Music Theory for Musicians and Normal People Diatonic …harmony. sextal harmony? septal harmony? as...

Diatonic

Harmony

Music Theory for Musicians

tobyrush.com

and Normal People

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 startedon tertial harmony

with the smallestchord possible:

the triad.

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

& œœœbb & œœœb & œœœ & œœœ#

the

dimini

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the

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the

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the

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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

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

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

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

œœœ rootthirdfifth

Triads in Inversion

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ladies and gentlemen, it’sfranz joseph haydn!

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

few triads.

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

triad! very nice.

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

a triad, though.

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

ooh! let’ssee ‘em!

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

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

different, somehow.

so the thing that makes atriad root position, first inversion

or second inversion is simplywhich note is in the bass?

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

much just because of thebass note.

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

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

bass, like the first chordwe looked at?

haydn

that’s calledroot position.

exactly! because thefifth is in the bass.

that’s right!and each onehas its owncharacter.

I know, right?it’s awesome.



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(5)(3)

6 6 6# 6# 6# ##Figure 1. The Basso Continuo

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

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

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

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

lastly, accidentals areapplied to the interval

they appear with. if youhave an accidental by

itself, it applies to thethird above the bass.

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

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

wooo!

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

don’t overthink these:if the composer wants

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

the key signature, thefigured bass will have

a natural, not a sharp.

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

if there areno numbers,

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

root position triad!

here, the sharpapplies to the

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

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

it to the third abovethe bass note.

note that there isa natural, not a flat,

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

would write a c flat.

a six by itselfindicates a sixth

and a third abovethe bass, whichcreates a first

inversion triad!

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

giving you a secondinversion triad!

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

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

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

Figured Bass

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

into the context of a key.

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

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

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

Triads Within Tonality

& œœœ œœœœœœ œœœ

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I ii iii IV V vi vii°

tonic

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media

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we refer tothese chords

with romannumerals asshown here.

notice howchord typeis shown by

capitals orlower case?

these chords are alsosometimes referred to by

their official names!

same namesand romannumerals...differentcapitalization!

this pattern ofmajor, minor and diminished

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

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

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

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

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

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

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

& œœœ œœœœœœ œœœ

œœœ# œœœœœœ#

i ii° III iv V VI vii°



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

confronted with an ugly truth:

there is a lot of musicin the history of the world

that is worth studying...

much more than we canhope to cover in the span

of a few semesters.

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

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

2000

1900

1800

1700

1600

1500

romantic early 20thcentury

contemporaryclassicalbaroquerenaissance

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

a common musical language during this time.

it’s especially worthstudying because

most of the piecescommonly performed

in concert arefrom this period...

...and the languageforms the basis forthe most popular

musical styles today.

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

luther j.s. bach

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

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

academic teeth into?

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

chorales have a fastharmonic rhythm, allowing

for a larger number ofchords per exercise.

a large percentage ofcommon practice period music

can be easily reduced tofour-voice counterpoint.

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

amount of consistently-writtenfour-voice chorales.

one of the changes to the catholic churchproposed by martin luther

was to allow members ofthe congregation to

participate in the singingof the liturgy.

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

of course, luther wasbranded a heretic for

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

each of these works,called cantatas, were built

around a hymn melodyharmonized in four partsfor congregational singing.

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Part-Writing: The Vertical Rules

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to best understand howcommon practice period composers

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

their musical style.

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

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

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

nor should we treat these as rulesfor writing music in general...

each style of writing has 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!

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Part-Writing: The Horizontal Rules

**

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..

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

awkward intervals or large leaps!

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

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

the bass line, since it providesthe foundation of the harmony

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

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

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

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

you may not move any voiceby an interval of an

augmented secondor an augmented fourth.

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

of the upper three voices.this is called contrary motion

and it helps maintainvoice independence.

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

the good news:you can avoid all three of

these by doing the followingwhenever possible:

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

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

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

of the texture would be reduced.

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

paralleloctaves!

parallelfifths!

parallelunisons!

in some cases, the voicecan simply stay on the same

note. This is calledkeeping the common tone,

and it’s always cool!

voice independence?



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

root position

bass

first inversion second inversion

in rootposition triads,

composers usuallydoubled the root,

which is in the

of the chord.

bass

in secondinversion triads,composers usuallydoubled the fifth,

which is in the

of the chord.

soprano

soprano

in major firstinversion triads,

composersdoubled the

of the chord.

bass

in minor firstinversion triads,

composersdoubled the

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

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

vii°6ii°6

the only “rule” regardingroot position triads

and first inversion triadsis that diminished triads are

always placed in first inversion.

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

if you write asecond inversion triad and

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

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

willy-nilly.

it’s second inversion triads thathave the big restrictions.

of the chord.

or

bass

in diminishedfirst inversion

triads, theydoubled the

of the chord.

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

64

the pedal chordis a second inversionchord where thebass is treated likea pedal tone:a note preceded andfollowed by thesame note.

64

the passing chordis a chord placed in

second inversionwhere the bass is

treated like apassing tone:

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 tones, becauseI’m a common practice period

progression, right?

okay, sure. so what’s wrong?

attention! attention!we need assistancewith a new patient

in emergency treatmentroom 3b... stat!

BX

i’ve gotaugmentedseconds!

*gasp*

X myaugmentedseconds...

they’recured!

all in a day’s work,my good man.

now let’s turn tothe unpleasant matter

of the bill.

in the commonpractice period,composers usedharmonic minor

by default. butwhen augmented

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

cure your augmented seconds with melodic minor today!

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

an unraised seventh!

v

and thatmakes aminor vchord!

B

BX

paging... dr. melodic minor!

