Chromatic circle

Comparing the gamma scale's approximations with the just values

Twelve-tone equal temperament vs. just

Theγ (gamma)scale is a non-octave repeatingmusical scale invented byWendy Carlos while preparingBeauty in the Beast (1986) though it does not appear on the album. It is derived from approximatingjust intervals using multiples of a single interval without, as is standard inequal temperaments, requiring anoctave (2:1). It may be approximated by splitting theperfect fifth (3:2) into 20 equal parts (3:2^1⁄20≈35.1 cents),^{[citation needed]} by splitting theneutral third into two equal parts, or ten equal parts of approximately 35.1 cents each (Play^ⓘ) for 34.188 steps per octave.^[1]

Thescale step may also precisely be derived from using20:11 (B↓, 1035 cents,Play^ⓘ) to approximate the interval3:2⁄5:4,^[2] which equals6:5 (E♭, 315.64 cents,Play^ⓘ). Thus the step is approximately 35.099 cents and there are 34.1895 per octave.^[2]

${\displaystyle \frac{20{\log }_2(3/2)+11{\log }_2(5/4)+9{\log }_2(6/5)}{{20}^2+{11}^2+9^2}=0.0292487852}$ and${\displaystyle 0.0292487852\times 1200=35.0985422804}$ (Play^ⓘ)

"It produces nearly perfect triads."^[3] "A 'third flavor', sort of intermediate to 'alpha' and 'beta', although a melodicdiatonic scale is easily available."^[1]

• Alpha scale
• Beta scale
• Delta scale
• Bohlen–Pierce scale
• Gamma chord

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