236edo

 ← 235edo 236edo 237edo →
Prime factorization 22 × 59
Step size 5.08475¢
Fifth 138\236 (701.695¢) (→69\118)
Semitones (A1:m2) 22:18 (111.9¢ : 91.53¢)
Consistency limit 5
Distinct consistency limit 5

236 equal divisions of the octave (abbreviated 236edo or 236ed2), also called 236-tone equal temperament (236tet) or 236 equal temperament (236et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 236 equal parts of about 5.08 ¢ each. Each step represents a frequency ratio of 21/236, or the 236th root of 2.

Theory

236edo is enfactored in the 5-limit, with the same tuning as 118edo, defined by tempering out the schisma and the parakleisma. The 7-limit mapping is worse over that of 118edo in terms of relative error, as it leans on the very sharp side. It tempers out 6144/6125 and 19683/19600, supporting hemischis. Using the 236e val 236 374 548 663 817], it tempers out 243/242, 1375/1372, 6250/6237, 14700/14641 and 16384/16335.

The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to quarter-comma meantone, although 205edo is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden diaschismic sequence.

Prime harmonics

Approximation of prime harmonics in 236edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.26 +0.13 +2.36 -2.17 -1.54 +1.82 +2.49 +2.23 -2.46 -0.97
Relative (%) +0.0 -5.1 +2.5 +46.4 -42.6 -30.4 +35.9 +48.9 +43.9 -48.4 -19.0
Steps
(reduced)
236
(0)
374
(138)
548
(76)
663
(191)
816
(108)
873
(165)
965
(21)
1003
(59)
1068
(124)
1146
(202)
1169
(225)

Subsets and supersets

Since 236 factors into 22 × 53, 236edo has subset edos 2, 4, 59 and 118. 472edo, which doubles it, provides good correction to harmonics 7 and 11.

Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3.5.7 6144/6125, 19683/19600, 390625/388962 [236 374 548 663]] -0.1830 0.03883 7.64