328edo: Difference between revisions
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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" | ||
|- | |||
! 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]] (%) | |||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 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 24: | 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 | ||
| Line 31: | Line 40: | ||
| 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 38: | 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 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
Note: 5-limit temperaments supported by 164et are not listed. | Note: 5-limit temperaments supported by 164et are not listed. | ||
{ | {| 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 | ||
| Line 83: | Line 99: | ||
| 567/512<br />(352/351) | | 567/512<br />(352/351) | ||
| [[Hemicountercomp]] | | [[Hemicountercomp]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
[[Category:Hemiwürschmidt]] | [[Category:Hemiwürschmidt]] | ||
[[Category:Semiporwell]] | [[Category:Semiporwell]] | ||