4096edo
| ← 4095edo | 4096edo | 4097edo → |
4096 equal divisions of the octave (abbreviated 4096edo or 4096ed2), also called 4096-tone equal temperament (4096tet) or 4096 equal temperament (4096et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4096 equal parts of about 0.293 ¢ each. Each step represents a frequency ratio of 21/4096, or the 4096th root of 2.
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 | -1 | +38 | +7 | +17 | -0 | -25 | +49 | +49 | -29 | -39 | |
| 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.