256edo
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The 256 equal division divides the octave into 256 equal parts of exactly 4.6875 cents each. It is contorted in the 5-limit, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this EDO attracts little interest.
Theory
| Prime number | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.00 | +1.17 | -1.94 | +1.49 | +1.81 | -1.47 | -1.83 | -2.20 | -0.15 | +1.67 | -1.29 | +1.78 | +2.19 | -0.58 | +0.12 |
| relative (%) | +0 | +25 | -41 | +32 | +39 | -31 | -39 | -47 | -3 | +36 | -27 | +38 | +47 | -12 | +3 | |
| Steps (reduced) | 256 (0) | 406 (150) | 594 (82) | 719 (207) | 886 (118) | 947 (179) | 1046 (22) | 1087 (63) | 1158 (134) | 1244 (220) | 1268 (244) | 1334 (54) | 1372 (92) | 1389 (109) | 1422 (142) | |
256edo is good at the 2.23.43.47 subgroup. If the error below 40% is considered "good", 256edo can be used to play no-fives 17 limit.
256edo can also be played using non-contorted harmonics, no matter how bad the approximation. Under such rule, 256edo supports the 2.7.13.19 subgroup. In the 2.7.13.19 subgroup in the patent val, 256edo tempers out 32851/32768, and supports the corresponding 20 & 73 & 256 rank 3 temperament.