Music Theory for Musicians and Normal People Chromatic...

ChromaticHarmony

Music Theory for Musicians

tobyrush.com

and Normal People

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

only the notes in the current key.

essentially, this meansno accidentals, with the

exception of the raised sixthand seventh scale degrees

in minor, which weconsider to bepart of the key.

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

then by definition it’s adiatonic chord!

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

been using.

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

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

whenever possible, resolve thealtered tones in the direction

of their alteration.

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

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

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

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

the door to notes outside the key...

these “altered chords” add acertain richness to the harmony

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

diatoni

c

alte

red

(chr

omatic)

diatonic triads

diatonic sevenths

extended harmonies

8

15

88

Altered Chords

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

however, there area few things thatthey all have incommon!

� @@ ÆÆÆK � @@ ÆÆÆV/V ii

altered diatonic

�

�

A

A

� � � � �

� ��

� � � �

ÆÆ ÆÆÆ� � �

Æ

ÆÆÆ@@I IV6 IV V7 vi

@VI

23

5

1

like the diatonic sevenths,however, the common root

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

to its diatonic counterpart.

�

�

@

@

Æ ÆÆ ÆÆ@ ÆÆ Æii°65 V

�

�

@

@

Æ ÆÆ Æ

Æ ÆÆ ÆK

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

BORROWEDCHORDS 26

NEAPOLITAN

SECONDARYDOMINANTS

dAUGMENTED

SIXTHS

V SecondarySubdominants

$

� @next

50 m

iles

27theory

Borrowed Chords

� @@@ TTTTTTT TTT TTT

TTTTTTTK

� TTT@TTTT@ TTT@@ TTT@

TTT@@TTTT,@

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

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

“borrowed”?why call them

that when majornever bringsthem back?

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

are borrowed from the parallel minor.

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

one possibility is using notes and chordsfrom the parallel minor.

ii°c: ii°7 III iv VI vii°7

ii°C: ii°7 III iv VI vii°7@ @

hey, minor!I’ll have themback by tuesday

this time, Ipromise!

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

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

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

by composers beforethe romantic era.)

some theoristsrefer to the use

of these chords asmode mixture. two of these chords,

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

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

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

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

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

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

seventh must be approachedand resolved properly.

the leading-tone fully diminishedseventh is the king of dominant

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

ii°6

vii°7

vii°7ii°7

III@VI@

VI@ V

VI@ V

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

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

use of contrarymotion is better.

�

�

Æ ÆÆ@ Æ

Æ@ ÆÆ@ Æ

5

�

�

Æ ÆÆ@ Æ

Æ@ ÆÆ@ Æ8

V7 ii°6i i VI Vg:

�

�

@@

@@

� � ��

Æ � � � �

G� ± G� ± � � � ��

T3T

TK3TI

the picardy third is a major tonic chord at the end of a minor piece, so many theorists consider it a borrowedchord. really, though, it’s not addingchromatic variety... it’s a last-minutemodulation!

named for24th-century

explorerjean-lucpicard!*

*Nope.



*****The Neapolitan Six

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

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

that chord is amajor triadbuilt on the

lowered secondscale degree.

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

the fact that it is almostexclusively used in first inversion.

seriously! although thischord is extremely common

in the common practiceperiod, there are very few

examples of it used inroot position.

second inversion iseven rarer.� TTT@@

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

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

Naples scarlatti

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

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

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

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

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

it’s called the neapolitan six-four.

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

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

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

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

�

�

Æ@ ÆÆ@ Æ

Æ ÆÆ Æ

Æ ÆÆ@ Æ

Æ@ ÆÆ Æ

N6 N6V42 I64C:



Secondary Dominants

the answer, of course, is with secondary dominants.

let’s say we wanted toapproach this vi chord.

what if we wanted to usethat dominant-tonic magic?

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

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

the tonic represents release.its simplest form, the authentic

cadence, has been ubiquitousin western music for centuries.

V

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

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

control that magic and make itobey our compositional whim?

vi

� ÆÆÆ?vi

vi

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

� ÆÆÆ�ÆÆÆ � ÆÆÆ�

ÆÆÆVa: C:i

� ÆÆÆ�ÆÆÆ

viVa

aV

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

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

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

related keys are secondary dominants.

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

like a temporary tonic chord.

in minor keys, the composers generallyonly used secondary dominants

of iv and of V.

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

actually be approached and resolvedusing the basic root movements!

yes. yes they do.

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

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

the secondary dominants

Vx x x x x

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

23

5

1

the basicroot movements

rock!



Fr.6on 2

I

Augmented Sixth Chords

first, we’ll start withthe doubled root of a

V chord...

V

�ÆÆ

...and approach thatoctave with a half stepbelow the top note,

...and a half step abovethe bottom note...

