Gamma scale
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.[citation needed] In another, it splits the neutral third into two equal parts, or ten equal parts of approximately 35.1 cents each[1] <phonos file="Gamma scale step on C.mid">Play</phonos>. At 35.1 cents per step this totals 34.188 steps per octave.[1]
It may be derived from using 20:11 <phonos file="Lesser undecimal neutral seventh on C.mid">Play</phonos> to approximate the interval 3:2/5:4,[2] which equals 6:5 <phonos file="Just minor third on C.mid">Play</phonos>.
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
Sources
- ↑ 1.0 1.1 1.2 Carlos, Wendy (1989-96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.
- ↑ 2.0 2.1 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."
- ↑ Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
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