258edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|258}} | |||
The equal temperament [[Tempering out|tempers out]] 10976/10935 ([[hemimage comma]]), 65625/65536 ([[horwell comma]]), and 235298/234375 ([[triwellisma]]) in the 7-limit as well as 250047/250000 ([[landscape comma]]), 823543/819200 ([[quince comma]]), and 1500625/1492992 ([[uniwiz comma]]). Using the patent val, it tempers out [[441/440]], 4375/4356, [[16384/16335]], and [[19712/19683]] in the 11-limit; [[364/363]], [[625/624]], and [[2200/2197]] in the 13-limit; [[375/374]], [[595/594]], [[833/832]], [[936/935]], [[2500/2499]], 4928/4913 in the 17-limit. It supports [[cotoneum]] and [[mutt]]. | |||
{{ | === Prime harmonics === | ||
{{Harmonics in equal|258}} | |||
=== Subsets and supersets === | |||
Since 258 factors into 2 × 3 × 43, 258edo has subset edos {{EDOs| 2, 3, 6, 43, 86, and 129 }}, and the equal temperament [[support]]s the [[meridic]] temperament, which tempers out the 43-15-comma, {{monzo| 168 -43 -43 }} and the mitonisma, 5250987/5242880. | |||
[[Category:Meridic]] | [[Category:Meridic]] | ||
Revision as of 04:54, 24 September 2023
| ← 257edo | 258edo | 259edo → |
The equal temperament tempers out 10976/10935 (hemimage comma), 65625/65536 (horwell comma), and 235298/234375 (triwellisma) in the 7-limit as well as 250047/250000 (landscape comma), 823543/819200 (quince comma), and 1500625/1492992 (uniwiz comma). Using the patent val, it tempers out 441/440, 4375/4356, 16384/16335, and 19712/19683 in the 11-limit; 364/363, 625/624, and 2200/2197 in the 13-limit; 375/374, 595/594, 833/832, 936/935, 2500/2499, 4928/4913 in the 17-limit. It supports cotoneum and mutt.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.37 | -0.27 | -1.38 | +2.17 | +1.33 | +2.02 | +0.16 | -0.37 | -1.67 | -0.85 |
| Relative (%) | +0.0 | +8.0 | -5.7 | -29.8 | +46.7 | +28.7 | +43.5 | +3.5 | -7.9 | -35.9 | -18.3 | |
| Steps (reduced) |
258 (0) |
409 (151) |
599 (83) |
724 (208) |
893 (119) |
955 (181) |
1055 (23) |
1096 (64) |
1167 (135) |
1253 (221) |
1278 (246) | |
Subsets and supersets
Since 258 factors into 2 × 3 × 43, 258edo has subset edos 2, 3, 6, 43, 86, and 129, and the equal temperament supports the meridic temperament, which tempers out the 43-15-comma, [168 -43 -43⟩ and the mitonisma, 5250987/5242880.