chapter.06.pdf

108 Chapter 6 Harmonic Progressions

Jazz Theory Resources

VI. HARMONIC PROGRESSIONSCOMMON ROOT MOVEMENT

The root of chords can move by any interval to the root of the next chord. Root movement can be byfifths and their inversion fourths, thirds and their inversion sixths, and seconds and their inversion sev-enths. Some interval motion and direction is more common than the others. The most powerfulmelodic motion is the downward fifth movement from the dominant to the tonic or its inversion,movement up a perfect fourth from dominant to tonic. The power of this motion has been surmised tobe due to its relationship to the overtone series: that the first interval in the series, other than the octave,is a perfect fifth above the fundamental. What is true for melodic motion is also true for root motion inharmonic progressions: the most common root movement is downward fifths (type 1). The second mostcommon root movements are upward in seconds (type 2) and downward in thirds (type 3). The inver-sion of these root movements are available, but less common.

The most common root movement of downward fifths is apparent in the most prevalent harmonic pro-gression: ii7 - V7 - I in major keys and iiø7 - V7 - i in minor keys. This progression occurs so often like abuilding block in major/minor system that it is imperative that they be memorized as any young studentmemorizes the multiplication tables. Fill out the two tables below and begin to memorize these chordsas a group. When a ii7 chord is encountered, the V7 and I may be next. Even if the progression is notfollowed through to the I chord, the ii7 and V7 chords point to and are still derived from the key of I.Remember to spell the chords correctly. The ii7 chord of F# major is G#m7, not Abm7. Spelling correctlywill save time and energy and earn respect from your peers. [Once, on a recording session, a composerhad written the melody in the key of six sharps, but wrote all the chord symbols in six flats. While onehand was playing G# - B - D#, the other hand had to think Ab - Cb - Eb. It was playable, but it unnecessarilydifficult and one of the worst violations of the “Ghoti” principle I have encountered.]

COMMON PROGRESSIONS in MAJOR

KEY ii7 V7 Imaj7C Dm7 G7 Cmaj7FBb

Eb

Ab

Db

Gb

F#

BEADG

Chapter 6 Harmonic Progressions 109


COMMON PROGRESSIONS in MINOR

KEY iiø7 V7 iA minor Bø7 E7 AmD minorG minorC minorF minorBb minorEb minorD# minorG# minorC# minorF# minorB minorE minor

A harmonic progression will not always follow one type of root movement and is usually a mixture ofseveral types. Root movement by seconds and thirds is used as a contrast before eventually returning tothe strong, more common downward fifth movement. The following progression begins with type 3 rootmovement of downward thirds, followed by type 2 movement up in seconds and then the final move-ment to the tonic is type 1 movement of a downward fifth.

[Down 3rd] [Down 3rd] [Up 2nd] [Down 5th]C Am7 | F G7 | CI vi7 IV V7 I

Type 1 movement can be inserted sooner using the ii7 chord in place of the IV chord. The roots movedown a third, down a fifth, down a fifth, and down a fifth. This progression is stronger because of themore frequent downward fifth movement.

[Down 3rd] [Down 5th] [Down 5th] [Down 5th]C Am7 | Dm7 G7 | CI vi7 ii7 V7 I

This common progression is often repeated to make longer phrases. When repeated, the second tonicchord is often replaced with a iii7 chord. This removes the downward fifth movement (V7 - I) and re-places it with a downward third movement (V7 - iii7), but the continuation of the line (iii7 - vi7 - ii7 - V7- I) is all type 1 downward fifth movement. Another possibility is using the tonic chord in first inversionin place of the I or iii7 chord. The tonic inversion and the iii7 chord are often interchangeable and in-distinguishable from each other.

[Dn. 5th] [Dn. 3rd]|C Am7 | Dm7 G7 | C Am7 | Dm7 G7 | C

[Dn. 3rd] [Dn. 5th]|C Am7 | Dm7 G7 | Em7 Am7 | Dm7 G7 | C

|C Am7 | Dm7 G7 | C/E Am7 | Dm7 G7 | C



These same progressions are logical and musical in the parallel minor key.

C m Abmaj7 | Fm7 G7 | Cm . . .i bVI7 iv7 V7 i

C m Abmaj7 | Dø7 G7 | Cm . . .I bVI7 iiø7 V7 i

The progression is often inverted, aiming for, rather than beginning with the tonic chord.

| Dm7 G7 | C Am7 | Dm7 . . . ii7 V7 I vi7 ii7

| Dø7 G7 | Cm Abmaj7 | Dø7 . . . iiø7 V7 i bVI7 iiø7

APPLICATION of HARMONIC ANALYSIS

Recognizing that several chords are derived from one key allows an improviser to think in that one keyfor larger sections of a piece. In the following progression, the Roman Numeral Analysis (RNA) tells usthat the source for all of these chords is the key of C (I). Two facts can be deduced from that: (1) if thechords were constructed from a C major scale, it follows that a C major scale is a source for melodicmaterial over the chords; (2) If the chords are functioning to point to C as a tonic chord, it follows thata C major triad could be used for harmonic generalization over the passage. One scale works for allthose chords because those chords were derived from the scale. Since all the chords are functioning topoint to the C tonic triad, then melodies which generalize the tonic triad will function the same way ona different level. Any vertical dissonances are resolved as the line progresses towards its goal.Understanding RNA is more than assigning numbers to chords; it is directly related to melodic improvi-sation decisions.

| Em7 | Am7 | Dm7 | G7 | Cmaj7 | Fmaj7 . . .iii7 vi7 ii7 V7 I IV7

Implications:(1) C major scale works for melodic generalization . . .(2) C major triad works for melodic generalization . . .

HIERARCHY of CHORDS

The harmonic progressions ii7 - V7 - I in major keys and iiø7 - V7 - i in minor keys also illustrate the hi-erarchy of chords. The tonic chord, as the tonic pitch, is by definition where all progressions point.When preceded by its dominant, the strongest cadence or conclusion is perceived. The ii7 chord is themost common of several chords that precede the dominant. The chart below classifies the most com-mon pre-dominant., dominant, and tonic chords available from the major and harmonic minor scales.

PRE-DOMINANT CHORDS DOMINANT CHORDS TONIC CHORDSIV V7 Iii7 viiø7 (rare) iiiø7 vii°7 I6 or iii as substitute for Iiv7 (sometimes vi7 as substitute for I)

bVImaj7**bVI can be a predominant chord because of its similarity to iiø7 and iv7 and it can point to V7.



From the chart, it is clear that a ii7 and iiø7 chords both function as pre-dominant chords. This conceptcan lead to modal mixture where chords from the parallel minor key are used in place of the corre-sponding diatonic chords from the major key. The progression may point to the same tonic, but willsuggest a minor modality. These chords are said to be “borrowed” from the parallel minor key.

|Dm7 G7 | C ii7 V7 I

with a borrowed supertonic chord would become:

| Dø7 G7 | Ciiø7 V7 I

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| C Am7 | Dm7 G7 | CI vi7 ii7 V7 I

with borrowed submediant and supertonic chords would become:| C Abmaj7 | Dø7 G7 | C

I bVI7 iiø7 V7 I

When improvising through a passage of borrowed chords, remember that the source scale and tonicchord have changed. The harmonic minor scale and tonic minor triad may be used for melodic mate-rial through the chords borrowed from minor.

The dominant seventh chords for both major and minor appear the same when using RNA. To deter-mined the scale from which the V7 chord is derived, examine the preceding chords. If a V7 is precededby pre-dominant chords from major (ii7 or IV) it is probably also derived from major. If a V7 chord ispreceded by pre-dominant chords from harmonic minor (iiø7, iv7, bVI) then the dominant should con-tinue as the V7 of a minor tonic. Examining the melody will provide clues. If notes from the minor keyare in the melody, then the V7 chord is derived from the minor key.

