Each whole tone scale replicates itself when re-ordered in a revolving manner.
Pitch-classes remain identical, the “spacing” remains identical, although
enharmonic spellings are freely used.

Figure 3.26

Revolving Whole Tone Scales

Audio 17

Whole Tone Scale Rotations

(click to see video)

Because of these properties there are only two whole tone scales aurally. All other
versions are re-orderings of either

WT I

or

WT II

, but will assume individual

identities according to their use is specific contexts.

Octatonic Scale

Another commonly used symmetrical scale is called the

Octatonic

Scale

26

.Theoretically, any scale with eight constituent members is an octatonic

scale. The versions described here are those most commonly used. In Jazz pedagogy,
these versions are called “diminished scales” or “symmetrical diminished scales”
because of the structures formed by alternate scale degrees. The two related forms
of the Octatonic Scale divide the octave into eight portions consisting of either
alternating half steps and whole steps, or alternating whole and half steps.

26. An eight-tone scale. The most

common form is the
symmetrical division of the
octave into eight portions of
either alternating half steps
and whole steps, or alternating
whole steps and half steps

Chapter 3 The Foundations Scale-Steps and Scales

3.5 Other Commonly Used Scales

115