337edo: 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| -534 337 }} | | {{monzo| -534 337 }} | ||
| {{mapping| 337 534 }} | | {{mapping| 337 534 }} | ||
| 0.1487 | | +0.1487 | ||
| 0.1487 | | 0.1487 | ||
| 4.18 | | 4.18 | ||
Line 24: | Line 33: | ||
| 15625/15552, {{monzo| -88 57 -1 }} | | 15625/15552, {{monzo| -88 57 -1 }} | ||
| {{mapping| 337 534 782 }} | | {{mapping| 337 534 782 }} | ||
| 0.3495 | | +0.3495 | ||
| 0.3089 | | 0.3089 | ||
| 8.67 | | 8.67 | ||
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| 15625/15552, 16875/16807, 7381125/7340032 | | 15625/15552, 16875/16807, 7381125/7340032 | ||
| {{mapping| 337 534 782 946 }} | | {{mapping| 337 534 782 946 }} | ||
| 0.2870 | | +0.2870 | ||
| 0.2886 | | 0.2886 | ||
| 8.10 | | 8.10 | ||
|} | |||
=== 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 | ||
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| 14/11 | | 14/11 | ||
| [[Sqrtphi]] (337, 11-limit) | | [[Sqrtphi]] (337, 11-limit) | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | == Music == |