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. At 78 cents per step, this totals approximately 15.385 steps per octave. The scale step may be precisely derived from using 9:5 to approximate the interval $3:2/5:4$, which equals 6:5.

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," ( and ) 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 [octave] inversion of $7/4$, i.e., $8/7$." More accurately the alpha scale step is 77.965 cents and there are 15.3915 per octave.