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The γ ( gamma) scale is a non-octave repeating invented by while preparing Beauty in the Beast (1986) though it does not appear on the album. It is derived from approximating using multiples of a single interval without, as is standard in equal temperaments, requiring an (2:1). It may be approximated by splitting the (3:2) into 20 equal parts (3:2≈35.1 cents), by splitting the into two equal parts, or ten equal parts of approximately 35.1 cents each () for 34.188 steps per octave.Carlos, Wendy (1989–96). "Three Asymmetric Divisions of the Octave", WendyCarlos.com.

The may also precisely be derived from using (B, 1035 cents, ) to approximate the interval , which equals (E, 315.64 cents, ). Thus the step is approximately 35.099 cents and there are 34.1895 per octave.Benson, Dave (2006). Music: A Mathematical Offering, p.232-233. . "Carlos has 34.188 γ-scale degrees to the octave, corresponding to a scale degree of 35.1 cents."

\frac{20\log_2{(3/2)}+11\log_2{(5/4)}+9\log_2{(6/5)}}{20^2+11^2+9^2}=0.0292487852 and 0.0292487852\times1200=35.0985422804 ()

"It produces nearly perfect triads."Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard. "A 'third flavor', sort of intermediate to 'alpha' and 'beta', although a melodic is easily available."

interval namesize
(steps)
size
(cents)
just
ratio
just
(cents)
error
minor third9315.896:5315.64+0.25
major third11386.095:4386.31−0.22
perfect fifth20701.983:2701.96+0.02


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