256edo

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← 255edo256edo257edo →
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.