A12 () 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), A12 is based on a triad of harmonics 4:7:10 (root, harmonic seventh, and compound major third). Discovered by Heinz Bohlen between 1972 and 1973,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. it was named "A12" by Enrique Moreno. Cited in "Other Unusual Scales", The Bohlen–Pierce Site. 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 0 0 0 1 11/10 165.00 158.50 -6.50 2 6/5 315.64 316.99 1.35 3 30/23 459.99 475.49 15.50 4 10/7 617.49 633.99 16.50 5 11/7 782.49 792.48 9.99 6 7/4 968.83 950.98 -17.85 7 21/11 1119.46 1109.48 -9.99 8 21/10 1284.47 1267.97 -16.50 9 23/10 1441.96 1426.47 -15.49 10 5/2 1586.31 1584.97 -1.35 11 11/4 1751.32 1743.46 -7.86 12 3/1 1901.96 1901.96 0
See also 833 cents scale Bohlen–Pierce scale
References