330edo: Difference between revisions
Cleanup and expansion |
Added regular temperament properties |
||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|330}} | {{EDO intro|330}} | ||
==Theory== | |||
330edo has a flat tendency, with its 3rd, 5th, and 7th harmonics tuned progressively flatter. In the 11-limit, the 330e [[val]] {{val| 330 523 766 926 '''1141''' }} scores significantly better in [[TE error]] than its [[patent val]] {{val| 330 523 766 926 '''1142''' }} and allows an extension to the 13-limit. | 330edo has a flat tendency, with its 3rd, 5th, and 7th harmonics tuned progressively flatter. In the 11-limit, the 330e [[val]] {{val| 330 523 766 926 '''1141''' }} scores significantly better in [[TE error]] than its [[patent val]] {{val| 330 523 766 926 '''1142''' }} and allows an extension to the 13-limit. | ||
| Line 13: | Line 15: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 330 factors into 2 × 3 × 5 × 11, it has subset edos {{EDOs| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}. | Since 330 factors into 2 × 3 × 5 × 11, it has subset edos {{EDOs| 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, and 165 }}. | ||
==Regular temperament properties== | |||
{| 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 | |||
|- | |||
|2.3 | |||
|{{monzo|-523 330}} | |||
|{{val|330 523}} | |||
| 0.0432 | |||
| 0.0432 | |||
| 1.19 | |||
|- | |||
|2.3.5 | |||
|32805/32768, {{monzo|-2 -50 35}} | |||
|{{val|330 523 766}} | |||
| 0.1521 | |||
| 0.1581 | |||
| 4.35 | |||
|- | |||
|2.3.5.7 | |||
|32805/32768, 250047/250000, 703125/702464 | |||
|{{val|330 523 766 926}} | |||
| 0.2524 | |||
| 0.2212 | |||
| 6.08 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! Associated<br>ratio | |||
! Temperaments | |||
|- | |||
|1 | |||
|137\330 | |||
|498.182 | |||
|4/3 | |||
|[[Helmholtz]] | |||
|- | |||
|3 | |||
|137\330<br>(27\330) | |||
|498.182<br>(98.182) | |||
|4/3<br>(200/189) | |||
|[[Term]] | |||
|} | |||
[[Category:Canou]] | [[Category:Canou]] | ||
[[Category:Semicanousmic]] | [[Category:Semicanousmic]] | ||
[[Category:Keenanismic]] | [[Category:Keenanismic]] | ||