Alpha scale

The α (alpha) scale is a non-octave-repeating musical scale. In one version it splits the perfect fifth (3:2) into nine equal parts of approximately 78.0 cents. In another it splits the minor third into two equal parts, or four equal parts of approximately 78 cents each Play . At 78 cents per step, this totals approximately 15.385 steps per octave. The scale step may be precisely derived from using 9:5  Play  to approximate the interval 3:2/5:4, which equals 6:5  Play .

It was invented by Wendy Carlos and used on her album Beauty in the Beast (1986).

Though it does not have an octave, the alpha scale produces, "wonderful triads," ( Play major  and  minor triad ) and the beta scale has similar properties but the sevenths are more in tune. However, the alpha scale has, "excellent harmonic seventh chords...using the inversion of 7/4, i.e., 8/7." Play  More accurately the alpha scale step is 77.965 cents and there are 15.3915 per octave.

See also