There is no difference between a G7 chord from C major and a G7 chord from C minor if the chord isonly spelled to the seventh: they are both spelled G-B-D-F. The difference occurs when consideringpassing tones between the chord tones. The key of C contains En and An, while C minor contains Eb andAb. When upper tertian extensions are added, the difference also becomes apparent. The ninth of a G7chord is An in the key of C major and Ab in the key of C minor. The thirteenth of a G7 chord is an En inthe key of C and an Eb in the key of C minor. Learning to recognize these basic alterations will helpidentify the sound called for in chord notation. In the chords below that include a thirteenth, the fifthwas eliminated.

6.1 Differences between V7 of C major and V7 of C minor

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G7 G9 G913

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G7 G7b 9 G7b 13

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Modal mixture and substituting more common root progressions can energize this simple progression.

| F | Em7 | Dm7 | CIV iii7 ii7 I

The first stepwise progression has more forward motion when chords are added between the originalchords which change the root movement to downward fifths.

| F | Em7 Am7 | Dm7 G7 | CIV iii7 vi7 ii7 V7 I

Adding three chords (iv7, iiø7 and G7b9) from the parallel minor add another colorful dimension.

| F Fm7 | Em7 Am7 | Dø7 G7b9 | CIV iv7 iii7 vi7 iiø7 V7 I

CLOSELY RELATED KEYS

Up to now this discussion has been confined to harmonic progressions that stay in one key center. Mostcompositions do not stay in one key, but temporarily modulate or tonicize keys that are closely related.Some progressions point away from the tonic almost immediately and go on long harmonic excursionsbefore returning to the home key. While it is possible to find music that journeys to very remote keys, agreat deal of music is created which moves in and out of closely related keys.

Closely related keys are those whose key signatures are one accidental away from the tonic key. If the keyof C is the home key, then related keys would be the relative minor which shares the same key signature(A minor), the key of 1b (F major and D minor), and the key of 1# (G major and E minor).

Primary Closely Related Keys to C major

1b 0#/0b 1#

F C(home key)

G

Dminor

Aminor

Eminor

If these related keys are lined up alphabetically, it is apparent that the closely related keys are also thefive other stable diatonic chords in the key of C major: (The chord on the seventh degree of major is anunstable chord because of its diminished fifth, and there is no diminished key.) The closely related keyshave a Roman numeral listed below indicating their relationship to the original key. D minor is the keyof ii, and so on.

Home: Closely Related KeysC major D minor E minor F major G major A minor

I i i iii IV V vi

Borrowed chords were discussed before as a way to get from a major key area to its parallel minor key.Jumping from the key of C with no sharps or flats to the key of three flats may appear to be remote, butconsidering that C major and C minor are parallel and they share the same dominant chord, then thejump is not so far. The closely related keys to parallel key of C minor (three flats) would be the keys oftwo flats and four flats. From the parallel move to C minor, the keys of Eb major, F minor, G minor, Ab

major, and Bb major become available.



Secondary Keys Available to C major through parallel C minor

4b 3b 2b

Fminor

Cminor(parallelhome key)

Gminor

Ab

majorEb

majorBb

major

C minor is parallel to the home key of C major. F minor and G minor are parallel to the primaryclosely related keys of F and G major.

The secondary closely related are shown with a Roman numeral listed below indicating their relation-ship to the original key. These Roman numerals do not indicate a chord function.

Parallel Home: Secondary Keys from Modal Mixture:C minor Eb major F minor G minor Ab major Bb major

i bIII iv v bVI bVII

A third level of closely related keys are available through another modal mixture. C minor and C majorare related as a parallel tonal centers but one is minor and the other major. The three primary closelyrelated minor keys to C major are D minor, E minor and A minor; the keys of ii, iii and vi. Each of theseprimary closely related keys has a parallel major so that D major (II), E major (III), and A major (VI)are available from the key of C major through modal mixture of close diatonic chords.

This chart illustrates several possible levels of modulation from the primary key of C major.

Tertiary Keys from modal mixture D major (II) A major (VI) E major (III)

D minor (ii) A minor (vi) E minor (iii)PRIMARY KEYS F major (IV) C major (I)

(home key)G major (V)

↓

Secondary Keys from parallel minor F minor (iv) C minor (i) G minor (v)Ab major (bVI) Eb major (bIII) Bb major (bVII)

The combined keys available for smooth modulation from the home key of C major are illustrated inthe chart below. The keys are shown by the three levels: closely related diatonic keys with one accidentaldifference; keys closely related to the parallel minor; and keys available using modal mixture with thekeys of second, third and sixth degrees of the home key. The Roman numerals in this case do not referto chords, but to the new key in relationship to the home key. For example, the key of Bb is the major keyon the bVII related to the key of C; does not refer to a chord built on the seventh degree of the C majorscale.

Closely Related Diatonic I ii iii IV V viFrom Parallel Minor i bIII iv v bVI bVIIUsing Modal Mixture II III VI



SECONDARY DOMINANTS

The primary chords are built without alterations on diatonic scale degrees. There is only one dominantand its function is to point out the tonic chord. If other dominants occur in a progression other thanthe primary dominant, then some chord has been chromatically altered to create the new dominantand this new dominant will point to a key other than tonic. This new key is a secondary key from theoriginal making the dominant chord a secondary dominant. The dominant chord is the most identifi-able indicator in the harmonic progression because it occurs only on the dominant pitch in major andminor. Minor seventh chords that can occur as ii7, iii7, vi7 or iv7 do not point as conclusively.Modulations to the closely related and remote keys are usually accomplished with the use of a sec-ondary dominant.

In the key of C, expect modulations or temporary tonicizations, and look for the dominants of theclosely related keys. If any dominant other than the primary dominant G7 is encountered, it is a sec-ondary dominant pointing away from the primary key and to a secondary key. Look for the dominantspointing to the closely related keys of D, E and A minor and F and G major.

An A7 points to the key of D minor. It cannot be considered a VI chord in the key of C: there is no C#

available in the key of C; it must be a secondary dominant. The RNA for this chord is V7/ii. The “V7”defines its relationship to D minor; the “ii” defines the relationship of the secondary key to the homekey of C. This symbol, V7/ii, means “A7 is the dominant (V7) of the D minor, the minor key on thesecond degree (ii) of C major.” It also suggests that individual pitches have been changed. The key of Dminor has to have a C# leading tone in order to create the A7 chord, and a Bb by its key signature defi-nition. These pitches are necessary in order to modulate from C major to D minor and define the dif-ference between the two keys. The chromatically altered pitches want to resolve in the direction in whichthey have been altered. The C# points up to D and the Bb down to A. With D and A as targets, it is easyto see and hear how D minor is temporarily tonicized by the A7.

The dominant for E minor is B7 and is shown with the symbol V7/iii. The key signature for E minor isone sharp plus the leading tone D# needed to create the dominant chord. The F# and D# are the pitchesnecessary to modulate from the key of C to the key of E minor. Both the F# and D# resolve up in the di-rection in which they have been altered to E and G, two primary pitches in the key of E minor.

The dominant for F major, the key of IV, is a C7 chord. This is often erroneously labeled as I7. Therecannot be a dominant chord on a pitch other than the dominant pitch and since there is no Bb in thekey of C, this chord must be the V7/IV. The Bb is the defining difference between the keys of C and Fmajor. The Bb wants to resolve down to the A, the note that defines the major quality in the key of F.

D7 is the V7/V. The F# that is needed to create the D7 chord is the one sharp from the key signature ofG. The Fn in the key of C usually points down to the En. The F# points up to G.

C major and A minor share the same key signature but there must be a leading tone in the key of A mi-nor in order to create a dominant chord. E7 is the V7/vi. The pitch G# distinguishes the keys of C majorand A minor and creates the E7 dominant chord.

The following chart reviews the closely related keys to the key of C major, their secondary dominants,RNA and lists the necessary accidentals needed to tonicize or modulate to the secondary keys.

