Alpha scale

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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.[citation needed] 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]

interval name size
(steps) 		size
(cents) 		just ratio just
(cents) 		error
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 -3 966.11 7:4 968.83 −2.72
octave 15 1169.48 2:1 1200.00 −30.52
octave 16 1247.44 2:1 1200.00 −47.44

See also

Sources

  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", 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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