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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|308}}
{{ED intro}}
 
== 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.
308edo only is [[consistent]] in the [[5-odd-limit]]. Ignoring the [[harmonic]]s [[7/1|7]], [[11/1|11]] and [[13/1|13]], it is strong in the 2.3.5.17.19.23.29.31 [[subgroup]].


308et tempers out following commas:
Using the [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[19683/19600]], [[65625/65536]], and [[390625/388962]] in the 7-limit, and [[243/242]], 1375/1372, [[6250/6237]], [[9801/9800]], and 14700/14641 in the 11-limit.


7-limit commas: 4096000/4084101, [[390625/388962]], 26873856/26796875, [[19683/19600]], [[78125000/78121827]], [[65625/65536]], [[1640558367/1638400000]]
Using the 308d val, it supports [[unidec]] and [[gammic]].


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
=== Prime harmonics ===
{{Harmonics in equal|308}}


Using the 308d val, it supports [[Unidec]] and [[Gammic]].
=== Subsets and supersets ===
===Prime harmonics===
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 }}.
{{Harmonics in equal|308}}
===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}}.


==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" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|-122 77}}
! rowspan="2" | [[Comma list]]
|{{val|308 488}}
! rowspan="2" | [[Mapping]]
| 0.2070
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -122 77 }}
| {{mapping| 308 488 }}
| +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}}
| {{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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! 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 />(126/125)
|[[Oquatonic]]
| [[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
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