A12 scale

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

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	Template:Audio-nohelp	0	Template:Audio-nohelp	0	0
1	11/10	Template:Audio-nohelp	165.00	Template:Audio-nohelp	158.50	-6.50
2	6/5	Template:Audio-nohelp	315.64	Template:Audio-nohelp	316.99	1.35
3	30/23	Template:Audio-nohelp	459.99	Template:Audio-nohelp	475.49	15.50
4	10/7	Template:Audio-nohelp	617.49	Template:Audio-nohelp	633.99	16.50
5	11/7	Template:Audio-nohelp	782.49	Template:Audio-nohelp	792.48	9.99
6	7/4	Template:Audio-nohelp	968.83	Template:Audio-nohelp	950.98	-17.85
7	21/11	Template:Audio-nohelp	1119.46	Template:Audio-nohelp	1109.48	-9.99
8	21/10	Template:Audio-nohelp	1284.47	Template:Audio-nohelp	1267.97	-16.50
9	23/10	Template:Audio-nohelp	1441.96	Template:Audio-nohelp	1426.47	-15.49
10	5/2	Template:Audio-nohelp	1586.31	Template:Audio-nohelp	1584.97	-1.35
11	11/4	Template:Audio-nohelp	1751.32	Template:Audio-nohelp	1743.46	-7.86
12	3/1	Template:Audio-nohelp	1901.96	Template:Audio-nohelp	1901.96	0

References[edit | edit source]

↑ "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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