Gamma Scale
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Gamma Scale
Neutral third:
just 347.41 cents About this sound Play ,
ET 350 cents About this sound Play ,
Gamma scale 351 cents About this sound Play 

The ? (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]About this sound Play . At 35.1 cents per step this totals 34.188 steps per octave.[1] More accurately, but still approximately, the gamma scale step is 35.099 cents and there are 34.1895 per octave.[2]

It may be derived from using 20:11 About this sound Play  to approximate the interval ​,[2] which equals 6:5 About this sound 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]

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. ^ a b c Carlos, Wendy (1989-96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.
  2. ^ a b Benson, Dave (2006). Music: A Mathematical Offering, p.232-233. ISBN 0-521-85387-7. "Carlos has 34.188 ?-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.

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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