A12 scale

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A12 triad (4:7:10) in conventional notation. About this soundPlay 
Octave 12-tet (left) compared with tritave 12-tet (right)

A12 (About this soundPlay ) 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), About this soundPlay  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 About this soundPlay 0 About this soundPlay 0 0
1 11/10 About this soundPlay 165.00 About this soundPlay 158.50 -6.50
2 6/5 About this soundPlay 315.64 About this soundPlay 316.99 1.35
3 30/23 About this soundPlay 459.99 About this soundPlay 475.49 15.50
4 10/7 About this soundPlay 617.49 About this soundPlay 633.99 16.50
5 11/7 About this soundPlay 782.49 About this soundPlay 792.48 9.99
6 7/4 About this soundPlay 968.83 About this soundPlay 950.98 -17.85
7 21/11 About this soundPlay 1119.46 About this soundPlay 1109.48 -9.99
8 21/10 About this soundPlay 1284.47 About this soundPlay 1267.97 -16.50
9 23/10 About this soundPlay 1441.96 About this soundPlay 1426.47 -15.49
10 5/2 About this soundPlay 1586.31 About this soundPlay 1584.97 -1.35
11 11/4 About this soundPlay 1751.32 About this soundPlay 1743.46 -7.86
12 3/1 About this soundPlay 1901.96 About this soundPlay 1901.96 0

See also[edit]

References[edit]

  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.