:

G: G:

e: e:

vi

iv6

V iv V

really, its thepsych-out cadence,in thatyouexpect it to resolve to tonic, but itdoesnt.

and, in fact, its more common to see this inthemiddle of the phrase rather than theend...

where you might call it a cadence-like structure!




24/50ii iii vii

6V IC:

how did composers of thecommonpractice perioddecide which orderto putchords in? did they just throwthem down on paperhaphazardly?

s a matter of fact, there are certain chord progressions that appearmorerequently,and there are others that areavoided pretty consistently. whilehe choices were always based on whatsounded goodto the composer, asheorists there is apattern in their choices that we can use to easily rememberhich chord progressions work and which onesdont.

o understand this pattern, we need to think in terms ofroot movements.a root movementhe basic interval between the root of one chord and the root of the next chord. youont have to worry about the intervals inflection, just itsdistance anddirection.

or example, to determine the root movementere, we look at theroot (notbass) of eachhord and figure the interval between them.

so heres the pattern: common practiceperiod composers generally used root

movements ofup a second, down athird, anddown a fifth!

remember... sincenflection doesnt

matter, we cannoreaccidentalswhen we figure the

root movements.

so, for example, ag chordto ane chord is down a third, but so is

gtoe flat,andg sharptoe flat!

thats not say that theynever used other rootmovements, but it didnthappen very often.

sequences of chords thatdontfollow this patternare calledretrogressions,and they are consideredunstylistic.

here are also four simple exceptions to this pattern:

any chord canmove to tonic,

tonic can moveto any chord,

any chord canmove to dominant,

and the leading-tonetriad must move to tonic

itsdown a seventh, butsince octaves dont matter,we invert it toup a second

armonic Progression

2

3

5

I I V vii I

lets try it...say you havea supertonicchord and

you are tryingto decide what

chord to useto follow it. yo

u

can

move

upasecondto

a

me

diantchord...

yo

u

can

move

dow

nafifthto

a

dom

inantchord...

oryo

u

can

use

the

first

exception

and

go

to

a

tonicchord!

yo

u

can

move

dow

nathirdto

aleading-tone

chord...




25/50

iatonic Common Chord Modulationmodulation is the process ofchanging to a different keywithin a piece of music.

there are several differentways to modulate; perhaps the

simplest is theunpreparedmodulation, where the musicpauses and suddenly changes

key, often up ahalf-step.

common practice period composers,however, preferred a particular typeof modulation that required a littlemore planning: thediatonic common

chord modulation.as the namesuggests, this uses a chord whichisdiatonic in both the outgoing keyand thenew key.

lets say were starting off inc major...here is a list of all the keys whichhave chords in commonwith c major (the specific chords are highlighted):

ys which haveords in commone this arelledrelated keys.

notice how these keyare all close to on

another on thcircle of fifths

hey... what is thisportrait doing here?

manilow

i ii III iv V VI viia:

I ii iii IV V vi viiB :i ii III iv V VI viib:

I ii iii IV V vi viiD:

i ii III iv V VI viid:

i ii III iv V VI viie:I ii iii IV V vi viiF:

I ii iii IV V vi viiG:

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

to use this type ofmodulation, a composerouldpivot the harmonyaround the chord that

fit into both keys.As theorists, we show

thispivot chordbyanalyzing the chord in

both keys.

note that the pivotchord isalwaysthe

last chordthat canbe analyzed in theold key...the firstaccidentals will alwaysoccur in the chord

immediately followinthepivot chord!




26/50

uspensions are typically further identifiedy number.The first number represents theterval between thenote of suspensionandhebass.The second number represents theterval between thenote of resolutionandhebass.

he exception to this rule is the2-3orasssuspension, where the numbersepresent the intervals between thebasswhere the suspension occurs) andhichever voice has the note which is a

econd (not counting octaves) abovehe bass.

anon-harmonic toneis a note thadoesnt fit into a chord. we classifynon-harmonic tones by how they are

approached andresolved!

