137edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| -217 137 }} | ||
| {{ | | {{Mapping| 137 217 }} | ||
| 0.3865 | | +0.3865 | ||
| 0.3866 | | 0.3866 | ||
| 4.41 | | 4.41 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| -21 3 7 }}, {{monzo| -13 17 -6 }} | ||
| {{ | | {{Mapping| 137 217 318 }} | ||
| 0.3887 | | +0.3887 | ||
| 0.3157 | | 0.3157 | ||
| 3.60 | | 3.60 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| 3\137 | | 3\137 | ||
| 26.28 | | 26.28 | ||
| | | 49/48 | ||
| [[Sfourth]] ( | | [[Sfourth]] (137d…) | ||
|- | |- | ||
| 1 | | 1 | ||
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| 315.33 | | 315.33 | ||
| 6/5 | | 6/5 | ||
| [[Parakleismic]] | | [[Parakleismic]] (137d) / [[counterpara]] (137) | ||
|- | |- | ||
| 1 | | 1 | ||
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| 11/8 | | 11/8 | ||
| [[Emka]] (137d) / [[emkay]] (137) | | [[Emka]] (137d) / [[emkay]] (137) | ||
|} | |||
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | |||
== Diagrams == | == Diagrams == | ||