NEW KEY AREA TO TONICIZE SECONDARY DOMINANT NECESSARY ACCIDENTALSii: D minor A7 (V7/ii) Bb and C#

iii: E minor B7 (V7/iii) F# and D#

IV: F major C7 (V7/IV) Bb

V: G major D7 (V7/V) F#

vi: A minor E7 (V7/vi) G#

Note that all twelve pitches are used in the chart above. The are seven pitches in the C major scale andthe accidentals needed for modulation comprise the remaining five.



Secondary dominants create more forward motion in a harmonic progression. The introduction ofchromatic notes shifts the focus away from the tonic to secondary chords. The secondary chords thenprogress back to the tonic. Some of the basic progressions that were shown before using only chordsfrom one key area can be enhanced using secondary dominants to point to diatonic chords.

A tonic chord can move to any diatonic chord but this progression may be strengthened with theaddition of the secondary dominant. The downward fifth motion and the addition of chromatic pitchestemporarily removes the focus from the original key making the resolution to the diatonic chordstronger.

C A7 Dm7I V7/ii ii

C B7 Em7I V7/iii iii

C C7 FI V7/IV IV

C D7 GI V7/V V

C E7 Am7I V7/vi vi

The following progression to the ii7 chord includes just chords from the key of C major:

C Em7 Am7 Dm7I iii7 vi7 ii7

A secondary dominant can be added to both emphasize the pull away from the tonic and point towardsother chords. A7 as the secondary dominant for D minor can replace Am7. Dm7 is still ii7, it has justbeen tonicized with its dominant. Em7 is still the iii7 chord in the key of C, not the ii7 chord in the keyof D minor. Eø7 is the iiø7 chord in D minor. The basic melodic resources would come from the key ofC major except for the A7 chord. The A7 chord, as the RNA implies, uses the D harmonic minor scale,with C# and Bb being the important distinguishing tones.

C Em7 A7 Dm7I iii7 V7/ii ii7

The progression to the A could be strengthened by using its dominant instead of the iii7 chord. The E7,V7/vi, points to A minor, but at the resolution, A minor is a dominant chord pointing to the key of Dminor. When the progression arrives at Dm7, it is not actually in the key of D minor, as Dm7 is a ii7chord in the original key of C major. The C and Dm7 chords are still derived from the C major scale,and the notes from that scale can be used as a melodic resource. The E7 is derived from the A har-monic minor scale and would use that scale as a melodic resource.

C E7 A7 Dm7I V7/vi V7/ii ii7

A7 is V7/ii only in the key of C. D minor may be the ii, iii, vi in major keys, or i and iv in minor keys, soits dominant can also be shown in relationship to other keys. For example, if A7 occurs in a passage inthe key of Bb pointing to the iii7 chord, Dm7, the A7 would be the V7/iii. If A7 occurs in a passage in thekey of F major, then A7 would be V7/vi. In the key of A minor, A7 points to the iv chord and would be



labeled V7/iv. Everything is labeled relative to the tonic key. But in all of those cases, the melodic re-source for the A7 chord is still the D harmonic minor scale.

One of the most common progressions is I - vi7 - ii7 - V7. Secondary dominants are often used to in-crease the level of tension and forward motion. The most common substitution replaces the vi7 chordwith a V7/ii. In the key of Bb, the original progression would be Bb - Gm7 - Cm7 - F7, often returning tothe tonic chord. With the secondary dominant of Cm (G7 = V7/ii) in place of the Gm7, the progressionwould be Bb - G7 - Cm7 - F7. The pull away from the key of Bb is intensified by the G7 chord, as it has aBn and an implied Ab from the C minor key signature. These two notes that changed the key from Bb tothe key of C minor and are often the first notes played by experienced jazz musicians. Below are two ex-amples from improvisations by Charlie Parker. In both of these examples Parker addressed the sec-ondary dominant chords by immediately playing the pitches necessary to modulate or tonicize the sec-ondary key. To tonicize C minor from the key of Bb, a Bn and Ab must be heard, and they are the first twonotes Parker played over the G7 (V7/ii) in the first example. To get from the key of Ab ( four flats) to thekey of ii, Bb minor, two accidentals are needed: the fifth flat (Gb) and the leading tone (An). These werealso the first two pitches played by Parker in the second example. The examples are identical except forthe octave displacement in the first one, which suggests that Parker had practiced these lines in all keys.

6.2 I - V7/ii - ii7 I - V7/ii - ii7

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Clifford Brown played exactly the same melodic figure in ex. 6.3 as Parker did in ex. 6.2. Brown began inG major. To modulate from G (1#) to the key of A minor (0#, 0b), the F# must become Fn, and the leadingtone G# is needed. These were the first pitches sounded by Brown at the E7. Red Garland used manychromatic embellishments and approaches, but at the point of the G7, he played the Bn and Ab calledfor by the secondary dominant below.

6.3 I - V7/ii - ii7 I - V7/ii - ii7

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In this Jimmy Guiffre example, the iii7 chord follows the V7, substituting for the I chord. This keeps theprogression moving in downward fifths from the Em7 to the A7 (iii7 - V7/ii). As in examples above,Guiffre knows the tones necessary for modulation (Bb from the key signature of D minor and the leadingtone, C#) and plays them immediately at the occurrence of the secondary dominant A7.

6.4 ii7 - V7 - iii7 (instead of I) - V7/ii - ii7

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Since a V7 chord is often preceded by the ii7 or iiø7, secondary ii7 and iiø7 chords may precede sec-ondary dominant chords. The roots of the chords on the top line move in descending thirds. Beforeeach new chord, a secondary dominant may be inserted with its corresponding ii7 or iiø7 chord. Thecadences to Gm7, Ebmaj7 and Cm7 are strengthened by their preceding ii7 - V7 or iiø7 - V7 chords.

Bb Gm7 Ebmaj7 Cm7I vi7 IV vi7

Bb [ Aø7 - D7 ] Gm7 [ Fm7 - Bb7 ] Ebmaj7 [ Dø7 - G7 ] Cm7I iiø7 - V7 vi7 ii7 - V7 IV iiø7 - V7 vi7

vi IV ii

Review what each RNA symbol actually means to the sound. The Aø7 - D7 indicates a temporary modu-lation to the key of G minor with the necessary leading tone F#. The F# is the most important identifyingnote for the D7 chord. The Fm7 - Bb7 indicates a modulation to the key of Eb major and necessitates theaddition of an Ab. The Ab is the most important identifying note for the Fm7 chord, and is the seventhof the Bb7 chord. The Ab resolves down to a Gn, the most important identifying note for the Eb majorchord. The Dø7 - G7 indicates a modulation to the key of C minor, which demands an Ab and a Bn. TheBn is the most important identifying note for the G7 chord which points to C minor. RNA can help iden-tify the most important tones that indicate the harmonic direction. If those tones are emphasized formelodic direction, then linear harmony, lines with strong harmonic implications, will be the result.

In the following progression of roots moving upward in seconds, three possible sets of secondarychords are shown. All are possible and often occur interchangeably in jazz performances. The D7, F#°7,or Aø7 - D7 indicate the key change from F major to G minor, requiring an F# and an Eb. The E7, G#°7,or Bø7 - E7 chords indicate a key change to A minor, requiring an G# and an Bn. Notice how importantthose pitches are to the identification of the corresponding chords.

F Gm7 Am7I ii7 iii7

F D7 Gm7 E7 Am7I V7/ii ii7 V7/iii iii7

F F#°7 Gm7 G#°7 Am7I vii°7/ii ii7 vii°7/iii iii7

F Aø7 - D7 Gm7 Bø7 - E7 Am7I iiø7 V7 ii7 iiø7 V7 iii7

ii iii

The very simple progression shown below moves down in diatonic seconds and can be altered usingsecondary dominants.

