236edo: Difference between revisions

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Eliora (talk | contribs)
118edo has just ~20% error on 7/4, this has over 40%
Yourmusic Productions (talk | contribs)
m More temperament notes
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236edo is [[enfactoring|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, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].  
236edo is [[enfactoring|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, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{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.  
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 ===
=== Prime harmonics ===

Revision as of 11:53, 28 August 2023

← 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

Template:EDO intro

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, 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, 53 and 118.

472edo, which doubles it, provides good correction to harmonics 7 and 11.