Figure 3.27

Octatonic I (Oct I) and Octatonic II (Oct II)

Audio 18

Octatonic Scales

(click to see video)

Oct I

and

Oct II

have only three forms each.

Figure 3.28 "Octatonic Rotations"

shows

Oct I

with additional re-orderings on successively higher scale degrees. Observe

that, after the original form and two additional transpositions have been listed, the
fourth ordering is equivalent to the first, the fifth is equivalent to the second, and
so forth. The same holds true for

Oct II

.

Figure 3.28

Octatonic Rotations

“Augmented” Scale

Another commonly used hexatonic scale pattern is sometimes called the

“Augmented” scale

27

.This hexachord, along with the Whole Tone, Octatonic, and

Chromatic scales are labeled “Modes of Limited Transposition” in 20th-century
composer Olivier Messiaen’s

Techniques de mon langage musical

. This label refers to

the chords built upon alternate scale degrees. This is also a symmetrical construct,
evenly dividing the octave by the pattern, “half step and a step and a half.” It’s
related counterpart divides the octave by the reverse pattern, “step and a half and
halfstep.”

27. A hexatonic scale that

symmetrically divides the
octave by alternating half step
and step-and-a-half, or the
reverse.

Chapter 3 The Foundations Scale-Steps and Scales

3.5 Other Commonly Used Scales

116