At the heart of Barry Harris’s Theory of Evolution is the chromatic scale, shown on the top staff with enharmonic equivalents (i.e., different note names representing the same pitch, such as D sharp and E flat).Separate the solid and hollow noteheads, and you’ve got the two whole-tone scales (middle staff). Also derived from the chromatic scale are the three diminished 7th chords (bottom staff). Note that each includes two tritones: one from each whole-tone scale.
Each diminished 7th chord yields four dominant 7th chords. Just pick a note and lower it one-half step; this note then becomes the root of the dominant 7th chord. Shown below are the four dominant 7ths that relate to C#dim7 – Barry Harris would like you to keep the relationship between these four dominant 7ths in mind. Did the math already? That’s right, three diminished 7th chords means twelve dominant 7ths in all.
Dominant 7th chords generated by the same diminished 7th chord are functionally related. You can use them as substitutes for one another or choose one as the basic voicing and combine it with any of the others to make an extended dominant.
From the diminished 7th chord you can also create major 6th chords (left) and minor 6th chords (right). These chords sound the same as their corresponding minor 7th and minor 7 flat 5 chords, respectively. For functional reasons that we’ll cover in subsequent examples, think of them in their 6th forms.
Thinking of C as the tonic for both a major and a minor scale, here are major and minor 6th chords of that scale along with a diminished 7th chord. See examples 6 and 7.
Put the major 6th chord in Example 5 together with a diminished 7th chord, and you get what Barry likes to call the major 6 diminished scale.
Put the minor 6th chord of Example 5 together with a diminished 7th chord, and you get Barry’s minor 6 diminished scale.
An interesting and useful feature of the major 6 diminished scale is that it contains two dominant 7th chords: the V7 of the tonic and the V7 of the relative.
Playing a minor 6 diminished scale beginning a half-step higher than the root of a dominant 7th chord covers the root, 3rd, minor 7th, and all of the commonly used altered tones. You can even think of the minor 6 diminished scale as an altered scale when you use it this way.
Here are some starting points for seeing the relationships between 6th voicings and their functional equivalents: a) For major 7th chords, play the major 6th chord whose root is the fifth degree of the major scale. b) One approach to a dominant 7th voicing is to play the minor sixth chord on the fifth degree of the dominant. c) Another dominant 7th approach is to use the minor 6th chord whose root is one-half step up from the root of the dominant. d) Minor 7th chords are just inversions of major 6th chords, so this combination is natural. e) The same goes for minor 7 flat 5 and minor 6th chords. With the latter two examples, thinking in terms of 6th voicings opens up the possibility of moving voicings along a corresponding major or minor 6 diminished scale and then resolving to the next chord, rather than to simply hold a static voicing.