JAZZIN’ AROUND

The Overtone Series Part 4

Diminished triads and diminished 7th chords from the overtone series.

The II -V - I progression in Major and Minor.

By Anthony Lillywhite

Ex. 1 shows (once again) the overtone series from ‘C2’ (the C that is two 8ves below middle C) as shown in my previous three articles about the overtone series. The numbers shown are the ‘Partial Numbers’ by which the overtones are identified. In this article we will be focusing on the 5th, 6th, 7th and 9th partials.

Ex.1

In Ex. 2 below, the 1st bar shows the 5th, 6th and 7th partials forming a close root position E diminished triad. The 2nd bar shows the 5th, 6th, 7th and 9th partials forming an E half diminished 7th chord. The 3rd bar shows the 4th, 5th, 6th, 7th and 9th partials forming a C9th chord.

In my first article about the overtone series, I wrote: ‘The E diminished triad is really a C7 without its root; likewise, the E half diminished 7th chord is really a C9th without its root.’ This can be seen in Ex 2; the C shown on the bass staff in each bar is the 1st partial, i.e. the acoustical root of each of these chords. Therefore ‘E’ is referred to as the ‘apparent root’ of the E diminished triad and E half diminished 7th chords; the true acoustical root is C2.

Ex. 2 a tick alongside it to indicate that it has been altered (in the same manner as the altered 5th and 7th partials in my previous articles). Comparing E dim7 with the C7b9 in the 2nd bar, we see that E dim7 is really a C7b9 chord without its root

Ex. 3

Building a triad on the 7th degree of the major scale (i.e. the Ionian mode) results in a diminished triad consisting of the leading note, supertonic and subdominant. However when a 7th is added to this triad, the result is a half diminished 7th chord consisting of the leading note, supertonic, subdominant and mediant. See Ex 4.

Ex. 4

The 7th chords built on each of the degrees of the major scale are as shown in Ex. 5. Note the partial numbers placed alongside each chord.

In my previous two articles, I showed that minor triads have an altered 5th partial, and that major 7th chords have an altered 7th partial.

Consequently, of the diatonic 7th chords built on the degrees of the major scale, only the V7 and vii halfdim7 chords contain accurate partial numbers. This may be a reason why historically, their use purely as harmonic structures generally preceded the others.

Ex. 5

Building 7th chord on the 7th degree of the harmonic minor scale produces a diminished 7th chord. Of the commonly used diatonic scales in the tonal system, the harmonic minor is the only scale in which a diminished 7th is found.

Note the partial numbers; in both Ex5. and Ex 6. the chords built on the first six degrees have a 4th partial as their root. The 4th partial represents the acoustical root being 2 8ves below it. Only the diminished 7th and half diminished 7th chords built on the 7th degrees have an apparent root, (the 5th partial); the true acoustical root being represented by the 4th partial i.e. a major 3rd below the apparent root.

Ex. 6

Diminished 7th chords however are commonly used as ‘VII chords’ in major keys. This means that the 7th above the root is lowered by accidental. This note could be referred to as the ‘Minor Submediant’; a note that in classical theory is borrowed from the parallel minor. It is also commonly applied to the II and IV chords making them diminished and minor respectively.

The minor submediant has been utilized this way as an expressive device since the 18th century, becoming more prevalent from the 19th century onwards.

Arguably, the most important chord progression in jazz is the II - V, or II - V - I progression. When working from a chord chart or lead sheet, jazz musicians identify this progression as being major or minor from the chord symbols in this way:

IIm7 - V7 - Imaj7 indicates a major key,

IIm7b5 - V7b9 - Imin indicates a minor key. See Ex. 7 and Ex. 8

It is also not uncommon to see the minor II - V lead to a I major, and vice versa. See Ex. 9 i and ii.

Also the progression: IIm7 - V7b9 - Ima7 is very common. In major keys, it is usually possible to choose to add either a major 9th or minor 9th (b9) to a V7 chord. The minor 9th is the minor submediant of the key as mentioned above. See Ex. 10 i and ii.