6.5 Diatonic chords

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Fmaj7 Em7

IV iii7

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Preceding each diatonic chord with its dominant adds momentum to this progression. The root pro-gression is made stronger moving down in fifths than in seconds.

6.6 With added secondary dominants

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The progression initially began on the diatonic IV chord. By substituting the F#ø7, a secondary iiø7chord from the key of Em, all the root movement is by descending perfect fifths. The G7 chord is bor-rowed from the parallel key C minor which yields the Ab, the b9 of G7.

6.7 With added secondary dominants

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There are many tunes that stay within one key signature for almost the entire form. The contrast betweenthe two keys, major and relative minor, and their corresponding progressions provides enough interest-ing diversions. The following progression, shown in the key of no sharps or flats, is found in thousandsof compositions from the Baroque era to current popular music and has been used by several jazzcomposers from Antonio Carlos Jobim to Chick Corea.

Dm7 G7 Cmaj7 Fmaj7 Bø7 E7 Am7

Is this passage in the key of C major or A minor? The first few measures sound like the key of C major.The key of A minor is not heard or anticipated until at least the Bø7 chord. While the Bø7 chord is theviiø7 of C, it is more often heard as the iiø7 in minor. The E7 definitely points the progression to A mi-nor. Is it in the key of C (I) and then modulates to A minor (vi), or in the key of A minor (i) and modu-lates from the Dm7 chord (iv7) to the relative key of C (I/bIII) and back again to A minor. How this isanalyzed may depend on the larger context. Initially, most would hear the Dm7 as the ii7 in the key of Cmajor, and not expect A minor until the more definitive pointers Bø7 and E7. Here is one analysis withthe progression based in C major. The E7 is shown as the secondary dominant to A minor. It is possibleto tonicize the Dm7 (ii7) with its dominant so that an A7 chord is inserted after the Am7 and before re-peating the progression.

Dm7 G7 Cmaj7 Fmaj7 Bø7 E7 Am7ii7 V7 I IV iiø7/vi V7/vi vi7



The progression could be analyzed relating to the key of A minor. The major area is so strong that itfeels less like a departure than the A minor area. Note that ending the progression with an A minorchord without a seventh makes it feel more like A minor is the ultimate destination of the progression.When it ends with an Am7, the Am7 feels like a vi7 chord even when preceded by its dominant, E7.

Dm7 G7 Cmaj7 Fmaj7 Bø7 E7 Amiv7 V7/bIII I/bIII bVI iiø7 V7 i

Could the G be labeled bVII and the C bIII in the key of A minor? These would be diatonic chords de-rived from A natural minor. Remember that minor harmony is derived from the harmonic minorscales in order to get the leading tone G#. G7 to C so convincingly suggests C as tonic that it is almostimpossible to hear these chords as related to A minor.

Here is another progression with roots descending in downward fifths. Even though the following pro-gression starts with an Am7, it sounds more like a progression in the key of C major starting on the vi7.

Am7 Dm7 G7 Cmaj7 Fmaj7 Bø7 E7 Am7vi7 ii7 V7 I IV iiø7/vi V7/vi vi7

These two cycles will help aural recognition of the secondary dominant related to diatonic chords.Practice them at a keyboard in this key and others.

Secondary Dominant Cycle No. 1: DEVELOPING AURAL HARMONIC RECOGNITIONDescending diatonic chords with secondary dominants:I - V7/vi - vi - V7/V - V - V7/IV - IV - V7/iii - iii - V7/ii - ii - V7 - I

Play at the keyboard:

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c

c

œœ

œœ

œœœœ

#

œœ

œœ

n

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#

œœ

œ#œ

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œœ

œœ

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bœ

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##

œ

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œ

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œœ

œœ

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n

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œ

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Secondary Dominant Cycle No. 1: DEVELOPING AURAL MELODIC RECOGNITIONDescending diatonic chords with secondary dominants:I - V7/vi - vi - V7/V - V - V7/IV - IV - V7/iii - iii - V7/ii - ii - V7 - I

Play the lower part on the keyboard and sing the upper part to master hearing the identifyingtones necessary for tonicization:

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c

c

œ

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œœ

œœ

œœ

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œ

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œ

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œ#

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œœ

œœ

œnœ

œœ

œ

œœ

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Secondary Dominant Cycle No. 2: DEVELOPING AURAL HARMONIC RECOGNITIONAscending diatonic chords with secondary dominants:I - V7/ii - ii - V7/iii - iii - V7/IV - IV - V7/V - V - V7/vi - vi - V7/V - V - V7 - I

Play at the keyboard

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c

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œ

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Secondary Dominant Cycle No. 2: DEVELOPING MELODIC RECOGNITIONAscending diatonic chords with secondary dominants:I - V7/ii - ii - V7/iii - iii - V7/IV - IV - V7/V - V - V7/vi - vi - V7/V - V - V7 - I

Play the lower part on the keyboard and sing the upper part to master hearing the identifyingtones necessary for tonicization:

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c

.œ

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œbœ

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It is useful to fill out a chart for each of the thirteen major keys (including F3 and Gb) like the one shownbelow for the key of C. The charts will reinforce the memorization of secondary dominant relationships,the necessary accidentals for modulations, and the proper chord spelling.

HOME KEY: C major PRIMARY KEY SIGNATURE: No #s or bsNEW KEY AREA TO

TONICIZESECONDARYSUPERTONIC

SECONDARYDOMINANT

NECESSARYACCIDENTALS

ii: D minor (1b) Eø7 (iiø7/ii) A7 (V7/ii) Bb and (LT) C#

iii: E minor (1#) F#ø7 (iiø7/iii) B7 (V7/iii) F# and (LT) D#

IV: F major (1b) Gm7 (ii7/IV) C7 (V7/IV) Bb

V: G major (1#) Am7 (ii7/V) D7 (V7/V) F#

vi: A minor Bø7 (iiø7/vi) E7 (V7/vi) (LT) G#



DECEPTIVE RESOLUTIONS

The definition of functional harmony submits that dominant chords point towards tonic and that otherchords progress to particular places that ultimately lead back to tonic. Composers use the natural ten-dencies of these harmonic progressions to manipulate a listener’s expectations. It is important to under-stand that while certain chords point clearly to a specific chord, in musical situations, they do not al-ways resolve as expected. If each chord always resolved as expected, music would be unbearably boring.On the other hand, if these chords were not expected to resolve certain ways, and if listeners universallydid not anticipate these resolutions, then the deceptive resolutions would have little emotional or dra-matic impact on the music. Fortunately for composers, listeners do react to the unexpected, which im-plies they do listen and listen with certain expectations. Deception is the device that comedians, magi-cians, storytellers and musicians count on to work their craft. For a joke to work, a certain possibility isanticipated, and then a surprise turn triggers the laugh. The magician with one hand draws your atten-tion away then pulls the coin out of your ear with his other hand. The playwright uses our sense of ex-pectation to elicit a response to a unexpected dramatic turn. The fact that deceptive resolutions are ef-fective in music is proof of the functional harmony system. If the deceptions did not surprise to a de-gree, then the listeners had no expectations.

Try this on a group of students of any age. Play the first measure and stop before resolving to the tonicchord. Everyone, musicians with training and even those without, anticipate the tonic chord. Play thesecond or third example when the G chord resolves to the A minor or Ab major and the reaction will belaughs and raised eyebrows. No one is reacting because from years of music theory study, reacting tosome technical concept. They are reacting instinctively to the unexpected resolutions, proving that whatwas expected was the tonic chord.

