Alpha scale

Minor third (just: 315.64 cents  Play ,
12-tet: 300 cents  Play ,
Alpha scale: 312 cents  Play 

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,[1] or four equal parts of approximately 78 cents each[2]  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,[3] 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.[1] However, the alpha scale has, "excellent harmonic seventh chords...using the inversion of 7/4, i.e., 8/7."[4]  Play  More accurately the alpha scale step is 77.965 cents and there are 15.3915 per octave.[3][5]

See also

Sources

  1. 1 2 Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
  2. ↑ Carlos, Wendy (2000/1986). "Liner notes", Beauty in the Beast. ESD 81552.
  3. 1 2 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."
  4. ↑ Carlos, Wendy (1989–96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.
  5. ↑ Sethares, William (2004). Tuning, Timbre, Spectrum, Scale, p.60. ISBN 1-85233-797-4. Scale step of 78 cents.
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