A12 scale

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

Play (help·info)

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

A12 (Play (help·info)) 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 (help·info) 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

References[]

^ "Other Unusual Scales". The Bohlen–Pierce Site. Retrieved 27 November 2012.
^ 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.
^ 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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[Other-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.

[1]

[2]

[3]

A12 scale

See also[]

References[]