6.8a. Expected Resolution b. Unexpected c. More Unexpected

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All would agree that the G chord is a V chord in the first example above as it functions properly resolv-ing to the I chord. Is it still the V chord when it resolves to the vi or the bVI chords? A V chord meansthat it points in a specific direction, it does not insist on a particular resolution. In all three cases theexpectation was for the V chord to resolve to I: that is what makes it a V chord. In the two cases wherethe V chord resolved unexpectedly, the surprise is precisely because the G chord is the V of C and isexpected to resolve accordingly. Route 66 winds from Chicago to LA, but one could stop or turn offanywhere along the road (Flagstaff, Arizona, don’t forget Winona), without changing the fact that Route66 still points from Chicago to LA. Chords function to point to specific tonic chords whether they actu-ally arrive where expected. (I often call this the “Route 66” principle.)

In the following progression the G7 (V7 of C) resolves to Em7 once and to C later. G7 is the V7 in bothinstances. The resolution to Em7 is not a very deceptive resolution as Em7 can be a substitute for C orfor C/E in first inversion.

| C Am7 | Dm7 G7 | Em7* Am7 | Dm7 G7 | CV7 iii7 V7 I



DOMINANT SEVENTH CHORDS & DECEPTIVE RESOLUTIONS

The most common deceptive resolution is V7 resolving to vi (a.). This element of surprise has been di-minished because these deceptive resolutions have occurred with such frequency for the last few hun-dred years. No one will hear these and be shocked. The deception is relative, but the terms and conceptsare useful. The deceptive resolution is the same in the parallel minor (b.). A V7 in a major key is also ef-fective in the deceptive resolution to bVI of the parallel minor key.

a. b. c.Dm7 G7 Am7 Dø7 G7 Abmaj7 Dm7 G7 Abmaj7ii7 V7 vi7 ii7 V7 bVI ii7 V7 bVI

DIMINISHED SEVENTH CHORDS & DECEPTIVE RESOLUTIONS

Diminished seventh chords are the most often misunderstood and misspelled. Since they are related tothe dominant chords, they are often involved in deceptive resolutions. Diminished seventh chords canonly be found within the major/minor system as the vii°7 in minor. The classification of a vii°7, just likethe V7 chord and Route 66, does not change because of an irregular resolution. Diminished seventhchords that resolve deceptively often get mislabeled and cause much confusion, but chords still func-tion, as the V7 chords function above, even when resolving deceptively.

Diminished seventh chords sound and function as V7 chords in first inversion. The common deceptiveresolution in minor is V7 - bVI. Dominant seventh chords are often found in first inversion with thethird in the bass. The V7 in first inversion is often replaced by the vii°7 chord which creates the vii°7 -bVI deceptive resolution. Listen in ex. 6.9 how the vii°7 resolves to i (G#°7 - Am) and then listen to thevii°7 - bVI deceptive resolution (G#°7 - F). This diminished chord is one of the most misspelled chords. Itis often labeled Ab°7. This of course is an enharmonic spelling of the same pitches, yet it makes nosense. If a diminished chord is from the seventh degree of a minor key, then Ab is the seventh degree ofBbb minor, which is the key of twelve flats! The key of no sharps and flats is clearly preferable.

The vii°7, i, and bVI chord may occur in other inversions. In ex. 6.10 the vii°7 chord is shown resolvingto the i with both chords in first inversion. The second measure shows the vii°7 chord in first inversionresolving to the bVI chord in second inversion. The vii°7 chord is still spelled G#-B-D-F, as it should bein the key of A minor. When used in inversions, it is often misspelled. The G#°7/B below is often spelledB°7 rather than G#°7. A pianist reading the B°7 may play the same enharmonic notes, but the misla-beled chord confuses the function. A B°7 is the vii°7 of C minor which has nothing to do with theseprogressions in the key of A minor.

The G#°7 chord in ex. 6.11 is often labeled F°7. Because of the bass note, it may be a convenient but in-correct label. F°7 is the vii°7 of Gb minor, the key of nine flats; a long way from A minor.

6.9 6.10 6.11

vii°7 - i vii°7 - bVI6 vii°65 - i

6 vii°65 -

bVI64 vii°65 - i

64 vii°6

5 - bVI

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Why is it important to name and spell the chords correctly? Ab°7, B°7, D°7, F°7 or G#°7 may sound thesound the same, but will have completely different implications. Each of the G#°7 chords in ex. 6.9-6.11are derived from the same scale (A harmonic minor), and spelling the chord correctly as a G#°7 makes



it easier to comprehend. Any other spelling invites confusion. It takes no more effort and time to cor-rectly label a chord and it saves time on the interpretation of its function. However, be prepared to seeany number of enharmonic spellings in published and unpublished music.

The key of bVI is a closely related key in minor. A progression in A minor may move to the key of Fusing the secondary ii7 and V7 chords. A minor may be tonicized by it own dominant.

Am E7 Am Gm7 C7 Fi V7 i ii7 V7 I

bVI

It is easy to see that E7 is the V7 of Am in the example above. Confusion arises when the E7 progressesdirectly to the G minor (ii7/bVI). How can it be the V7 of Am if it does not resolve to A minor? It is thesame with all deceptive resolutions, it illustrates the “Route 66” principle in action. Even more confusionis produced when the vii°7 (G#°7) chord is used in the place of the V7 chord. The bass line from A tothe G# to the G is very smooth. The principle of chromatics suggests the bass line should be written A -Ab - G, and this is the reason this diminished chord is often spelled Ab°7. But no matter the enharmonicspelling, the function of the diminished chord remains vii°7 of A minor. Some call this a passing dimin-ished, and it does pass between the A minor and G minor chords, but it is vii°7 of A minor in both thefirst and third measure of ex. 6.12 below.

6.12

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If these diminished seventh chords and their deceptive resolutions were isolated instances or alwaysconfined to small rhythmic units, understanding their function would be less important. These dimin-ished chords last for several beats in many settings and an improviser must understand their function inorder to effectively create melodies over the harmonic passages. If the diminished chord lasts for twoentire measures, it cannot be ignored. A strategy should be available for addressing these diminishedchords. Labeling the chords “passing diminished” offers nothing in the way of melodic resources fordealing with the progression. Consider the following progression from a standard jazz bossa nova. Thefirst version is how it appears in many printed versions. The Ab°7 and the F°7 spellings reflect the basslines, but how and what should be played over the chords? Some have explained the Ab°7 is a passingchord and that the F°7 is really just non-harmonic tones that resolve to the F major chord. Both as-sessments are correct and yet neither offer a strategy for playing through the passage. The second pas-sage spells both diminished chords as G#°7 which facilitates the understanding of its function in bothplaces as the vii°7 of A minor. It functions as vii°7 in both places even though resolving deceptively. Ifthe diminished chords are both derived from the A harmonic minor scale, then the A harmonic minorscale is a source for melodic material.

6.13a Typical printed version:

Am7 ‘ Ab°7 Gm7 C7 F°7 Fmaj7

6.13b Accurate spellings indicate function:

Am7 ‘ G#°7 Gm7 C7 G#°7/F Fmaj7



Transposing this progression to other keys may make it easier to understand. In Cm, which would yourather see: Cm - Cb°7 - Bbm7 or Cm - B°7 - Bbm7? The B°7 is related to the Cm and not to the Bbm7chord that follows, just as the G#°7 is related to the Am.

6.13c Transposed to Cm:

Cm7 ‘ B°7 Bbm7 Eb7 B°7/Ab Abmaj7

A vii°7 chord is useful as a secondary leading tone chord to modulate from I to the key of iii. In G, thatwould be an A#°7 pointing to B minor. In ex. 6.14a, the A#°7 resolves deceptively back to the G. Thismeans the A# and C# act as leading tones or lower neighbor tones to the pitches from the G triad: B andD. The A#°7 chord could have easily resolved to a B minor chord. This resolution is exactly the samekind as seen in sixth measure of ex. 6.13a-c. Chord symbols for this passage might have read G°7 - G,which would have been incorrect and misleading. A similar example of non-harmonic tones creating adeceptive diminished chord resolving to I is often used in the beginning to Misty. It could be arguedthat these chords are not actually deceptive in that many would not expect them to resolve in these con-texts to the minor key from which these chords were derived. But understanding their relationship to theharmonic minor source is important for identifying melodic material.

