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" | {| 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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| {{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 | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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|- | |- | ||
| 28 | | 28 | ||
| 128\308<br>(4\308) | | 128\308<br />(4\308) | ||
| 498.70<br>(15.58) | | 498.70<br />(15.58) | ||
| 4/3<br>(126/125) | | 4/3<br />(126/125) | ||
| [[Oquatonic]] (308) | | [[Oquatonic]] (308) | ||
|} | |} | ||
<nowiki>* | <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 | ||