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Jazz Theory and Practice

Module 5 a, b, c

Dim. 7th & 9th Chords; Extensions to the 13th;

Other Harmonic Structures

A. Diminished 7th chords; 9th chords

1. Diminished and half-diminished 7th chords.

The basic harmonic vocabulary of Jazz Theory was introduced in Module 2: dominant 7th chords in Module 2(a), minor 7th chords in

Module 2(b), major 7th and half-diminished 7th chords in Module 2(c). If we build 7th chords on every note of the major scale, and the natural

minor scale (Aeolian) all the chords belong to these four basic types of

seventh chords:

5a1

In traditional Music Theory these are called the diatonic 7th chords,

because all of the notes fall within the diatonic (7-note) scale. In minor scales, however, the seventh note is often raised a half-step.

This produces some new harmonic resources for the minor scale:

©2015 Peter J. Clements

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5a2

This version of the minor scale, always a part of traditional Music

Theory, is called the Harmonic Minor Scale. When 7th chords are generated for the harmonic minor scale, the raised 7th step produces

four chords (I7, III7, V7, and #VII7) that are not in the natural minor scale, but, as shown, the III7 is seldom used with the raised 7th step.

What are frequently used are a diminished 7th chord, and the V7, identical to the one in the parallel major.

Just as the Mixolydian scale has a natural “fit” with the dominant 7th

chord, the harmonic minor scale (starting on the 7th note) fits the diminished-7th chord. Another scale that is a perfect fit is the

diminished scale (also called the octatonic scale), constructed with alternating half-steps and whole-steps:

5a3

The diminished-7th chord is a symmetrical chord; it divides the octave into four equal parts (all minor 3rds), and on the keyboard there really

are only three different diminished-7th chords:

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5a4

If you look carefully at the 4th chord, you will discover that the notes

enharmonically are identical to the notes in the first chord. Notice, as well, that diminished-7th chords will often contain “unusual” notation.

In the first chord, the 7th must be B-double flat, but if that note were

moved to the bottom, the chord would be A - C - Eb - Gb. The second

chord seems unusual because it contains both a sharp and a flat; that often happens with diminished-7th chords.

Since it is a symmetrical chord, and sounds exactly the same no

matter which note is in the bass, the diminished 7th chord really has no root, or at best the root is ambiguous. This ambiguity allows the

diminished 7th chord to be used in all sorts of different ways.

In the previous Module, we used a diminished 7th chord as part of a turnaround:

5a5

There are two functions working here: (a) the diminished 7th is a

passing chord between I and II: notice the rising half-steps in the bass, and the smooth connections among the other parts. (b) the

diminished 7th chord can also be described as a leading-tone chord moving to II, like a VII7 in D minor. In traditional theory this chord

would be called VII7/II.

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In one of the many variations of the 12-bar blues progression, a

diminished-7th chord appears in the 8th bar. It serves as a passing chord, and as a chord leading to II, just as in the previous example:

5a6

The diminished-7th chord is also useful as a descending passing chord. In these two excerpts from Baubles, Bangles, and Beads the

descending chromatic bass is harmonized with a diminished-7th chord between two minor-7th chords. Notice that the two melody notes are

not in the diminished-7th chord, and one note of the chord is missing:

5a7

The following fragment from Everything Happens to Me shows how a descending passing diminished-7th chord can be used in a tritone

substitution. The three minor-7th chords are a cycle of fifths; substituting the diminished-7th chord produces a descending chromatic

bass, as in the previous example:

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5a8

The opening bars of Spring is Here show another use for the versatile diminished-7th chord. In traditional music theory this is called the

“common-tone diminished 7th”; in this example the common tone is

the Ab in the bass through the first four bars. The G in the melody is

dissonant against the diminished-7th chord, moving to the Ab at the end

of the bar.

5a9

The half-diminished 7th chord only differs by one note from a

diminished 7th, but it usually functions in a totally different way. In traditional harmony the half-diminished 7th is often used as a passing

chord, ascending or descending. In jazz harmony, however, the half-diminished chord is almost always used as a predominant chord (II7)

in the minor key. Even in major keys, the half-diminished chord appears frequently as part of a minor key tonicization. For example,

look at the next two bars of Spring is Here:

5a10

Notice the “Cm7(b5)” label, often used for the half-diminished 7th.