6.14 a b.Mozart: Piano Sonata, K. 545, Andante Popular Cadence

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Consider the enharmonic spellings carefully when labeling diminished chords. It may be sensible to la-bel certain chords dictated by the logic of the bass line, but this also may cause confusion. Diminishedchords often occur that are misspelled vii°7 chords. Determining the functional relationship of the en-harmonically spelled diminished chords will unlock melodic resources.

The following harmonic passage is found in many jazz standards. The Eb°7 spelling correctly reflects thedownward chromatic root movement and the internal line (G - Gb - F), but offers no clue to availablemelodic resources. Spelling it as a vii°7 in the key of E minor suggests the E harmonic minor scale as amelodic resource. How can it be vii°7/iii if there is no E minor around? The D#°7 is derived from the Eharmonic minor scale regardless of the resolution.

6.15Typical incorrect spelling Correct spelling indicates function

I6 ? ? ? ii7 I6 vii°7/iii ii7

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The diminished chord in the second measure of ex. 6.15 can be proven to be the vii°7/iii by examiningit in context from different perspectives. Take the chord tones (D# - F# - A - C) and add the Bn found inthe melody. These together suggests a B7 in first inversion. If it were notated as a B7 it is doubtful any-one would question it being the V7 of E minor. The five pitches suggested by the melody and the chordsymbol are two notes short of a scale: B - C - D# - ? - F# - ? - A. What kind of an E and G would fit withthe given five notes? Examining the surrounding chords leaves no doubt they should be E and Gn. Theresulting scale? B - C - D# - E - F# - G - A, all the notes of E harmonic minor.

The vii°7/iii chord may follow or precede the iii chord. When it follows the iii7 chord it may decep-tively resolve to the ii7 chord in progressions like the following: In the first progression, the D#°7 seemsto clearly be the vii°7/iii as it resolves up to the Em7 chord. When ascending the D#°7 is the vii°7/iii, soit is rational to conclude that it is the same chord when descending, regardless of its resolution. If a G7that resolves deceptively to Am is still the V7 of C, then a D#°7 can be the vii°7/iii even when resolvingto Dm7.

6.16a D#°7 (vii°7/iii) with typical and deceptive resolutions:

Cmaj7 Dm7 – D#°7 Em7 – D#°7 Dm7 – G7 Cmaj7I ii7 – vii°7/iii iii7 – vii°7/iii ii7 – V7 I

6.17b D#°7 (vii°7/iii) with deceptive resolutions:

Cmaj7 – Dm7 Em7 – D#°7 Dm7 – G7 Cmaj7I – ii7 iii7 – vii°7/iii ii7 – V7 I

The vii°7/iii is used in place of the V7 chord in this progression, but it is not the V7 of I. When the ii7 -V7 points back to the I chord and the iii7 chord is used in its place, the iii7 chord can then be precededby its dominant or dominant substitute. E7 (V7/iii) is the dominant of Am7 and G#°7 (vii°7/ii)i is adominant substitute.

6.18

Fmaj7 Gm7 – C7 Am7 OR Fmaj7 Gm7 – G#°7 Am7I ii7 – V7 iii7 I ii7 – vii°7/iii iii7

This imposition of a vii°7/iii can be used whether or not the progression actually goes to the iii7 chord.In this excerpt from a Charlie Parker improvisation, the G#°7 was used to progress to the I chord and notthe iii7 chord. Is it a vii°7/iii? If it is, then the notes necessary for modulation or tonicization would bethe Bn to change the key signature to no sharps or flats, and the leading tone G#. Parker plays those nec-essary tones clearly and unambiguously.

6.19

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Gm7 G#°7

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F



VALUE & LIMITS of ROMAN NUMERAL ANALYSIS (RNA)

RNA should identify what is heard. It is not an abstract theoretical concept, but a tool explaining what isexperienced musically. As with all tools, there are limits to their use. A hammer is inefficient with ascrew and a screw driver will not drive a nail. Resist the temptation to force square pegs into roundholes. RNA is useful when analyzing music within the major/minor system. When chords are arrangedwithin functional harmony, i.e., harmony that functions to point to a tonic chord or pitch, then the RNAidentifies the key signatures and the basic melodic materials. RNA proves useful for a large body of mu-sic including most of the jazz standards.

There is also a large body of music that was not conceived with functional harmony, and so RNA is thewrong tool for analysis. If a composer has deliberately used harmony to obscure the sense of a tonalcenter, then a system designed to describe how chords function to point to a tonal center will be of nouse. There are some compositions where there is a mixture of approaches: a section of the piece willhave no relation to functional harmony relying on color harmony or modes, followed by a sectionwhere the harmony is quite traditional using ii7 - V7 progressions. To dissect this music, two or moreanalytical tools may be needed. The first section of the book is concerned with establishing an under-standing of the major/minor system which is used as a foundation for so much of the literature per-formed by jazz artists. With the foundation established, the exceptions, additions and departures studiedin the second part of the book will make more sense.

Chords can also be built on many different scales and modes, and can be built using a wide variety andmixture of intervals. These chords can be used to create music, but they are not necessarily functioningin the major/minor system of which RNA is designed to define. Some of these other sounds will be ex-plored in later chapters.

RNA is not just labeling each chord with a Roman numeral. This imparts no helpful information. If thepoint is to label the chords, then use chord symbols. RNA is more useful in the practice room than onthe bandstand. When Roman numerals are used correctly, they identify all the important pitches thatimply the harmonic motion that may be used for melodic material. Used incorrectly, they are just num-bers. If part of a progression includes chords from other keys, then modulation or tonicization has oc-curred and the RNA should identify those new keys and the pitches necessary for modulation. Thepitches necessary for modulation are the most important source for harmonic specific melodies.

A progression like the one below cannot be in one key, because there is not one key that contains allthese chords. This example shows an incorrect use of Roman numerals. There cannot be F#ø7, B7 or A7chords built using tones from the C major scale. The numbers reflect the proper intervals related to thetonic pitch, but are erroneous and misleading. The symbol “#ivø7” indicates that the half-diminishedchord is from the raised fourth of C major. There is no raised fourth in C major! The “VII7” symbolsuggests there is a D# and a F# in the key of C, and the “VI7” is suggests the impossible C# in the key of C.The symbols, if used correctly, should identify the keys. This progression cannot be from one key.

6.20 Incorrect RNA:

Cmaj7 F#ø7 – B7 Em7 – A7 Dm7 – G7 Cmaj7I #ivø7 – VII7 iii7 – VI7 ii7 – V7 I

The symbols below disclose more useful information. The F#ø7 - B7 is identified as being from the keyof iii, E minor. D# and a F# then can be identified as the necessary tones needed to clarify this part ofthe progression. Knowing that the A7 chord is not just a dominant chord built on the sixth degree of theC major scale, but is the dominant of D minor, the key of ii, yields the necessary pitches C#, the leadingtone, and Bb from the key signature.



6.21 Correct RNA:

Cmaj7 F#ø7 – B7 Em7 – A7 Dm7 – G7 Cmaj7I iiø7 – V7

iiiiii7 – V7/ii ii7 – V7 I

RNA is a tool used to explain the aural experience of harmony. Anyone listening to the progressionabove would know, upon hearing the F#ø7, B7 and A7 chords, that the key of C had been left behind.Leaving the home key is what makes the music interesting, and listeners respond accordingly. RNA canfacilitate the understanding of these harmonic diversions. The most important part of understanding isbeing able to hear these progressions, the pitches that determine the tonic key and the pitches that cre-ate modulations to remote keys.

