Music Theory for Musicians and Normal People Diatonic …harmony. sextal harmony? septal harmony? as...
Transcript of Music Theory for Musicians and Normal People Diatonic …harmony. sextal harmony? septal harmony? as...
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Diatonic
Harmony
Music Theory for Musicians
tobyrush.com
and Normal People
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C+Cc° c
although a chord is technically any combination of notesplayed simultaneously, in music theory we usually definechords as the combination of three or more notes.
Triadssecundalharmonyœœœœœœœ
chords built fromseconds formtone clusters,which are not
harmonic so muchas timbral.
tertialharmony
œœœ
quartalharmonyœœœ
chords built fromperfect fourthscreate a different
sound, used incompositions fromthe early 1900s
and onward.
quintalharmonyœœœ
chords built fromperfect fifths
can be respelled asquartal chords,and as such theydo not create a
separate system ofharmony.
sexta
l h
armony? s
epta
l h
armony?
as w
ith q
uin
tal h
armony, t
hese
are t
he s
ame a
s t
ertia
l a
nd
secundal h
armony, r
espectively.
chords built fromthirds (MORE
SPECifically, frommajor thirds and
minor thirds)form the basis ofmost harmony in
the commonpractice period.
is the chord still tertialif it is built from diminished
thirds or augmented thirds?
well, diminished thirds soundjust like major seconds, andaugmented thirds sound justlike perfect fourths, so...
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
shed
triad
the
mino
r
triad
the
majo
r
triad
the
augm
ente
d
triad
a triad is defined as a three-note chord,but in practice it is almost always used
to refer to tertial three-note chords.
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
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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
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Triads in Inversion
haydn
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ladies and gentlemen, it’sfranz joseph haydn!
thank you for having me.in this piece I use quite a
few triads.
here’s one: it has the notesc, e and g. it’s a c major
triad! very nice.
thank you. see how the notesare spread out, and not juststacked in thirds? it’s still
a triad, though.
that’s because the third of thechord is in the bass... when that happens,we say the chord is in first inversion.
ooh! let’ssee ‘em!
and he’s brought amovement from his 1767sonata in g major.
this one is g, b, and d...a g major triad! but it sounds
different, somehow.
so the thing that makes atriad root position, first inversion
or second inversion is simplywhich note is in the bass?
it’s hard to believe that thesound of the chord can change so
much just because of thebass note.
so this one with d, f, and ais a d minor triad... insecond inversion!
first inversion? what is it called when the root is in the
bass, like the first chordwe looked at?
haydn
that’s calledroot position.
exactly! because thefifth is in the bass.
that’s right!and each onehas its owncharacter.
I know, right?it’s awesome.
music theory for musicians and normal people by toby w. rush
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what a
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6
(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
&
?
##
##
jœœœ œœ œœ œœ#œ œ œ# œœ œ œ
œ œ# œ œ œ œ œ œ
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œ# œ œ œ œ œ œœ#
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Jœ œ Jœ#œ œ œ œ
? ## œ œ# œ œ œ œ œ œ œ# œ œ œ œ œ œœ# œ œ œ œj.S. Bach: brandenberg concerto no. 5, bwv 1050
6 6 9 55
65
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so this...
could be played as this!
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music theory for musicians and normal people by toby w. rush
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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
œœœ œœœœœœ
I ii iii IV V vi vii°
tonic
Superto
nic
media
nt
subdo
min
ant
do
min
ant
subm
edia
nt
leadin
g-t
one
we refer tothese chords
with romannumerals asshown here.
notice howchord typeis shown by
capitals orlower case?
these chords are alsosometimes referred to by
their official names!
same namesand romannumerals...differentcapitalization!
this pattern ofmajor, minor and diminished
triads is the same in every major key!the subdominant triad is always major,
and the leading-tone triad is alwaysdiminished, whether you’re inc major or f sharp major!
why is the sixth chord called the submediant?well, just as the mediant chord is halfway
between the tonic and dominant chords,the submediant chord is halfway between thetonic... and the subdominant a fifth below!
the diatonic triads in minor work the same way... since we’re dealing with chords, weuse the harmonic minor scale. however, it’s important to note that common practiceperiod composers raised the leading tone only over dominant function harmony:the dominant and leading-tone triads!
because the dominant and leading-tone triads bothhave a strong tendency to resolve to tonic, we say they
have a “dominant function.” the subdominant and supertonic chords both tend toresolve to the dominant, so we say they both have a “subdominant function.”
