236edo: Difference between revisions
m More temperament notes |
No edit summary |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|236}} | {{EDO intro|236}} | ||
==Theory== | |||
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]]. | ||
| Line 11: | Line 11: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs| 2, 4, 53 and 118 }}. | Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs| 2, 4, 53 and 118 }}. | ||
==Regular temperament properties== | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|Comma List]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | |||
! colspan="2" |Tuning Error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo|-187 118}} | |||
|{{val|236 374}} | |||
| 0.0820 | |||
| 0.0821 | |||
| 1.61 | |||
|- | |||
|2.3.5 | |||
|32805/32768, {{monzo|8 14 -13}} | |||
|{{val|236 374 548}} | |||
| 0.0365 | |||
| 0.0930 | |||
| 1.83 | |||
|} | |||
472edo, which doubles it, provides good correction to harmonics 7 and 11. | 472edo, which doubles it, provides good correction to harmonics 7 and 11. | ||