2. 9th chords; “rootless” 9th chords.

The jazz keyboard or guitar player will often play half-diminished 7th chords that are really 9th chords. This “rootless voicing” is frequently

used for 9th chords; a full 5-note voicing for a 9th chord is often difficult to manage, and in many settings a bass player is playing the root

anyway.

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5a11

There are a number of different 9th chords, and each one has a rootless voicing with the same notes as a common 7th chord:

9th Chord Symbol Rootless Version Symbol

Dominant 9th C9 Half-diminished 7th Em7(b5)

Dominant 7th (b9) C7(b9) Diminished 7th Edim7

Major 9th CMaj9 Minor 7th Em7

Minor 9th Cm9 Major 7th EbMaj7

Minor 7th (b9) Cm7(b9) Dominant 7th Eb7

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5a12

3. Dim. 7th chords, 9th chords and voice-leading

In Module 2, when the dominant-7th chord was discussed, it was noted

that, in traditional classical theory, the 7th of the chord almost always resolves (moves down by step). In general, this applies to all 7th

chords: the connection to the following chord works best if the 7th resolves, unless the 7th also appears as a note in the following chord,

then the logical connection is to the common note. The third of the 7th chord usual resolves upwards, unless there is a common note in the

following chord:

5a13

In the example above observe that there are two “tendency” notes, forming a dissonant tritone in the dominant-7th chord. Common

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voice-leading practice is to resolve both notes. If the dominant-7th

moves to another 7th chord, however, the common note connection is often available.

A unique property of the diminished-7th chord is that there are two

tritones in the chord. Generally the 7th is almost always resolved, and at least one of the dissonant tritones. Look at the following examples:

5a14

When a 9th is added, it typically has a strong tendency to resolve down, like the 7th; this is especially obvious in rootless voicings, where

the 9th appears to be a 7th. There are two notable exceptions: one where the 9th is a common tone within the next chord; and where the

9th chord assumes some stability, and may not be followed by anything, as the final chord of a piece, for example. In the 9/6 version

of the 9th chord discussed below, the 9th needs no resolution.

5a15

In the top line, above, there are three 9th chords where the 9th resolves down by step. In the first and third bars the 9th doesn’t

appear in the chord label, but it is the melody note, so the first chord is really a G 6/9, and the chord in the 3rd bar is an Am9. This

“incomplete labelling” is a common practice.

In the second line there are actually two 9th chords in the first bar, but the 9ths are created by passing scale notes. In the second bar the G7

chord is really a G9 when the melody note is included, and the excerpt

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ends with a 6/9 chord, with the root in the melody. This is a typical

“stable” chord that often ends a piece.

4. The 6/9 chord

Both major 6th and minor 6th chords can have a ninth added. The

result is the 6/9 chord, used frequently. In addition to rootless voicing, the fifth is often omitted. Notice the typical quartal (chord

built of 4ths) structure:

5a16

Here is one harmonization of the final bars of Baubles, Bangles, and

Beads: a circle of fifths using four different ninth chords, including the 6/9. Notice how the 9ths are often actual melody notes:

5a17

In this example the final melody note is the 9th of the chord, but if the

Ab were used it could be harmonized with the 6/9 chord as well,

producing a less dissonant sound than the major 7th.

Something to listen to:

Black Orpheus: In the minor key, with lots of II7 – V7 – I where the II7 is half-diminished. There are dozens of versions; try the one by

Paul Desmond with the Jim Hall Quartet.

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Baubles, Bangles and Beads: Many 9th chords are required for this

melody, also diminished 7ths as shown in the examples. There are many great recordings; try the one with Frank Sinatra and Antonio

Carlos Jobim.

Emily: Both 9th chords and 6/9 chords are needed to harmonize the melody. Find versions by Tony Bennett or Frank Sinatra

The Girl from Ipanema Heavily coloured with 9th chords, with major

and minor 7ths. The Stan Getz version is legendary.

How Long Has This Been Going On. Find the version by Ella Fitzgerald. The first two phrases use a descending passing diminished 7th in the

second bar, easily heard in the solo piano background.

How Insensitive: Good piece for both descending passing dim. 7ths,

and half-diminished chords introducing II7 � V7 � I7 in the minor. Many versions available; try Diana Krall.

Return to the menu, and try the PLAY/SING and WRITE exercises for

Module 5a.