Non-Harmonic Tones

passing

tone

name

abbr

eviatio

n

appr

oach

reso

lutio

n

notes

exam

ple

step steppt

resolves by continuing inthe same direction as the

approach.

ppoggiatura leap stepapp resolves in oppositedirection from approach.

changingtones

any step cttwo non-harmonic toneson either side of thenote of resolution.

suspension commontone

stepsus a note held over froma previous chord andresolved down.

pedal tone common

tonecommon

toneped

4-3sus

9-8sus

2-3(bass)sus

7-6sus

a chord tone whichtemporarily becomesa non-harmonic tone.

eighboringtone

step step Ntresolves by returning tothe note preceding the

non-harmonic tone.

scape tone step leapet resolves in opposite

direction from approach.

anticipation any common

toneant

a chord tone playedbefore the rest ofthe chord arrives.

retardation common

tone stepret

a note held over froma previous chord and

resolved up.




27/50


4I6

4

IV V6

C:

vi VC:

thisais thenote of suspension...

it doesnt belong inthisg major triad.

it resolves tothisg,whichdoesfit in the chord.its thenote ofresolution!

when analyzing suspensions, it is important to identify both thenote of suspension(the non-harmonic toitself) and thenote 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 the

note of suspensionand thebass,and theinterval between the

note of resolution

and thebass.

the only exception to thisis the2-3 suspension,wherthe suspension occurs in the

bass.for this one, we look

at the interval between thenotes of suspension andresolution and thenearest

chord tone,whichever voiceit may be in.

when writing an example whichincludes a suspension, it is veryoften useful tobegin by writingthe chord that is going to contain

the suspension, then adding thesuspension, and finishing by writingthechord of approach.

*translation:

y,kids!



Q:

A:

WOOF!*

Dear Sparky:

Can you elaborate on why suspensions are identified by numbers? Also, what

should one watch out for when writing suspensions in four-part harmony?

--S.S., Detroit, MI

IV V6

C:

this a6th

this isa 7th!

...so its a7-6 suspension!

this isa2nd!

this isa3rd!

...so its a2-3 suspension!

I6

II6

I6

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

for the 9-8 suspension,the suspension resolvesto an octave above thebass... thatseasy,sinceany chord can include

an octave.I6

I

for the 4-3 suspensionand2-3 suspension,you

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

use anythingexcept asecond inversiontriad.

for the 7-6 suspension,the suspension resolvesto ansixth above thebass. that means youcant use a chord in

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

second inversiontriad!



28/50


were going to take a little breakfrom the usual stuff and... hey,

itsludwig van beethoven!

Ill tell you whatsgoing on: ImgrumpyI bet archduke rudolp

20 guldenthat Icould write

500 measures

of music this week andso far Ive onlycome up with

four stinkin notes!

whats going on, maestro?

repetition

motive repetition

nversion

nterval contraction

nterval expansion

diminution

augmentation

rhythmic

metamorphosis

mitation

hey, itscool,mr. b...we can use these notesas amotive,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 and

weep,rudy!

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

4/4 time,right?

so lets use2/4 timeinstead!

uh, yeah...

so, heh heh....hat gets us to253

measures...

beethoven

aw, dang!lets go

double or

nothing!

bbb J J bbb J J J

motive

motive

augmentation of original motive

metamorphosis of original motive

motive

imitation

int. expansion

sequence

inversion of original motive

sequence sequence

bbb bbb .

bbb bbbbbb

j .

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

dont 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 motives rhythm(other than just changing the

tempo, as described above)

an echo effect between different voices

(between instruments in an ensemble, forexample, or between registers on the piano)

original motive



29/50

when we talk about theform 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.

inary Form

baroque dance suites were written for varying instrumentation; many were writtenforkeyboard(usuallyharpsichord orclavichord), others were written for chamber

groups, and some were even written forfull orchestra.

each movement of these suites would be written in the style of a particular baroque danceallemande, 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 tobaroque dance form.

