232edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|232}} | {{EDO intro|232}} | ||
== Theory == | |||
232edo [[support]]s and provides the [[optimal patent val]] for the [[13-limit]] [[mystery]] temperament, the rank-3 [[pele]] temperament and the rank-3 [[trimyna]] temperament and other temperaments tempering out [[196/195]], for which it gives the optimal patent val for the corresponding rank-5 temperament. | 232edo [[support]]s and provides the [[optimal patent val]] for the [[13-limit]] [[mystery]] temperament, the rank-3 [[pele]] temperament and the rank-3 [[trimyna]] temperament and other temperaments tempering out [[196/195]], for which it gives the optimal patent val for the corresponding rank-5 temperament. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 232 factors into 2<sup>3</sup> × 29, 232edo has subset edos {{EDOs| 2, 4, 8, 29, 58, and 116 }}. | Since 232 factors into 2<sup>3</sup> × 29, 232edo has subset edos {{EDOs| 2, 4, 8, 29, 58, and 116 }}. | ||
==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 | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.3 | |||
|{{monzo|46 -29}} | |||
|{{val|232 368}} | |||
| -0.4711 | |||
| 0.4709 | |||
| 9.10 | |||
|- | |||
|2.3.5 | |||
|{{monzo|17 1 -8}}, {{monzo|46 -29 0}} | |||
|{{val|232 368 539}} | |||
| -0.5461 | |||
| 0.3989 | |||
| 7.71 | |||
|} | |||
=== 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 | |||
|75\232 | |||
|387.93 | |||
|5/4 | |||
|[[Würschmidt]] | |||
|} | |||
[[Category:Mystery]] | [[Category:Mystery]] | ||