Alpha scale

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Minor third (just: 315.64 cents About this soundPlay ,
12-tet: 300 cents About this soundPlay ,
Alpha scale: 312 cents About this soundPlay 

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.[citation needed] In another it splits the minor third into two equal parts,[1] or four equal parts of approximately 78 cents each[2] About this soundPlay . At 78 cents per step, this totals approximately 15.385 steps per octave. The scale step may be precisely derived from using 9:5 About this soundPlay  to approximate the interval ​3:25:4,[3] which equals 6:5 About this soundPlay .

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," (About this soundPlay major  and About this soundminor 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 [octave] inversion of ​74, i.e., 87."[4] About this soundPlay  More accurately the alpha scale step is 77.965 cents and there are 15.3915 per octave.[3][5]

interval name size
just ratio just
septimal major second 3 233.90 8:7 231.17 +2.72
major third 5 389.83 5:4 386.31 +3.51
perfect fifth 9 701.69 3:2 701.96 −0.27
harmonic seventh 12 935.58 7:4 968.83 −33.25
octave 15 1169.48 2:1 1200.00 −30.52
octave 16 1247.44 2:1 1200.00 +47.44

See also[edit]


  1. ^ a b 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. ^ a b 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",
  5. ^ Sethares, William (2004). Tuning, Timbre, Spectrum, Scale, p.60. ISBN 1-85233-797-4. Scale step of 78 cents.