& œœœ œœœœœœ œœœ
œœœ# œœœœœœ#
i ii° III iv V VI vii°
music theory for musicians and normal people by toby w. rush
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Introduction to Part-Writingas we look ahead, we’re
confronted with an ugly truth:
there is a lot of musicin the history of the world
that is worth studying...
much more than we canhope to cover in the span
of a few semesters.
since we can’t cover it all, we have to choose a specific musical language to study in depth.
let’s start by narrowing things down to the common practice period.
2000
1900
1800
1700
1600
1500
romantic early 20thcentury
contemporaryclassicalbaroquerenaissance
the common practice period is the music of the baroque,classical and romantic eras in europe and america.the name comes from the fact that most composers used
a common musical language during this time.
it’s especially worthstudying because
most of the piecescommonly performed
in concert arefrom this period...
...and the languageforms the basis forthe most popular
musical styles today.
by analyzing bach’s cantatas, we can construct a set of “rules” for writing infour-voice common practice period musical style, allowing us to study it in depth.
luther j.s. bach
but there is a ton ofcommon practice period music...
more than we can hope to cover. is there arepresentative style we can sink our
academic teeth into?
four-voice chorale writing is a good style to study for several reasons:
chorales have a fastharmonic rhythm, allowing
for a larger number ofchords per exercise.
a large percentage ofcommon practice period music
can be easily reduced tofour-voice counterpoint.
the cantatas of j.s. bachprovide us with a tremendous
amount of consistently-writtenfour-voice chorales.
one of the changes to the catholic churchproposed by martin luther
was to allow members ofthe congregation to
participate in the singingof the liturgy.
more than two hundred years later, j.s. bachwas appointed musicaldirector at the st. thomaschurch in leipzig, germanyand, in the spirit of luther,wrote five years’ worthof liturgical music.
of course, luther wasbranded a heretic for
his proposals, and beganhis own church in whichto implement his ideas.
each of these works,called cantatas, were built
around a hymn melodyharmonized in four partsfor congregational singing.
st. t
ho
mas c
hurch
leip
zig
, germ
any
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Part-Writing: The Vertical Rules
&
?
œœ
œœ
to best understand howcommon practice period composers
wrote music, we are going tolearn how to write music using
their musical style.
so the patterns we see in their music,the things they consistently did
or didn’t do, are going to become“rules” for us in our writing.
it’s wrong to think these were“rules” for the composers...they were just writing whatsounded good to them.
nor should we treat these as rulesfor writing music in general...
each style of writing has itsown set of patterns, and thus
its own “rulebook.” as a composer,you get to write your ownrules for your own style!
we’re going to start with thevertical rules... that is, the rulesthat pertain to building a singlechord in four-voice harmony.soprano
soprano
alto
alto
tenor
tenor
bass
bass
first, the distance betweensoprano and alto and betweenalto and tenor must be anoctave or less.
the tenor and bass can be asfar apart as you want!
second, the voices must be kept intheir proper order; for example,the tenor shouldn’t be higherthan the alto. (Bach did this nowand then, but it was only when hewanted to incorporate some specialmelodic shapes.)
third, since we have four voicesand only three notes in a triad,one of the notes should bedoubled. for triads in rootposition, we typically double theroot of the chord unless forced(by other rules) to do otherwise.
lastly, each voice shouldstay in its range. these
are conservative rangesfor modern singers, but
remember that bach’schorales were really
written for amateurs:the common people who
attended church in leipzig!
&
?
œœ
œœ
œœ
œœ
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music theory for musicians and normal people by toby w. rush
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Part-Writing: The Horizontal Rules
**
J.S
. Bach
canta
ta b
wv 5
5
“ich a
rm
er m
ensch, ic
h s
undenknecht”
..
the supreme goal of part-writing is good voice leading...making each individual voice part easy to sing by avoiding
awkward intervals or large leaps!
before we get to the specific dos and don’ts, let’s take a lookat some important characteristics of four-voice part-writing:
note how each voice movesas little as possible, goingto the nearest chord 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?
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music theory for musicians and normal people by toby w. rush
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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.
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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?
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music theory for musicians and normal people by toby w. rush
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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
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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...
