Gamma scale

Neutral third:
just 347.41 cents  Play ,
ET 350 cents  Play ,
Gamma scale 351 cents  Play 

The γ (gamma) scale is a non-octave repeating musical scale. In one interpretation, it splits the perfect fifth into 20 equal parts of approximately 35.1 cents each. In another, it splits the neutral third into two equal parts, or ten equal parts of approximately 35.1 cents each[1]  Play . At 35.1 cents per step this totals 34.188 steps per octave.[1]

It may be derived from using 20:11  Play  to approximate the interval 3:2/5:4,[2] which equals 6:5  Play .

It was invented by Wendy Carlos. "It produces nearly perfect triads."[3] "A 'third flavor,' sort of intermediate to 'alpha' and 'beta', although a melodic diatonic scale is easily available."[1]

More accurately the gamma scale step is 35.099 cents and there are 34.1895 per octave.[2]

See also


  1. 1 2 3 Carlos, Wendy (1989-96). "Three Asymmetric Divisions of the Octave",
  2. 1 2 Benson, Dave (2006). Music: A Mathematical Offering, p.232-233. ISBN 0-521-85387-7. "Carlos has 34.188 γ-scale degrees to the octave, corresponding to a scale degree of 35.1 cents."
  3. Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
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