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

aandb.

the sections might be contrastinginmood, tempo, key,or even in a

combination of these characteristics.

A Bb i n a r y f o rm

another somewhat rare variation ofbinary form isrounded binary form,where theAsection returns after theend of thebsection. this reprise of

theasection, however, isshortened,

so we refer to it as a prime.

A ABrou n ded b i n a r y f o rm

binary form is used inbaroque dancesuitesin a very specific way. In thesepieces, both sections are repeated.theAsection begins in the primary keyand modulates to thekey of the

dominant,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 roqu e d a n c e f o rm

I V V I

1010111011011110111011100100001001000000101100101101111011101010010000001

00010111001001100101001000000111001001100101011000010110110001101100011110

10010000001101001011011100110001101110010011001010110010001101001011000100

11011000111100100100000011001110110010101100101011010110111100100101110




30/50

ernary Form

in ternary form, theasection appearsboth at the beginning and at the end;

like binary form, thebsection iscontrasting in character.

the reprisedasection may be an exactrepeat of the firstA,or it may be

slightly different, but thelength oftheasections should be similar.

theminuet and triois a variation on

ternary form used for instrumentalmusic. instead of writing out the reprised

asection, the score will place theinstruction da capo al fineafter the

bsection, which means to return to thebeginning, play through theasection,and end the piece.

its worth mentioning thatthere is a common formthat is descended from

minuet and trioform:themilitary march form

favored by john philipsousa and other american

march composers.

in themilitary march form,the a section is split into twosubsections, called thefirst strainandsecond strain.the trioadds a flat(or removes a sharp) from the keysignature, modulating to the key of thesubdominant.most marches begin with a shortfanfare, and repeat thetrio, placing a short, intensely dramatic passage between

repetitions called thedogfight orbreakstrain.

this is different fromrounded binary,where the reprisedasection (which wecalleda prime) issignificantly shorterthan the firstasection.

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

when playing through the repriseda section.

ternary formis a three-part form.rather than using three completelydifferent sections,most pieces internary form consist of two sections,

the first of which isreprised.

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 ch f o r m

A B(dogfight)

fanfare

1st & 2nd

strains

trio

I IV

sousa




31/50

sonata allegro formis a specific form

first used byearly classicalcomposers i

opening movements of multi-movement

works for solo, chamber or large groups

it was eventually adopted by other composers

of the classical and early romantic eras.

he form itself is based from

ternary form, in that the

irst large section is reprised

at the end of the form,

one of the most important features of sonata allegro form is the two primary themes

hat make up the exposition. THese two themes will beconstrasting in characterand, at

east in the exposition, will be indifferent keys.in a major work, the second theme will

e in the key of thedominant;in a minor piece, the second theme will be in therelative

major.in therecapitulation,however,both themes are played in the tonic!

he diagram above shows therequired elementsof sonata form; in the diagram below,

everal other elements, which are optionallyincluded, are also shown.

ear in mind that composers did what they wanted to... some of the greatest pieces written

n sonata allegro form feature places where the composer artfullybroke these rules!

onata Allegro Form

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

A ABfirst

theme

major

keys:

minor

keys:

second

theme

development

of main themes

first

theme

second

theme

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 ts )

A ABintroductio

n

transition

codetta

coda

first

theme

second

theme

development

of main themes

addition of

others

first

theme

second

theme

development recapitulationexposition

I V I I

i III i i

major

keys:

minor

keys:




32/50

iatonic Seventh ChordsWhat are they?

Remember,diatonic

means from the key.

so a diatonic chord is one

that only uses notes in

the key signature.

No accidentals!

w w w w w w wdiatonic seventh chordsare the

seventh chords you can create using

only the notes in a particular key.

