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

• 833 cents scale
• Bohlen–Pierce scale