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 (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

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 -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.