236edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|236}}
{{ED intro}}
==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]].  
== 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 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]] {{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.
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.
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=== 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, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.


==Regular temperament properties==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| 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
! rowspan="2" | [[Subgroup]]
|{{monzo|-187 118}}
! rowspan="2" | [[Comma list]]
|{{val|236 374}}
! rowspan="2" | [[Mapping]]
| 0.0820
! rowspan="2" | Optimal<br />8ve stretch (¢)
| 0.0821
! colspan="2" | Tuning error
| 1.61
|-
|-
|2.3.5
! [[TE error|Absolute]] (¢)
|32805/32768, {{monzo|8 14 -13}}
! [[TE simple badness|Relative]] (%)
|{{val|236 374 548}}
|-
| 0.0365
| 2.3.5.7
| 0.0930
| 6144/6125, 19683/19600, 390625/388962
| 1.83
| {{mapping| 236 374 548 663 }}
| −0.1830
| 0.03883
| 7.64
|}
|}
472edo, which doubles it, provides good correction to harmonics 7 and 11.