239edo: Difference between revisions
m Infobox ET now computes most parameters automatically |
Expand on theory and misc. cleanup |
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== Theory == | == Theory == | ||
239edo has a sharp tendency, with [[prime harmonic]]s 3 through 11 all tuned sharp. The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[5120/5103]], and 29360128/29296875 in the 7-limit, [[support]]ing the [[hemififths]] temperament and providing an excellent tuning. It also supports and provides a good tuning for [[quasiorwell]] and [[alphaquarter]]. In the 11-limit, it tempers out [[3025/3024]], [[4000/3993]], [[5632/5625]], and 12005/11979. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|239}} | {{Harmonics in equal|239}} | ||
=== Subsets and supersets === | |||
239edo is the 52nd [[prime edo]]. | |||
== 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|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal 8ve <br> | ! rowspan="2" | Optimal 8ve <br>Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 23: | Line 24: | ||
| 2.3 | | 2.3 | ||
| {{monzo| 379 -239 }} | | {{monzo| 379 -239 }} | ||
| | | {{mapping| 239 379 }} | ||
| -0.307 | | -0.307 | ||
| 0.307 | | 0.307 | ||
| Line 30: | Line 31: | ||
| 2.3.5 | | 2.3.5 | ||
| {{monzo| 3 -18 11}}, {{monzo| 32 -7 -9 }} | | {{monzo| 3 -18 11}}, {{monzo| 32 -7 -9 }} | ||
| | | {{mapping| 239 379 555 }} | ||
| -0.247 | | -0.247 | ||
| 0.265 | | 0.265 | ||
| Line 37: | Line 38: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 5120/5103, 29360128/29296875 | | 2401/2400, 5120/5103, 29360128/29296875 | ||
| | | {{mapping| 239 379 555 671 }} | ||
| -0.204 | | -0.204 | ||
| 0.241 | | 0.241 | ||
| Line 44: | Line 45: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 2401/2400, 3025/3024, 4000/3993, 5120/5103 | | 2401/2400, 3025/3024, 4000/3993, 5120/5103 | ||
| | | {{mapping| 239 379 555 671 827 }} | ||
| -0.220 | | -0.220 | ||
| 0.218 | | 0.218 | ||
| Line 53: | Line 54: | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br> | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 113: | Line 114: | ||
| [[Neptune]] (7-limit) | | [[Neptune]] (7-limit) | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[Category:Hemififths]] | [[Category:Hemififths]] | ||
[[Category:Quasiorwell]] | [[Category:Quasiorwell]] | ||
[[Category:Alphaquarter]] | [[Category:Alphaquarter]] | ||