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

I prescribe a raised sixth scale degree!

ooh... 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.

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

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

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

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

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

both chords must bein root position

the soprano mustend on the tonic

the soprano mustmove by step

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

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

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

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

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

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

both chords must bein root position

the soprano mustend on the tonic

the soprano mustkeep the common tone

****it occurs only in minor

it uses a iv chord moving to v

the soprano and bass moveby step in contrary motion

the soprano and bass bothend on the fifth scale degree

V I vii°6 I V64 I

IV I IV6 I ii I6

I V

VG:

G:

G:

G: G: G:

G: G:

e: e:

vi

iv6 V iv V

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

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

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



ii iii vii°6 V IC:

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

as a matter of fact, there are certain chord progressions that appear morefrequently, and there are others that are avoided pretty consistently. whilethe choices were always based on what sounded good to the composer,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-tonetriad 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&

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

you are tryingto decide whatchord to useto follow it.

you c

an m

ove

up a

seco

nd to

a m

edia

nt c

hord...

you c

an m

ove

do

wn a

fif

th to

a d

om

inant c

hord...

or y

ou c

an u

se t

he

fir

st e

xceptio

n a

nd

go to a

to

nic

chord!

you c

an m

ove

do

wn a

thir

d to

a l

eadin

g-t

one

chord...



&˙̇̇ ˙̇̇

˙

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

there are several differentways to modulate; perhaps the

simplest is the unpreparedmodulation, where the musicpauses and suddenly changes

key, often up a half-step.

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

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

keys which havechords in commonlike this arecalled related keys.

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

approached and resolved!

Non-Harmonic Tones

passingtone

name

abbr

eviat

ion

appr

oach

reso

lutio

n

note

s

exam

ple

step stepptresolves by continuing inthe same direction as the

approach.

appoggiatura leap stepapp resolves in oppositedirection from approach.

changingtones

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

suspensioncommon

tonestepsus

a note held over froma previous chord and

resolved down.

pedal tonecommon

tonecommon

toneped

4-3sus

9-8sus

2-3(bass)sus

7-6sus

a chord tone whichtemporarily becomesa non-harmonic tone.

neighboringtone

step stepNtresolves by returning tothe note preceding the

non-harmonic tone.

Escape tone step leapet resolves in oppositedirection from approach.

anticipation anycommon

toneant

a chord tone playedbefore the rest ofthe chord arrives.

retardationcommon

tonestepret

a note held over froma previous chord and

resolved up.




4 I6 4IV V6C:

vi VC:

this a is thenote of suspension...

it doesn’t belong inthis g major triad.

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

resolution!

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

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

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

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

*translation:

Hey,

kids!

it’s Sparkythe music theory dog!

DOING STUFF THE SPARKY WAY IS ALWAYS FUN!

Q:

A: WOOF!*

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

--S.S., Detroit, MI

IV V6C:

this isa 6th!

this isa 7th!

...so it’s a7-6 suspension!

this isa 2nd!

this isa 3rd!

...so it’s a2-3 suspension!

I6 II6 I6

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

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

an octave.

I6 I

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

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

use anything except asecond inversion triad.

for the 7-6 suspension,the suspension resolves

to a 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-tone

overdominant-functionharmony!

wwwwthe

majo

r

seve

nth

major 7thabove root

major triad

wwwwb

wwwwbb

wwwwbbb

wwww∫bb

the

majo

r-mi

nor

seve

nth

the

mino

r

seve

nth

the

half

-dim

inish

ed

seve

nth

the

full

y dim

inish

ed

seve

nth

minor 7thabove root

major triad

minor 7thabove root

minor triad

minor 7thabove root

diminished triad

diminished 7thabove root

diminished triad

we use “07” forhalf-diminished sevenths

and “07” forfully diminished sevenths.

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

& ˙̇̇˙̇̇ ˙̇̇ ˙̇̇ ˙̇̇˙

˙̇̇˙ ˙̇̇˙

˙̇̇˙ ˙̇̇˙V7 I7ii7vi7iiivii°IVIV 7

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

root movementsas triads use.

2

35

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

1

V7VV7 V

respect the seventh!respect the seventh!

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

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

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

You must never approachthe seventh by a leap fromabove!

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

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

doing so will cause youcertain death!

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

doubling, double the root and omit the fifth.

the a

dd-a

-seventh-inato

r

pat. p

endin

g



The Dominant Seventh

I

I

I

IVV7 V7V7 I6

V7 V6V7

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

for one thing, thedominant seventh is,

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

common practice period.

first, a note on terminology:

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

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

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

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

apply to the other diatonicseventh chords.

& wwwwb

it’s just a major-minor seventh...

until it’s placed in a particular key!

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

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

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

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

the voice thathad the seventhresolves up,usually by step.

after the V7

returns, thevoice that hasthe seventhshould stillresolve itappropriately!

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

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

seventh

seventh

ornamentresolution

resolution

transferredto tenor

ornamental resolutionthe

delayed resolutionthe

bass resolutionthe

transferred resolutionthe

&

?

#

#

œ œ œ œ œ ˙˙ ˙˙ ˙˙ ˙

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

&

?

#

#

œ œ œœ œ œœ œ œœ œ œ

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

5

&

?

#

#

œ œ œ œœ œ œ œœ œ œ œœ œ œ œ

&

?

#

#

œ œœ œœ œœ œ

resolutionseventh



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 usedmuch 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!

Music Theory for Musicians and Normal People Diatonic …harmony. sextal harmony? septal harmony? as...

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Transcript of Music Theory for Musicians and Normal People Diatonic …harmony. sextal harmony? septal harmony? as...