A12 scale
A12 triad (4:7:10) in conventional notation.
Play 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).[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 |
Cents (just) |
Cents (ET) |
Difference |
|---|
| 0 |
1/1 |
0 |
0 |
0 |
| 1 |
11/10 |
165.00 |
158.50 |
-6.50 |
| 2 |
6/5 |
315.64 |
316.99 |
1.35 |
| 3 |
30/23 |
459.99 |
475.49 |
15.50 |
| 4 |
10/7 |
617.49 |
633.99 |
16.50 |
| 5 |
11/7 |
782.49 |
792.48 |
9.99 |
| 6 |
7/4 |
968.83 |
950.98 |
-17.85 |
| 7 |
21/11 |
1119.46 |
1109.48 |
-9.99 |
| 8 |
21/10 |
1284.47 |
1267.97 |
-16.50 |
| 9 |
23/10 |
1441.96 |
1426.47 |
-15.49 |
| 10 |
5/2 |
1586.31 |
1584.97 |
-1.35 |
| 11 |
11/4 |
1751.32 |
1743.46 |
-7.86 |
| 12 |
3/1 |
1901.96 |
1901.96 |
0 |
See also
Sources
- ↑ "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.
