# 256edo

 ← 255edo 256edo 257edo →
Prime factorization 28
Step size 4.6875¢
Fifth 150\256 (703.125¢) (→75\128)
Semitones (A1:m2) 26:18 (121.9¢ : 84.38¢)
Consistency limit 3
Distinct consistency limit 3

256 equal divisions of the octave (abbreviated 256edo or 256ed2), also called 256-tone equal temperament (256tet) or 256 equal temperament (256et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 256 equal parts of about 4.69 ¢ each. Each step represents a frequency ratio of 21/256, or the 256th root of 2.

256edo is enfactored in the 5-limit with the same tuning as 128edo, and the error of harmonic 7 leads to inconsistency, which is likely one of the reasons this edo attracts little interest. To start with, consider the sharp-tending 256c val 256 406 595 719 886], which tempers out 2401/2400, 3388/3375, 5120/5103, so that it supports 7-limit hemififths and 11-limit semihemi. The patent val 256 406 594 719 886] tempers out 540/539, 2200/2187, 4000/3969, 12005/11979, among others. It is best tuned in the 2.3.7.11 subgroup, in which it is consistent to the 11-odd-limit minus intervals involving 5.

In the higher limits, it approximates harmonics 23, 43, and 47 quite accurately.

### Odd harmonics

Approximation of odd harmonics in 256edo
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 (%) +25.0 -41.4 +31.7 +49.9 +38.6 -31.3 -16.4 -39.0 -46.9 -43.3 -3.2
Steps
(reduced)
406
(150)
594
(82)
719
(207)
812
(44)
886
(118)
947
(179)
1000
(232)
1046
(22)
1087
(63)
1124
(100)
1158
(134)

### Subsets and supersets

Since 256 factors into 28, 256edo has subset edos 2, 4, 8, 16, 32, 64, and 128.