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). Discovered by Heinz Bohlen between 1972 and 1973, it was named "A12" by Enrique Moreno. 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

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.