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 .
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.
- Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
- Carlos, Wendy (2000/1986). "Liner notes", Beauty in the Beast. ESD 81552.
- Benson, Dave (2006). Music: A Mathematical Offering, p.232-233. ISBN 0-521-85387-7. "This actually differs very slightly from Carlos' figure of 15.385 α-scale degrees to the octave. This is obtained by approximating the scale degree to 78.0 cents."
- Carlos, Wendy (1989–96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.
- Sethares, William (2004). Tuning, Timbre, Spectrum, Scale, p.60. ISBN 1-85233-797-4. Scale step of 78 cents.