330edo: Difference between revisions
Cleanup; review RTT tables; clarify the title row of the rank-2 temp table |
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" |
||
| (6 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 13: | Line 13: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 330 factors into | Since 330 factors into {{factorisation|330}}, 330edo has subset edos {{EDOs| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}. | ||
== 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]] (%) | ||
| Line 50: | Line 51: | ||
=== 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 | ||
|- | |- | ||
| Line 61: | Line 63: | ||
| 498.182 | | 498.182 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 137\330<br>(27\330) | | 137\330<br />(27\330) | ||
| 498.182<br>(98.182) | | 498.182<br />(98.182) | ||
| 4/3<br>(200/189) | | 4/3<br />(200/189) | ||
| [[Term (temperament)|Term]] | | [[Term (temperament)|Term]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 137\330<br>(27\330) | | 137\330<br />(27\330) | ||
| 498.182<br>(98.182) | | 498.182<br />(98.182) | ||
| 4/3<br>(200/189) | | 4/3<br />(200/189) | ||
| [[Semiterm]] (330eff) | | [[Semiterm]] (330eff) | ||
|- | |- | ||
| 22 | | 22 | ||
| 137\330<br>(2\330) | | 137\330<br />(2\330) | ||
| 498.182<br>(7.273) | | 498.182<br />(7.273) | ||
| 4/3<br>({{monzo| 16 -13 2 }}) | | 4/3<br />({{monzo| 16 -13 2 }}) | ||
| [[Major arcana]] (5-limit) | | [[Major arcana]] (5-limit) | ||
|} | |} | ||
<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:Canou]] | [[Category:Canou]] | ||
[[Category:Semicanousmic]] | [[Category:Semicanousmic]] | ||
[[Category:Keenanismic]] | [[Category:Keenanismic]] | ||