A12 scale

A12 (Play ) is a non-octave-repeating scale or musical tuning featuring twelve steps to the tritave. As twelve steps to the octave is based on a triad of harmonics 4:5:6 (root, major third, perfect fifth), Play  A12 is based on a triad of harmonics 4:7:10 (root, harmonic seventh, and compound major third).[1] Discovered by Heinz Bohlen between 1972 and 1973,[2] it was named "A12" by Enrique Moreno.[3] Bohlen considered this scale less logically consistent than the Bohlen–Pierce scale, which has thirteen steps in the twelfth.

Step Ratio Audio Cents (just) Audio Cents (ET) Difference
0 1/1 Play 0 Play 0 0
1 11/10 Play 165.00 Play 158.50 -6.50
2 6/5 Play 315.64 Play 316.99 1.35
3 30/23 Play 459.99 Play 475.49 15.50
4 10/7 Play 617.49 Play 633.99 16.50
5 11/7 Play 782.49 Play 792.48 9.99
6 7/4 Play 968.83 Play 950.98 -17.85
7 21/11 Play 1119.46 Play 1109.48 -9.99
8 21/10 Play 1284.47 Play 1267.97 -16.50
9 23/10 Play 1441.96 Play 1426.47 -15.49
10 5/2 Play 1586.31 Play 1584.97 -1.35
11 11/4 Play 1751.32 Play 1743.46 -7.86
12 3/1 Play 1901.96 Play 1901.96 0
A12 triad (4:7:10) in conventional notation. Play 
Octave 12-tet (left) compared with tritave 12-tet (right)

See also

References
  1. "Other Unusual Scales". The Bohlen–Pierce Site. Retrieved 27 November 2012.
  2. Bohlen, Heinz: 13 Tonstufen in der Duodezime. Acustica, vol. 39 no. 2, S. Hirzel Verlag, Stuttgart, 1978, pp. 76 - 86. Cited in "Other Unusual Scales", The Bohlen–Pierce Site.
  3. Moreno, Enrique Ignacio (Dec 1995). "Embedding Equal Pitch Spaces and The Question of Expanded Chromas: An Experimental Approach". Dissertation. Stanford University: 12–22. Cited in "Other Unusual Scales", The Bohlen–Pierce Site.


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