308edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 308 factors into 2<sup>2</sup> × 7 × 11, 308edo has subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}. | Since 308 factors into {{nowrap|2<sup>2</sup> × 7 × 11}}, 308edo has subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154 }}. | ||
== 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| -122 77 }} | | {{monzo| -122 77 }} | ||
| {{mapping| 308 488 }} | | {{mapping| 308 488 }} | ||
| 0.2070 | | +0.2070 | ||
| 0.2071 | | 0.2071 | ||
| 5.32 | | 5.32 | ||
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| {{monzo| -36 11 8 }}, {{monzo| -7 22 -12 }} | | {{monzo| -36 11 8 }}, {{monzo| -7 22 -12 }} | ||
| {{mapping| 308 488 715 }} | | {{mapping| 308 488 715 }} | ||
| 0.2241 | | +0.2241 | ||
| 0.1708 | | 0.1708 | ||
| 4.38 | | 4.38 | ||
|} | |||
=== 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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| 4/3<br />(126/125) | | 4/3<br />(126/125) | ||
| [[Oquatonic]] (308) | | [[Oquatonic]] (308) | ||
|} | |||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||