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The Harmonic CadencesA cadence is generally considered to be thelast two chords of a phrase, section or piece.there are four types of cadences, each withtheir own specific requirements and variations.
an authentic cadence consists of a dominant function chord (v or vii) moving to tonic.
perf
ect
auth
entic
impe
rfec
t
auth
entic
impe
rfec
t
auth
entic
perf
ect
plag
al
half
phry
gian
dece
ptive
phry
gian
impe
rfec
t
plag
al
impe
rfec
t
plag
al
to be considered a perfect authentic cadence,a cadence must meet all of the following criteria:
to be considered a perfect plagal cadence,a cadence must meet all of the following criteria:
if the cadencedoesn’t meetall of thosecriteria, it’sconsidered tobe animperfectauthenticcadence!*
***it must use a v chord(not a vii)
both chords must bein root position
the soprano mustend on the tonic
the soprano mustmove by step
a plagal cadence consists of a subdominant function chord (iv or ii) moving to tonic.
a half cadence is any cadence that ends on the dominant chord (v).
a deceptive cadence is a cadence where the dominant chord (V) resolves to somethingother than tonic... almost always the submediant chord (vi).
a specific type of half cadenceis the phrygian cadence, whichmust meet the following criteria:
if the cadencedoesn’t meetall of thosecriteria, it’sconsidered tobe 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”!
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music theory for musicians and normal people by toby w. rush
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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&
?
œ œ œ œ œœ œ œ œ œ
œ œ œ œ œœ œ œ œ œ
let’s try it...say you havea supertonicchord and
you are tryingto decide whatchord to useto follow it.
you c
an m
ove
up a
seco
nd to
a m
edia
nt c
hord...
you c
an m
ove
do
wn a
fif
th to
a d
om
inant c
hord...
or y
ou c
an u
se t
he
fir
st e
xceptio
n a
nd
go to a
to
nic
chord!
you c
an m
ove
do
wn a
thir
d to
a l
eadin
g-t
one
chord...
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&˙̇̇ ˙̇̇
˙
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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!
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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.
music theory for musicians and normal people by toby w. rush
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music theory for musicians and normal people by toby w. rush
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!
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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
music theory for musicians and normal people by toby w. rush
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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
music theory for musicians and normal people by toby w. rush
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V7& bb wwww
-
Extended Harmonies
diminished diminisheddiminished
doubly-diminisheddoubly-diminishedthirteenth chord
wwwwwww∫∫b
diminished diminisheddiminished
doubly-diminisheddiminished
thirteenth chord
wwwwwww∫∫b∫b∫
diminished diminisheddiminished diminished
diminishedthirteenth chord
wwwwwww∫∫bbb∫
diminished diminisheddiminished diminished
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
AUGMENTEDthirteenth chord
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
AUGMENTEDthirteenth chord
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
AUGMENTEDthirteenth chord
wwwwwww###‹‹
AUGMENTED AUGMENTEDDOUBLY-AUGMENTEDDOUBLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord
wwwwwww#‹#‹‹
AUGMENTED AUGMENTEDDOUBLY-AUGMENTEDTRIPLY-AUGMENTEDDOUBLY-AUGMENTEDthirteenth chord
wwwwwww#‹#‹#‹
AUGMENTED AUGMENTEDDOUBLY-AUGMENTEDTRIPLY-AUGMENTEDTRIPLY-AUGMENTEDthirteenth chord
##‹#‹
diminished diminisheddiminished
doubly-diminishedeleventh chord
wwwwwwb∫b∫
diminished diminisheddiminished diminished
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
doubly-augmentedeleventh chord
wwwwww‹#
augmented majormajor perfecteleventh chord
wwwwww#augmented majormajor augmentedeleventh chord
wwwwww##
augmented majoraugmented augmented
eleventh chord
wwwwww###
augmented majoraugmented
doubly-augmentedeleventh chord
wwwwww#‹#
augmented augmentedaugmented augmented
eleventh chord
wwwwww####
augmented augmentedaugmented
doubly-augmentedeleventh chord
wwwwww#‹##
augmented augmenteddoubly-augmenteddoubly-augmentedeleventh chord
wwwwww#‹‹#
augmented augmenteddoubly-augmentedtriply-augmentedeleventh chord
#‹#
diminished diminisheddiminished
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
music theory for musicians and normal people by toby w. rush
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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!