DOMINANT CHORD EXCEPTIONS

In the discussion of chord types and function, dominant chords were found only on the dominant pitchof major or minor keys. They functioned to point down a fifth to those tonic chords regardless of actualresolution. There are three other types of chords that will be encountered in jazz that sound like domi-nant chords but do not function as a V7 in major or minor. A tritone substitution dominant chord isthe substitution of a dominant chord a tritone away from the actual dominant which resolves down ahalf step in either major or minor keys. A chord which sounds like and is labeled a dominant seventhchord built on the flatted sixth degree in minor and resolves to the dominant chord is related to thetraditional augmented sixth chord. A backdoor dominant deceptively resolves up a whole step to ma-jor keys and is related to a plagal cadence.

TRITONE SUBSTITUTION

The dissonant augmented fourth interval between the fourth and seventh scale tones of a major or aharmonic minor scale is called a tritone (from the three whole steps between the pitches). The tritone isthe major third and minor seventh of the dominant chord, and the active tones of the chord. The tri-tone dissonance wants to resolve in contrary stepwise motion. At (a), the B pulls up to the tonic pitch Cand the F resolves down to the major or minor third.

6.22 (a) The tritone resolves in contrary stepwise motion:

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G7 C

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G7 Cm

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˙

Two dominant chords a tritone apart share the same tritone (b). A G7 and a Db7 have the same thirdand seventh, although inverted and with an enharmonic spelling. The F is the third of Db7 and the sev-enth of G7; the Bn is the third of G7 and Cb is the seventh of Db7. If the Cb is spelled as a Bn, an intervalof an augmented sixth in created between the Db and the Bn. In jazz chord notation practice, this chordis labeled a dominant seventh, as it sounds, rather than an augmented sixth chord as it may be spelled.Since these two dominants share the same tritone, and the tritone still wants to resolve in contrary step-wise motion, the Db7 chord can substitute for the G7 chord.



6.22 (b) G7 and a Db7 share the same tritone.

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b˙

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G7 Db7 Db7

37 3

7

˙

˙b ˙b

A6

˙

˙

˙

˙

Db7 C

˙b˙

˙

˙

˙

˙b

Db7 Cm

˙b˙

Any dominant chord may be replaced in a progression by the dominant chord a tritone away if its res-olution is down a half step to the tonic chord. (It is not used in the progression where the dominantmoves to chords other than tonic). This is called tritone substitution.

6.22 (c) Tritone Substitution: Db7 may substitute for the G7

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Dm7 G7

˙

˙

w

w

C

w

˙

˙

˙

˙

Dm7 Db7

˙ ˙b

w

w

C

w

The tritone substitute dominant chord will often contain the actual dominant pitch. The dominant pitchis critical in melodies as it helps extablish the tonality and its occurrence over the tritone substitutedominant supports this melodic function. The inclusion of the dominant tone in a tritone substitutedominant explains why it does not sound or function like a typical dominant. The tritone substitutedominant does not want to resolve down a perfect fifth. The Db7 in the example below contains thepitch “G,” which confirms its identity as the tritone substitute for the G7 chord. It is doubtful that anyonelistening to the passage would expect the Db7 to resolve to Gb major. It could be argued that the Db7chord is actually an inverted G7 chord evidenced by the enharmonic spelling: G - B - Db - F.

6.23 Tritone substitute dominants that contain the dominant pitch:

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œ

œ

œ#

œœ

œn

œœ

œ

Em7 A7 Dm7 G7

œ

œ

œ

œ

ww

w

Cmaj7

w

œ

œ

œ

œb

œœ

œ

œœ

œ

Em7 Eb7 Dm7 Db7

œ œbœ œb

A4

ww

w

Cmaj7

w

There is no traditional agreed upon RNA notation for a tritone substitution. There are symbols foraugmented sixth chords, but tritone substitute dominants do not behave as augmented sixth chords.Augmented sixth chords commonly substitute for a ii7 or a IV chord and resolve to a dominant chordso using the augmented sixth chord symbols here would be misleading. For the purposes of this book,the symbol “TT7” will be used to indicate a tritone substitute dominant chord. The two progressions at(c) above would then be: ii7 - V7 - I, and ii7 - TT7 - I.



Knowing that dominant chords a tritone apart function in similar ways complicates the harmonicanalysis process by only a small degree. Until now in this discussion, a dominant chord was always a V7pointing down a fifth to a tonic chord. Dominant chords substituting for V7 point down a half step tothe chord of resolution. It will be easy to determine the type of dominant by examining the context.

SECONDARY DOMINANTS & TRITONE SUBSTITUTION

A piece of music may modulate to closely related keys using secondary dominants. Any dominantchord may have a tritone substitution. The tritone substitution chord is usually spelled in the easiest toread enharmonic form, commonly avoiding chords like Fb7 and Bbb7. An example from the key of Cmajor is shown below.

TONIC KEY SECONDARYDOMINANT

TRITONESUBSTITUTEDOMINANT

NEW KEY

C A7 Eb7 D minorC B7 F7 E minorC C7 Gb7 F majorC D7 Ab7 G majorC E7 Bb7 A minor

Learn to recognize dominant chord paired with their tritone substitute chord and the home key to whichthey point.

DOMINANT CHORD

(V7)

TRITONE SUBSTITUTEDOMINANT

(TT7)

TONIC KEY

(I or i)G7 Db7 C major & C minorC7 Gb7 F major & F minorF7 B7 Bb major & Bb minorBb7 E7 Eb major & Eb minorEb7 A7 Ab majorD#7 A7 G# minorAb7 D7 Db majorG#7 D7 C# minorDb7 G7 Gb majorC#7 G7 F# major & F# minorF#7 C7 B major & B minorB7 F7 E major & E minorE7 Bb7 A major & A minorA7 Eb7 D major & D minorD7 Ab7 G major & G minor

TRADITIONAL AUGMENTED SIXTH CHORDS

Good music theory should always describe the way the music sounds. One exception in traditionalmusic theory is the augmented sixth chord. It sounds like a dominant seventh but is labeled a sixthchord because its spelling includes the interval of an augmented sixth. Adding to the confusion is thatthree geographical labels are often attached to these chords. The augmented sixth chord is usuallyfound in first inversion.



Historically, the entire concept of harmony came about as a result of melodic lines. The convergence oflinear materials evolved into the recognition of certain vertical sonorities, chords and finally harmonicprogressions. As certain sonorities occurred with more frequency, they became easier and necessary toname. The dominant seventh was not considered a chord at one time, but the voice leadingcircumstance of a dissonant passing tone (seventh) resolving to the third of the subsequent tonic triad.As composers used the chord with more frequency and for longer durations, the vertical sonoritybecame the dominant seventh chord. Similar histories are true for most chords including theaugmented sixth chord. The augmented sixth chord was originally considered a circumstance ofchromatic voice leading between the IV or iv chords and the V7 chord and not an independent chord.

When the IV chord (a) is in first inversion, the fourth scale degree may move up chromatically while thesixth degree moves chromatically down to the fifth degree, resolving to an octave. The interval betweenthe two chromatic passing tones is an augmented sixth (as shown between the Ab and F#). Though theactual tertian spelling of the chord at (a) is F# - Ab - C, it sounds like an Ab7 chord without the fifth (Ab -C - Gb). This type of augmented sixth chord is commonly labeled the “Italian sixth.” The “French sixth”at (b) is often preceded by a iiø7 chord in second inversion. The fourth scale degree moves through achromatic passing tone to the fifth, creating the augmented sixth interval between the Ab and F#. Thetertian spelling of the chord is D - F# - Ab - C, but with the Ab in the bass, to a jazz musicians, it soundslike an Ab7 chord with a b5 or a #11. The “German sixth” is often preceded by a iv7 chord in firstinversion. The fourth scale degree again progresses through a chromatic passing tone to the fifth,creating the augmented sixth interval. The resulting chord is spelled F# - Ab - C - Eb, but with the Ab in thebass, sounds like an Ab7 chord (Ab - C - Eb - Gb). An augmented sixth chord can occur following itssound-alike dominant seventh chord as in the modulation from C major to E minor shown at (d). The Cmoves to C7, the V7/IV, but with the enharmonic change of the Bb to A#, the chord becomes a “Germansixth” leading to the cadence to E minor. The international labels are meaningless. There are manyexamples in literature where all three of the defining notes are present melodically over the augmentedsixth chord. Example (e) is a virtual “Tour of Europe Sixth” chord.

