·         The idea that a chord is a scale in shorthand form may be extended to other important harmonic structures.

·         Consider Ao, comprising A C Eb Gb.  To flesh out this skeleton into a scale we need to insert notes between the notes of the chord.  We can make the pattern of intervals symmetrical by introducing notes each of which is either a semitone or a whole tone above a note in the chord of Ao.

·         The results are two different diminished scales, the so-called half tone-whole tone (HW) scale and the whole tone-half tone (WH) respectively. 

·         So to make the WH scale based on Ao, we slot in the note B between A and C.  Between C and Eb comes D.  Eb goes to Gb via F, and above Gb the last element is Ab (Example [9.1]).  Example [9.2] shows the HW scale of A diminished.

·         Diminished scales are beautiful, versatile and essential tools for the jazz musician.  A notable feature of the diminished scale is that there are nine notes from the root to the same note an octave higher.

·         You will recall that there are only three possible diminished chords (see Step 5).  Remind yourself of what they are.  Work out the WH and HW scales for each of these chords and you'll find that, in terms of the notes from which they're built, there are only three different diminished scales.

·         The whole-tone scale is usually considered to be the parent of the augmented chord.  D+ (D F# A#) is thus associated with D whole-tone (Example [9.3]).  Verify that the four possible augmented chords are associated with only two distinct whole-tone scales.

·         The whole-tone is another scale that departs from the familiar pattern of eight scale degrees from the root to the octave.  In this case there are seven notes from I to I¹.

·         A little experimentation with left-hand diminished and augmented shells set against right-hand improvised lines based on diminished and whole-tone scale material wouldn't do any harm at this stage.