328edo: Difference between revisions
Cleanup; clarify the title row of the rank-2 temp table; -redundant categories |
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 328 factors into | Since 328 factors into {{Factorisation|328}}, 328edo has subset edos {{EDOs| 2, 4, 8, 41, 82, and 164 }}. | ||
== 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]] (¢) | ||
| Line 25: | Line 26: | ||
| 2401/2400, 3136/3125, 589824/588245 | | 2401/2400, 3136/3125, 589824/588245 | ||
| {{mapping| 328 520 762 921 }} | | {{mapping| 328 520 762 921 }} | ||
| | | −0.298 | ||
| 0.229 | | 0.229 | ||
| 6.27 | | 6.27 | ||
| Line 32: | Line 33: | ||
| 2401/2400, 3136/3125, 9801/9800, 19712/19683 | | 2401/2400, 3136/3125, 9801/9800, 19712/19683 | ||
| {{mapping| 328 520 762 921 1135 }} | | {{mapping| 328 520 762 921 1135 }} | ||
| | | −0.303 | ||
| 0.205 | | 0.205 | ||
| 5.61 | | 5.61 | ||
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| 676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647 | | 676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647 | ||
| {{mapping| 328 520 762 921 1135 1214 }} | | {{mapping| 328 520 762 921 1135 1214 }} | ||
| | | −0.295 | ||
| 0.188 | | 0.188 | ||
| 5.15 | | 5.15 | ||
| Line 46: | Line 47: | ||
| 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125 | | 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125 | ||
| {{mapping| 328 520 762 921 1135 1214 1341 }} | | {{mapping| 328 520 762 921 1135 1214 1341 }} | ||
| | | −0.293 | ||
| 0.174 | | 0.174 | ||
| 4.77 | | 4.77 | ||
| Line 55: | Line 56: | ||
{| 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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|- | |- | ||
| 2 | | 2 | ||
| 111\328<br>(53\328) | | 111\328<br />(53\328) | ||
| 406.10<br>(193.90) | | 406.10<br />(193.90) | ||
| 495/392<br>(28/25) | | 495/392<br />(28/25) | ||
| [[Semihemiwürschmidt]] | | [[Semihemiwürschmidt]] | ||
|- | |- | ||
| 8 | | 8 | ||
| 136\328<br>(13\328) | | 136\328<br />(13\328) | ||
| 497.56<br>(47.56) | | 497.56<br />(47.56) | ||
| 4/3<br>(36/35) | | 4/3<br />(36/35) | ||
| [[Twilight]] | | [[Twilight]] | ||
|- | |- | ||
| 41 | | 41 | ||
| 49\328<br>(1\328) | | 49\328<br />(1\328) | ||
| 179.27<br>(3.66) | | 179.27<br />(3.66) | ||
| 567/512<br>(352/351) | | 567/512<br />(352/351) | ||
| [[Hemicountercomp]] | | [[Hemicountercomp]] | ||
|} | |} | ||
<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 | ||
[[Category:Hemiwürschmidt]] | [[Category:Hemiwürschmidt]] | ||
[[Category:Semiporwell]] | [[Category:Semiporwell]] | ||