308edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|308}} | {{EDO intro|308}} | ||
== Theory == | == Theory == | ||
308et only is consistent in the 5-limit. Ignoring the harmonics 7, 11 and 13, 308et is strong in the 2.3.5.17.19.23.29.31 subgroup. | 308et only is consistent in the 5-limit. Ignoring the harmonics 7, 11 and 13, 308et is strong in the 2.3.5.17.19.23.29.31 subgroup. | ||
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11-limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, [[243/242]], [[131072/130977]], [[6250/6237]], 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, [[9801/9800]], 539055/537824, 202397184/201768035 | 11-limit commas: 806736/805255, 1835008/1830125, 14700/14641, 26214400/26198073, 166698/166375, [[243/242]], [[131072/130977]], [[6250/6237]], 107495424/107421875, 9765625/9732096, 137781/137500, 180224/180075, 1375/1372, 17537553/17500000, 47265625/47258883, [[9801/9800]], 539055/537824, 202397184/201768035 | ||
Using the 308d val, it supports [[ | Using the 308d val, it supports [[unidec]] and [[gammic]]. | ||
===Prime harmonics=== | |||
=== Prime harmonics === | |||
{{Harmonics in equal|308}} | {{Harmonics in equal|308}} | ||
===Subsets and supersets=== | |||
=== Subsets and supersets === | |||
308 factors into 2<sup>2</sup> x 7 x 11, with subset edos {{EDOs| 2, 4, 7, 11, 14, 22, 28, 44, 77, and 154}}. | 308 factors into 2<sup>2</sup> x 7 x 11, with 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|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ![[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ![[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-122 77}} | | {{monzo| -122 77 }} | ||
|{{val|308 488}} | | {{val| 308 488 }} | ||
| 0.2070 | | 0.2070 | ||
| 0.2071 | | 0.2071 | ||
| 5.32 | | 5.32 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|{{monzo|-36 11 8}}, {{monzo|-7 22 -12}} | | {{monzo| -36 11 8 }}, {{monzo| -7 22 -12 }} | ||
|{{val|308 488 715}} | | {{val| 308 488 715 }} | ||
| 0.2241 | | 0.2241 | ||
| 0.1708 | | 0.1708 | ||
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|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator<br>( | ! Generator<br>(Reduced) | ||
! Cents<br>( | ! Cents<br>(Reduced) | ||
! Associated<br> | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|9\308 | | 9\308 | ||
|35.06 | | 35.06 | ||
|128/125 | | 128/125 | ||
|[[Gammic]] | | [[Gammic]] (308d) | ||
|- | |- | ||
|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>(2048/2025) | | 4/3<br>(2048/2025) | ||
|[[Oquatonic]] | | [[Oquatonic]] | ||
|} | |} | ||
{{Todo| review }} | |||