236edo: Difference between revisions
RTT table should start with the 7-limit as the 5-limit is enfactored; misc. cleanup |
→Theory: added section about 236dghin val |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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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. | ||
The 236dghin val makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[43-odd-limit]]. This works best with a stretched octave. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|236}} | {{Harmonics in equal|236}} | ||
{{Harmonics in equal|236|start=12}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
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== 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" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
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| 6144/6125, 19683/19600, 390625/388962 | | 6144/6125, 19683/19600, 390625/388962 | ||
| {{mapping| 236 374 548 663 }} | | {{mapping| 236 374 548 663 }} | ||
| | | −0.1830 | ||
| 0.03883 | | 0.03883 | ||
| 7.64 | | 7.64 | ||
|} | |} | ||