- See also
- Sources
| align =
| direction = vertical
| width =
| header = Chromatic circle
| image1 = Gamma scale chromatic circle.png
| caption1 = Comparing the gamma scale's approximations with the just values
| image2 = 12-tet scale chromatic circle for comparison with alpha scale et al.png
| caption2 = Twelve-tone equal temperament vs. just
}}
The γ (gamma) scale is a non-octave repeating musical scale invented by Wendy Carlos while preparing Beauty in the Beast (1986) though it is does not appear on the album. It is derived from approximating just intervals using multiples of a single interval without, as is standard in equal temperaments, requiring an octave (2:1). It may be approximated by splitting the perfect fifth (3:2) into 20 equal parts (3:2{{sup|{{frac|20}}}}≈35.1 cents),{{Citation needed|date=January 2012}} by splitting the neutral third into two equal parts, or ten equal parts of approximately 35.1 cents each ({{audio|Gamma scale step on C.mid|Play}}) for 34.188 steps per octave.[1]
The scale step may also precisely be derived from using 20:11 (B{{music|U11}}, 1035 cents, {{audio|Lesser undecimal neutral seventh on C.mid|Play}}) to approximate the interval {{Frac|3:2|5:4}},[2] which equals 6:5 (E{{music|b}}, 315.64 cents, {{audio|Just minor third on C.mid|Play}}). Thus the step is approximately 35.099 cents and there are 34.1895 per octave.[2]
and 
({{audio|Gamma scale step on C.mid|Play}})
"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
- Alpha scale
- Beta scale
- Delta scale
- Bohlen–Pierce scale
- Gamma chord
Sources
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."
3. ^Milano, Dominic (November 1986). "A Many-Colored Jungle of Exotic Tunings", Keyboard.
- Mitchell Cunningham
- Mitchell D. Eichen
- Mitchell Dening
- Mitchell (disambiguation)
- Mitchell District High School
- Mitchell Dodds
- Mitchell Downie
- Mitchell Duke
- Mitchell Duncan
- Mitchell Eisner
- Mitchell Electronics
- Mitchell Elementary School (disambiguation)
- Mitchell Elementary School (Mitchell, Illinois)
- Mitchell Elementary School (Richmond, British Columbia)
- Mitchell Elias "Mitch" Daniels, Jr.
- Mitchell Evans
- Mitchell family
- Mitchell Feldstein
- Mitchell Fields
- Mitchell Fowles
- Mitchell Frankovitch
- Mitchell Galin
- Mitchell Gary
- Mitchell Glacier
- Mitchell Goldberg