A12 scale

A12 triad (4:7:10) in conventional notation. Play^ⓘ

Octave 12-tet (left) compared with tritave 12-tet (right)

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

See also

• 833 cents scale
• Bohlen–Pierce scale

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.