4096edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|4096}} == Theory == {{Harmonics in equal|4096}} This is the 12th power of two EDO, and it is consistent in the 15-odd-limit, a first for a power of..." |
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== Theory == | == 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]]. | |||
{{Harmonics in equal|4096}} | {{Harmonics in equal|4096}} | ||
=== Subsets and supersets === | |||
4096edo is the 12th power of two edo, and has subset edos {{EDOs|1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048}}. | |||
[[Category:Jacobin]] | |||
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.
| 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.