236edo: Difference between revisions
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CompactStar (talk | contribs) Created page with "{{Infobox ET}} {{EDO intro|236}} ==Theory== {{Primes in edo|236}}" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|236}} | {{EDO intro|236}} | ||
== | |||
{{ | 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 of little improvement 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. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|236}} | |||
=== Subsets and supersets === | |||
Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs| 2, 4, 53 and 118 }}. | |||
472edo, which doubles it, provides good correction to harmonics 7 and 11. | |||
Revision as of 14:29, 2 July 2023
| ← 235edo | 236edo | 237edo → |
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 of little improvement 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.
Prime harmonics
| 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.