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A12 scale

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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.
Musical tunings
Measurement
Just intonation
Temperaments
Equal
Linear
IrregularWell temperament/Temperament ordinaire (Kirnberger, Vallotti, Werckmeister, Young)
Traditional
non-Western
Non-octave


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