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. In another, it splits the neutral third into two equal parts, or ten equal parts of approximately 35.1 cents each[1]
It may be derived from using 20:11
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]
interval name | size (steps) |
size (cents) |
just ratio |
just (cents) |
error |
minor third | 9 | 315.89 | 6:5 | 315.64 | +0.25 |
major third | 11 | 386.09 | 5:4 | 386.31 | −0.22 |
perfect fifth | 20 | 701.98 | 3:2 | 701.96 | +0.02 |
See also
Sources
- 1 2 3 Carlos, Wendy (1989-96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.
- 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."
- ↑ Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.