I7

ii7

iii7

IV7

V7

vi7

vii7

there are eight possible types of

seventh chords in tertial harmony

but the composers of the commo

practice period only usedfive:

C: w w w w w w wi7

ii7

III7

iv7

V7

VI7

vii7

a:

re they are

major and

minor.

emember:

we only

raise the

eading-tone

over

dominant-

function

harmony!

wthema

jor

seventh

major 7th

above root

major triadwwww

the

majo

r-mino

r

seventh

the

mino

r

seventh

the

half-diminish

ed

seventh

the

fullydi

minis

hed

sevent

h

minor 7th

above root

major triad

minor 7th

above root

minor triad

minor 7th

above root

diminished tria

diminished 7th

above root

diminished tria

we use 07 for

half-diminished sevenths

and 07 for

fully diminished sevenths.

n harmonic progressions,diatonic sevenths can

e used anywhere you can use a diatonic triad with the

ame root. V

7I7

ii7

vi7

iiiviiIVIV 7

in fact, these chords can

be approached and resolved

using any of the same threeroot movements

as triads use.

2

3

5

ith the diatonic seventh chords, we add a

ourth root movement: the common root.

owever, this root movement can only be

sed to increase tension,so going from

seventh chord to a triad is avoided.

1

V7

VV7

V

respect the seventh!respect the seventh!

hen using these chords in four-part writing in

act, when you useany seventh chord in four-part

riting, you must always,alwaysremember to...ww we seventh of the chordmost often approachedthe common tone.owever, it is okay toproach the seventhom below by a stepr a leap, or from above

a step.

u mustneverapproach

e seventh by aleapfrombove!

The seventh of the chord

isalways resolveddown

by step.always!

no, im serious. dontever

resolve the seventh of a

seventh chord any other

way.

doing so will cause you

certain death!

seventh chords havefour notes,so doubling in four-p

harmony is not an issue... but if you need to use irregu

doubling,double the root and omit the fif

theadd-a-seventh-inator

pat.pending




33/50

he Dominant Seventh

I

I

I

IVV7

V7

V7

I6

V7

V6

V7

V

7

V

7hedominant seventh is thediatonic seventhchordbuilt on thefifth scale degree.wealready discussed diatonic seventh chords...why give this oneall this special attention?for one thing, thedominant seventh is,

by far, themost common

seventh chordused bythe composers of the

common practice period.

rst, a note on terminology:

he terms major-minor seventhnd dominant seventh are notterchangeable! Major-minoreventh is the chords type,anddominant seventh is therole

he chord plays in thecontext

of a particular key.

the reason these are oftenconfused is that inpopular

and jazz theory,the termdominant is used to labelthe chord type as well asthe chordsrole.

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

there are a few thingsthat apply to it thatdont

applyto the other diatonicseventh chords.

w bb w

its just a major-minor seventh...

until its placed in a particular key!

he other important thing to know about the dominant seventh chord is that common practiceriod composers would sometimes use somenon-standardways of resolving thesevent

n this resolution, the seventh is stillresolveddown by step,but it takes anornamental detourbefore getting there.

Here, the resolution of the seventh isdelayed by moving to some other chord(usually thesubdominant) and having theseventh of the chordhold outuntil thedominant seventh returns.

in this resolution, the seventh of the choris still resolveddown by step,but the noit resolves to appears in thebass voice.

the voice thathad the seventhresolvesup,usually bystep.

after the V7

returns,thevoice that hasthe seventhshouldstill

resolve itappropriately!

this is the hot potato resolution: instead obeing resolved down by step in the same voicthe seventh ispassed to another voiceinanother dominant seventh chord.

the ornamentcan be anyshape orlength, but it

must resolveto the note

down a step

from theseventh of theseventh chord.

seventh

seventh

ornamentresolution

resolution

transferredto tenor

ornamental resolutionhe

delayed resolutionhe

bass resolutionthe

transferred resolutionthe

? the seventh stillneeds to resolvedown by stepbywhatever voice isthe last to have it.

? If the bass voice gets it, heresolves itimmediately,ending the fun for everyone.

