58edo: Difference between revisions
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== 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 | | 2.3.5 | ||
| Line 514: | Line 523: | ||
| 1.10 | | 1.10 | ||
| 5.33 | | 5.33 | ||
|} | |||
* 58et has a lower relative error than any previous equal temperaments in the 13-limit, and the next equal temperament that does better in this subgroup is [[72edo|72]]. | * 58et has a lower relative error than any previous equal temperaments in the 13-limit, and the next equal temperament that does better in this subgroup is [[72edo|72]]. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| 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* | |||
! Temperament | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 615: | Line 631: | ||
| 5/4<br />(91/90) | | 5/4<br />(91/90) | ||
| [[Mystery]] | | [[Mystery]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
58et can also be detempered to [[semihemi]] (58 & 140), [[supers]] (58 & 152), [[condor]] (58 & 159), and [[eagle]] (58 & 212). | 58et can also be detempered to [[semihemi]] (58 & 140), [[supers]] (58 & 152), [[condor]] (58 & 159), and [[eagle]] (58 & 212). | ||