358edo: Difference between revisions
Review |
m →Theory Tags: Mobile edit Mobile web edit |
||
| (2 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
358edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1|3]] is about halfway its steps. It is suitable for use with the 2.9.5.7.13 [[subgroup]] or even better the 2.9.15.7.13 subgroup. | 358edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1|3]] is about halfway its steps. It is suitable for use with the 2.9.5.7.13 [[subgroup]] or even better the 2.9.15.7.13 subgroup. | ||
In the 2.9.5.7.13 subgroup, the equal temperament [[tempering out|tempers out]] [[4096/4095]], 13720/13689, 59150/59049, 60025/59904, 142884/142805, and [[390625/388962]]. | In the 2.9.5.7.13 subgroup, the equal temperament [[tempering out|tempers out]] [[4096/4095]], [[13720/13689]], 59150/59049, 60025/59904, 142884/142805, and [[390625/388962]]. | ||
The [[patent val]] [[support]]s [[hypnos]] in the 11-limit and [[lee]] in the 2.3.7 subgroup. | The [[patent val]] [[support]]s [[hypnos]] in the 11-limit and [[lee]] in the 2.3.7 subgroup. | ||
| Line 17: | Line 17: | ||
== 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 29: | Line 30: | ||
| {{monzo| 1135 -358 }} | | {{monzo| 1135 -358 }} | ||
| {{mapping| 358 1135 }} | | {{mapping| 358 1135 }} | ||
| | | −0.0882 | ||
| 0.0882 | | 0.0882 | ||
| 2.63 | | 2.63 | ||