5

?

?

resolution

seventh




34/50

xtended Harmonies

diminished diminished

diminished

doubly-diminished

diminished

thirteenth chord

wbbdiminished diminished


diminished

thirteenth chord



minor

thirteenth chord


minor diminished

diminished

thirteenth chord


minor diminished minor

thirteenth chord


minor perfect minor

thirteenth chord

wbdiminished diminished

minor perfect MAJOR

thirteenth chord

wdiminished MINOR MINOR

DIMINISHED DIMINISHED

thirteenth chord

wbbdiminished MINOR MINOR

DIMINISHED MINOR

thirteenth chord

wbbdiminished MINOR MINOR

PERFECT MINOR

thirteenth chord

wbdiminished MINOR MINOR

PERFECT MAJOR

thirteenth chord

wdiminished MINOR MAJOR

PERFECT MINOR

thirteenth chord

wbdiminished MINOR MAJOR

PERFECT MAJOR

thirteenth chord

wdiminished MINOR MAJOR

AUGMENTED MAJOR

thirteenth chord

wMINOR MINOR MINOR

DIMINISHED MINOR

thirteenth chord

wbMINOR MINOR MINOR

PERFECT MINOR

thirteenth chord

wbMINOR MINOR MINOR

PERFECT MAJOR

thirteenth chord

wMINOR MINOR MAJOR

PERFECT MINOR

thirteenth chord

wbMINOR MINOR MAJOR

PERFECT MAJOR

thirteenth chord

wMINOR MINOR MAJOR

AUGMENTED MAJOR

thirteenth chord

wMINOR MINOR MAJOR

AUGMENTED AUGMENTED

thirteenth chord

wbMINOR MAJOR MINOR

PERFECT MINOR

thirteenth chord

wbMINOR MAJOR MAJOR

PERFECT MAJOR

THIRTEENTH CHORD

wMINOR MAJOR MAJOR

AUGMENTED MAJOR

thirteenth chord

wMINOR MAJOR MAJOR

AUGMENTED AUGMENTED

thirteenth chord

wMINOR MAJOR AUGMENTED

AUGMENTED MAJOR

thirteenth chord


AUGMENTED AUGMENTED

thirteenth chord


DOUBLY-AUGMENTED

AUGMENTED

thirteenth chord

wMAJOR MINOR MINOR

DIMINISHED MINOR

THIRTEENTH CHORD

wMAJOR MINOR MINOR

PERFECT MINOR

thirteenth chord

wMAJOR MINOR MINOR

PERFECT MAJOR

thirteenth chord

wMAJOR MINOR MAJOR

PERFECT MINOR

thirteenth chord

wMAJOR MINOR MAJOR

PERFECT MAJOR

thirteenth chord

wMAJOR MINOR MAJOR

AUGMENTED MAJOR

thirteenth chord

wMAJOR MINOR MAJOR

AUGMENTED AUGMENTED

thirteenth chord

wMAJOR MAJOR MAJOR

PERFECT MINOR

thirteenth chord

wbMAJOR MAJOR MAJOR

PERFECT MAJOR

THIRTEENTH CHORD

wMAJOR MAJOR MAJOR

AUGMENTED MAJOR

thirteenth chord

wMAJOR MAJOR MAJOR

AUGMENTED AUGMENTED

thirteenth chord

wMAJOR MAJOR AUGMENTED

AUGMENTED MAJOR

thirteenth chord


AUGMENTED AUGMENTED

thirteenth chord


DOUBLY-AUGMENTED

AUGMENTED

thirteenth chord

wGMENTED MAJOR MAJOR

PERFECT MAJOR

THIRTEENTH CHORD

wAUGMENTED MAJOR MAJOR

AUGMENTED MAJOR

thirteenth chord


AUGMENTED AUGMENTED

thirteenth chord

wAUGMENTED MAJOR

AUGMENTED AUGMENTED

MAJOR

thirteenth chord


AUGMENTED AUGMENTED

AUGMENTED

thirteenth chord

wAUGMENTED MAJOR

AUGMENTED

DOUBLY-AUGMENTED

AUGMENTED

thirteenth chord

wAUGMENTED MAJOR

AUGMENTED

DOUBLY-AUGMENTED

DOUBLY-AUGMENTED

thirteenth chord

wAUGMENTED AUGMENTED

AUGMENTED AUGMENTED

MAJOR

thirteenth chord


AUGMENTED AUGMENTED

AUGMENTED

THIRTEENTH CHORD


AUGMENTED

DOUBLY-AUGMENTED

AUGMENTED

thirteenth chord


AUGMENTED

DOUBLY-AUGMENTED

