137edo: Difference between revisions
274edo as a correction |
+regular temperament properties |
||
| Line 12: | Line 12: | ||
[[274edo]], which doubles it, provides a correction for its approximation to harmonic 7. | [[274edo]], which doubles it, provides a correction for its approximation to harmonic 7. | ||
==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|-217 137}} | |||
|{{val|137 217}} | |||
| 0.3865 | |||
| 0.3866 | |||
| 4.41 | |||
|- | |||
|2.3.5 | |||
|{{monzo|-21 3 7}}, {{monzo|-13 17 -6}} | |||
|{{val|137 217 318}} | |||
| 0.3887 | |||
| 0.3157 | |||
| 3.60 | |||
|} | |||
=== 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 | |||
|3\137 | |||
|26.28 | |||
|1594323/1562500 | |||
|[[Sfourth]] (5-limit) | |||
|- | |||
|1 | |||
|4\137 | |||
|35.04 | |||
|1990656/1953125 | |||
|[[Gammic]] | |||
|- | |||
|1 | |||
|31\137 | |||
|271.53 | |||
|75/64 | |||
|[[Orson]] | |||
|- | |||
|1 | |||
|36\137 | |||
|315.33 | |||
|6/5 | |||
|[[Parakleismic]] | |||
|- | |||
|1 | |||
|59\137 | |||
|516.79 | |||
|27/20 | |||
|[[Gravity]] | |||
|- | |||
|1 | |||
|63\137 | |||
|551.82 | |||
|9765625/7077888 | |||
|[[Emka]] (5-limit) | |||
|} | |||
== Diagrams == | == Diagrams == | ||