V

�Æ� ÆÆ@ Æ

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

V

�Æ� ÆÆÆ@ Æ

Æ Ælike that moment of incredible tension justbefore the hero finally kisses the leadinglady, the half-step is the go-to interval

for creating tension in music of the commonpractice period. it drives the entire style!

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

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

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

roots present in dominant triads.

however, they also oftenapproach tonic chords

in second inversion,which also contain a

doubled fifth scale degree.

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

�TTTT�@It.6

if we just usethree notes

and double thetonic, we get the

italianaugmented sixth.

�TTTT�@

Fr.6

if we add thesecond scale

degree insteadof doubling thetonic, we get the

frenchaugmented sixth.

�TTTT�@@

Ger.6

and if wereplace the

second scaledegree with thelowered thirdscale degree,

we get the

germanaugmented sixth.

Ger.6

�

�

Æ� ÆÆ Æ

Æ@ ÆKÆ@ ÆI6

4

@

�

�

Æ ÆÆ Æ

Æ ÆÆ@ Æ

Ger.6 V

�

�

Æ� ÆÆ ÆÆ@ ÆÆ@ Æ5

and, finally, when resolvingthe german augmented sixth

chord to a dominant triad,you might find yourself

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

mozart did it all the time!




IV6 V7

Ger.6C: V I

I IV VI V I

vii°7 vii°7

E: vii°6G: I

I

D :

F:C:

I IV VVI V I

F:E:

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

chord that was diatonic in boththe old and new keys?

altered common chord modulationis the same thing, only using the

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

or both.

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

� @ �� K

TTT

� @ �� K�

TTTK�

@

@

@

@

this technique isso — well, odd — that

there are onlytwo specific ways

to do it.

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

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

is different in the old and new keys.

Ger.6C: V7D :@

�TTTT�@@

TTTT@@@

ever notice that the germanaugmented sixth chord is just like

a major-minor seventh chordwith the seventh respelled

enharmonically?

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

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

yields another root-position fullydimished seventh chord.

meaning that a fully diminishedleading tone seventh chord

can be a pivot chord intothree other possible keys:

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

but resolved like anaugmented sixth chord!

beethovendid!

�

�

@@@@@

@@@@@

� � �K �� K �� K �K� � �K �

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

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

a°7 a°6 c°7

�TTTT@@ �

TTTT@@ �TTTT

�@@

inve

rt

respell

5

��

@ ��

��

@ ��@ ��@@K

��

@ ��@��K@

5

vii°7 vii°7

D : vii°4G: I

I3

vii°7 vii°7

B : vii°4G: I

I2

which can berespelled as




C:

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

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

chord from a related key, like IV of V?

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

to approach these chords,use any of the basic root

movements.

the most common way to resolvesecondary subdominants is to

the corresponding secondarydominant.which are awesome.

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

what one theorist might calla secondary subdominant:

another might call ashort modulation.

� ��@��

��K

V6 Iii°7

VV4

2

V

C:

C:

G:

� ��@��

��K

V6I6

Iii°7 V4

2

second, the only placewe find chords that

we can call secondarysubdominants is in the

music of thexromantic era.x

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

from closely related keys. Inother words, secondary subdominants

should only be “of IV” and “of V.”

ivIV iv

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

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

first, there arethe diatonic triads:

ii IV

next, the diatonicseventh chords:

ii7 IV7

and, lastly, a fewborrowed chords:

ii° ivii°7

so a secondary subdominant canhave any subdominant function

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

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

diminished supertonic seventh.

ii°7

IVii°7

VV7

Vii°7

V



IF: IV V I DM B M

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

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

as the “Common Practice Period.”

however, the music of the romanticera employed some interesting

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

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

@

2000

1900

1800

1700

1600

1500

romantic early 20thcentury

contemporaryclassicalbaroquerenaissance

Romantic Era Techniques

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

dominant eleventh andthirteenth chords,

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

V11

V13

III@

ii°IVii°Viv

IV

V7Ger.6

�

�

Æ� ÆKÆ ÆÆ@ ÆÆ@ Æ

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

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

this technique is calledthird relations because it

involves moving by rootmovements of a major or

minor third without respectto key signature.

for example...

here, we’rein F major...

*whump*

...third relations

are like turning

off the gravity

in the room

for a bit...

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

if you think oftonality like

being in aroom...

� @ �� ÆÆÆ� ÆÆÆK@

F M E M IB: IV V I� @

� @ ÆÆÆ�� ÆÆÆ@@ ��K��

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

and then we landin b major!

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



�K

Music Theory for Musicians and Normal People Chromatic...

Documents

Transcript of Music Theory for Musicians and Normal People Chromatic...