4096edo: Difference between revisions
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In the 11-limit, it is a tuning for the [[Van Gogh]] temperament. In the 13-limit, it tempers out [[6656/6655]], [[9801/9800]], 67392/67375, 105644/105625. In the higher 2.3.7.11.13.37.43 subgroup it tempers out the [[superparticular]] comma [[15093/15092]]. | In the 11-limit, it is a tuning for the [[Van Gogh]] temperament. In the 13-limit, it tempers out [[6656/6655]], [[9801/9800]], 67392/67375, 105644/105625. In the higher 2.3.7.11.13.37.43 subgroup it tempers out the [[superparticular]] comma [[15093/15092]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|4096}} | {{Harmonics in equal|4096}} | ||
Revision as of 14:08, 3 July 2023
| ← 4095edo | 4096edo | 4097edo → |
Theory
4096edo is consistent in the 15-odd-limit, although with a large error on the 7th harmonic. It has the highest consistency limit than any power of two edo before it. In higher limits, the best subgroup for 4096edo is 2.3.7.11.13.37.43.
In the 11-limit, it is a tuning for the Van Gogh temperament. In the 13-limit, it tempers out 6656/6655, 9801/9800, 67392/67375, 105644/105625. In the higher 2.3.7.11.13.37.43 subgroup it tempers out the superparticular comma 15093/15092.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.002 | +0.112 | +0.022 | +0.049 | -0.000 | -0.073 | +0.143 | +0.144 | -0.085 | -0.114 |
| Relative (%) | +0.0 | -0.6 | +38.3 | +7.4 | +16.8 | -0.1 | -24.8 | +48.9 | +49.0 | -29.0 | -38.8 | |
| Steps (reduced) |
4096 (0) |
6492 (2396) |
9511 (1319) |
11499 (3307) |
14170 (1882) |
15157 (2869) |
16742 (358) |
17400 (1016) |
18529 (2145) |
19898 (3514) |
20292 (3908) | |
Subsets and supersets
4096edo is the 12th power of two edo, and has subset edos 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048.