6.24(a) “Italian Sixth” (b) “French Sixth”

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IV6 A6A6

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n

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V V7

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iiø43 A6

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V64 V7

w

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(a) (b)

(c) “German Sixth” (d) “German sixth”

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(c) (d)



(e) “Tour of Europe Sixth” Chord

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Gr/Fr/It

The augmented sixth chord is relevant to jazz and occurs often in compositions in minor keys. Jazzmusicians, with the chord symbol shorthand notation, label the chord as it sounds, not as it may bespelled in 17th and 18th century part writing. This chord is used in place of other pre-dominant chordslike the IV, iv7, ii7 and iiø7 as any augmented sixth chord. The sound of a dominant chord resolvingdown a half step is related to the half step resolution of the tritone substitute dominant chord which alsohas the augmented sixth interval. The concept of chord symbol notation is to aid musicians in quickreading of the chord symbols. For this reason, this augmented sixth chord and the tritone dominantsubstitute are often identified with the easiest enharmonic spelling, usually avoiding chords like Bbb7 infavor of A7. The traditional notation of “A6” for augmented sixth, or some symbol indicating theinternational names (#ivIt, ii7Fr , #ivGr) are not used by jazz musicians. These symbols would only causeconfusion in a jazz world. The “A6” might be confused with the A triad with an added F#. Since thischord behaves as a tritone substitute dominant resolving down a half step, for analysis the symbol“TT7” will be used for this book. For jazz shorthand chord notation, all of the augmented sixth chordsabove (a-e) would be labeled as they sound: as Ab7 chords.

The augmented sixth chord could have presented simply as a dominant seventh chord that may resolvedown a half step to the dominant chord, but it is important to understand the historical background andrelationship of jazz music styles to those of other eras.

Complete the table below showing the typical pre-dominant - dominant resolving to minor progression.

Augmented6th chord

sounding likea dominantchord on bVI

V7 i

F7 E7 A minorD minorG minor

Ab7 G7 C minorF minorBb minorEb minor

Augmented6th chord

sounding likea dominantchord on bVI

V7 i

D# minorG# minor

A7 G#7 C# minorF# minorB minorE minor



BACKDOOR DOMINANTS

A backdoor dominant is a dominant chord that deceptively resolves up a whole step to major keys. It isoften preceded by the IV chord. It may resolve to the iii7 or the I6 chords which often substitute for the Ichord in the middle of a progression.

A plagal cadence occurs when IV resolves to I as in “amen” shown at (a). Another plagal cadence is theprogression iv - I, or IV - iv - I at (b). The natural tendency for roots to descend in fifths suggests thenatural evolution of the IV chord resolving to a chord on the lowered seventh degree at (c) in place ofthe iv chord. This chord then seems to resolve to the I chord from the backdoor.

6.25 Plagal Cadences(a) (b) (c)

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F C

IV I˙

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F Fm C

IV iv I˙

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F Bb9 Cmaj7

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The backdoor dominant chord may also contain the interval of an augmented fourth above the root.The major seventh of the IV chord is often retained in the backdoor dominant and anticipates themajor third of the tonic chord. This note is why the backdoor dominant typically resolves to major andnot minor. The Bb7 shown below will not sound like a V7 in the key of Eb because of the surroundingcontext of C major and the En occurring in the chord. The chords below are shown with more extendedvoicings. The F chord includes the major seventh and ninth. The Bb7 chord includes the 9 - #11 - 13. The9 - #11 - 13 (C - E - G) of the Bb7 chord are the primary pitches of the upcoming tonic chord “C.” Forthe purposes of this book, the symbol “BD7” will refer to this type of dominant chord. The Bb7 chord inthe second example is not a backdoor dominant. Backdoor dominants point to major keys and notminor keys. In this typical deceptive cadence, the Bb7 would be heard as the V7 or Eb and the Cm7 asvi7.

6.26Backdoor Dominant with Extended Voicings V7 - vi7 Deceptive Cadence

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Fmaj7 Bb9# 11 Cmaj7

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A4

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Fm9 Bb13 Cm9

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Simple harmonic passages can be energized by the addition of tritone substitutions and backdoordominants.

6.27Basic step progression: IV - iii7 - ii7 - Imaj7.

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Fmaj7

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Em7

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Dm7

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Cmaj7

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IVmaj7 iii7 ii7 Imaj7

A iv7 chord (Fm7) can be borrowed from the parallel minor. The ii7 (Dm7) chord can be preceded byits secondary dominant (A7 = V7/ii) and the tonic chord by the primary dominant (G7 = V7).

6.28

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Fmaj7 Fm7

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b

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Em7 A7

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Dm7 G7

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Cmaj7

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IVmaj7 iv7 iii7 V7/ii ii7 V7 I maj7

The backdoor dominant (Bb7) can replace the borrowed iv7 chord. This backdoor dominant did notresolve to the I chord, but moves to the substituting iii7 chord. The Eb7 is the tritone substitution for theA7 and the Db7 for the G7.

6.29

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b

Fmaj7 Bb7

˙

˙b

˙˙

˙˙

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Em7 Eb7

˙ ˙b

˙˙

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Dm7 Db7

˙ ˙b

ww

w

Cmaj7

w

IVmaj7 BD7 iii7 TT7/ii ii7 TT7 I maj7



The addition of these special dominant chords allows for several possible cadences to the tonic majoror minor chord. This is a list of possible chords. Not all pre-dominant chords lead to all dominantchords. The backdoor dominant is usually preceded by the IV or iv7 chord. A partial list ofcombinations follows this chart.

PRE-DOMINANT CHORDS DOMINANT CHORDS TONIC CHORDS

IV V7 I

ii7 viiø7 (rare) i

iiø7 vii°7 I6 or iii as substitute for I

iv7

Augmented 6th chord on bII as

tritone substitute dominant

(TT7)

(sometimes vi7 as deceptive

resolution)

V7/V Backdoor dominant on bVII

as plagal cadence (BD7)

vii°7/vvii°

65/iii

bVImaj7

Augmented 6th chord sounding

like a dominant chord on bVI

PARTIAL LIST of CADENTIAL COMBINATIONS

Diatonic Chords:

Dm7 G7 Cmaj7ii7 V7 I

Dø7 G7 C miiø7 V7 i

With Borrowed iiø7:

Dø7 G7 Cmaj7iiø7 V7 I

With Tritone Dominant Substitution:

Dm7 Db7 Cmaj7ii7 TT7 I

Dø7 Db7 C miiø7 TT7 i

With Tritone Dominant Substitution& Borrowed iiø7 chord:

Dø7 Db7 Cmaj7iiø7 TT7 I

Plagal Cadence with Backdoor Dominant:

Fmaj7 Bb7 Cmaj7IV BD7 I

With Secondary Dominant (V7/V):

D7 G7 Cmaj7V7/V V7 I

With Secondary Dominant (V7/V)& Tritone Substitution:

D7 Db7 Cmaj7V7/V TT7 I

With Tritone Dominant Substitutionfor Secondary Dominant:

Ab7 G7 Cmaj7TT7/V V7 I

Ab7 G7 C mTT7/V V7 i

With Tritone Dominant Substitutionfor Secondary Dominant & Dominant:

Ab7 Db7 Cmaj7TT7/V TT7 I

Ab7 Db7 C mTT7/V TT7 i

chapter.06.pdf

Documents

type of root movement

ii7 v7

ii7 chord of f

downward fifths type

seconds type

v7 chords

mostcommon root movements

iv chord