DOUBLY-AUGMENTED

thirteenth chord


DOUBLY-AUGMENTED

DOUBLY-AUGMENTED

AUGMENTED

thirteenth chord


DOUBLY-AUGMENTED

DOUBLY-AUGMENTED

DOUBLY-AUGMENTED

thirteenth chord


DOUBLY-AUGMENTED

TRIPLY-AUGMENTED

DOUBLY-AUGMENTED

thirteenth chord

w



eleventh chord


minor diminished

eleventh chord


minor perfect

eleventh chord

wdiminished minor

minor diminished

eleventh chord

wbdiminished minor

minor perfect

eleventh chord

wdiminished minor

major perfect

eleventh chord

wdiminished minor

major augmented

eleventh chord

wminor minor minor

diminished

eleventh chord

wminor minor minor

perfect

eleventh chord

wminor minor major

perfect

eleventh chord

wminor minor major

augmented

eleventh chord

wminor major major

perfect

eleventh chord

wminor major major

augmented

eleventh chord

wminor major

augmented augmented

eleventh chord

wmajor minor minor

perfect

eleventh chord

wmajor minor major

perfect

eleventh chord

wmajor minor major

augmented

eleventh chord

wmajor major major

perfect

eleventh chord

wmajor major major

augmented

eleventh chord

wmajor major

augmented augmented

eleventh chord

wmajor major

augmented

doubly-augmented

eleventh chord

waugmented major

major perfect

eleventh chord

waugmented major

major augmented

eleventh chord

waugmented major

augmented augmented

eleventh chord

waugmented major

augmented

doubly-augmented

eleventh chord

waugmented augmented

augmented augmented

eleventh chord


augmented

doubly-augmented

eleventh chord


doubly-augmented

doubly-augmented

eleventh chord

w


minor

ninth chord

wdiminished minor minor

ninth chord

wdiminished minor major

ninth chord

wminor minor minor

ninth chord

wminor minor major

ninth chord

wminor major major

ninth chord

wminor major

augmented

ninth chord

wmajor minor minor

ninth chord

wmajor minor major

ninth chord

wmajor major major

ninth chord

wmajor major

augmented

ninth chord

waugmented

major major

ninth chord

waugmented major

augmented

ninth chord


augmented

ninth chord

w

minished diminished

seventh chord

wdiminished minor

seventh chord

wminor minor

seventh chord

wminor major

seventh chord

wmajor minor

seventh chord

wmajor major

seventh chord

waugmented major

seventh chord

waugmented augmen

seventh chord

wdiminished triad

wminor triad

wmajor triad

waugmented triad

wso far, weve talked about two

types of tertial chords: triads and

seventh chords.remember, tertial

chords are chords constructed

by stackingmajorandminor thirds!

now, there arefourtypes of triads

andeight types ofseventh chords,

even though common practice period

composers only usedfive of them.

o that makes for twelve chord types so far... but what if we keep going? what other chor

pes can we make by stacking major and minor thirds? tertial chords withfive, sixandseve

otes are calledninth chords, eleventh chordsand thirteenth chordsrespectively.

ddenly the possibilities increase from twelve...

