A12 scale explained

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).^[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		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

Notes and References

1. Web site: Other Unusual Scales . The Bohlen–Pierce Site . 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 . 12–22 . Stanford University. Cited in "Other Unusual Scales", The Bohlen–Pierce Site.