256edo
| ← 255edo | 256edo | 257edo → |
256 equal divisions of the octave (256edo), or 256-tone equal temperament (256tet), 256 equal temperament (256et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 256 equal parts of about 4.69 ¢ each.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +1.17 | -1.94 | +1.49 | +2.34 | +1.81 | -1.47 | -0.77 | -1.83 | -2.20 | -2.03 | -0.15 |
| relative (%) | +25 | -41 | +32 | +50 | +39 | -31 | -16 | -39 | -47 | -43 | -3 | |
| Steps (reduced) |
406 (150) |
594 (82) |
719 (207) |
812 (44) |
886 (118) |
947 (179) |
1000 (232) |
1046 (22) |
1087 (63) |
1124 (100) |
1158 (134) | |
256edo 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. 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.