...to124!

thegood news:common

practice period composers

only used these extended

harmoniesasdiatonic

chordson thedominant.

seriously:these are the onlyextended harmonies used by

common practice period composers.

in fact, the v11and v13werent used

much before theromantic era.

what about afifteenth chord

try it: if you add another third

on top of a thirteenth, you

are just doubling theroot.

so tertial harmony stops at13!

G: V9

G: V11

G: V

13

? now, when we put these chords into

four-part harmony,weve got a

problem: they all have more than

four notes. So we have to make

the tough call: which ones do

we cut from the team?

finally, theninth, eleventhor

thirteenth of the chord is what

defines it as a ninth, eleventh

or thirteenth chord.

so how do you put these in

four-part harmony?

omit the fifthand use only

theninth, eleventhor

thirteenth as necessary.

oh, and if youre worried

about inversions:stop.

in the common practice

period, extended harmonies

are almost always found

inroot position.

root

third

thirteenth

we need to keep theroot

because it defines the chord.

similarly, the third is what

makes the chord tertial.

theseventh acts as abridge

to the extended harmony,

preventing the chord from

coming across as two separateharmoniesplayed at the same time.

C: V

13

seventh




35/50

up to this point, all the chords weve

been talking about have been built using

only the notes in thecurrent key.

essentially, this means

no accidentals,with the

exception of the raisedsixth

andseventh scale degrees

inminor,which we

consider to be

part of the key.

first, every altered chord has to

have at least oneaccidental...

f it doesnt have any accidentals,

then bydefinitionits a

diatonic chord!

with few exceptions,

altered chords can use

the samebasic root

movementsthat weve

been using.

avoidcross relations.

a cross relation occurs when a note

appears with two different accidentals

in two consecutive chords,in two

different voices.

lastly, when you use these chords

inpart-writing, you should,

whenever possible, resolve the

altered notesin thedirection

of their alteration.

so if a note has aflat, try to

resolve itdown by step or by leap.

and we generally avoiddoublingaltered tones,

since doing so would tend to causeparallel octaves

second, altered chords can be easily used in place of their

diatonic counterparts. in other words, you can add somepizazzto a composition by replacing adiatonic chordwith an

altered chord

that has the

same root.

now that weve covered all

the possiblediatonic chordsin

tertial harmony, its time to open

the door to notes outside the key

these altered chordsadd a

certain richness to the harmony

by using one or more notes

that arenot in the key signature

and thus requireaccidentals.

diat

onic

altere

d(c

hrom

atic)

27theory

diatoni

ctriads

diatoni

cseve

nths

extend

edhar

monies

8

15

88

5

Altered Chords

BORROWED

CHORDS 26NEAPOLITAN

SECONDARY

DOMINANTS

dAUGMENTED

SIXTHS

V Secondary

Subdominants

$

well be covering

several categories

of altered chords,

each of which have

their own unique

rules for use.

however, there are

a few things that

they all have in

common!

bb bb V/

V ii

altered diatonic

cc

I IV

6IV V

7vi

bVI

23

5

1

like the diatonic sevenths,

however, thecommon root

should only increase tension...dont move from an altered chord

to its diatonic counterpart.

bb

ii65 V

bb




36/50

orrowed Chords

bbb w w w w w w

w w w w w w

altered chords use notes outsidethe scaleas a means of adding adifferent colorto the chord.

for example, the following chords arediatonic chordsinc minor:

orrowed?hy call themt when majoreverbringsthem back?

but if we use them in a major key, they requireaccidentals and arethereforealtered chords.we call theseborrowed chordsbecause they

areborrowedfrom theparallel minor.

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

one possibility is using notes and chordsfrom theparallel minor.

iic: ii7 III iv VI vii7

iiC: ii7 III iv VI vii7b b

hey, minor!ll have themck by tuesdaythis time, Ipromise!

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

borrowed chordsin the commonpractice period. (One of them, the

major triad on the lower

music theory for musicians and normal people

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