239edo: Difference between revisions
m Text replacement - "rgent temperament" to "rgent tuning" |
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== Intervals == | == Intervals == | ||
{{ | {{Main|Table of 239edo intervals}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 31: | Line 31: | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 38: | Line 38: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 379 -239 }} | ||
| {{ | | {{Mapping| 239 379 }} | ||
| −0.307 | | −0.307 | ||
| 0.307 | | 0.307 | ||
| Line 45: | Line 45: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 3 -18 11 }}, {{monzo| 32 -7 -9 }} | ||
| {{ | | {{Mapping| 239 379 555 }} | ||
| −0.247 | | −0.247 | ||
| 0.265 | | 0.265 | ||
| Line 53: | Line 53: | ||
| 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 60: | Line 60: | ||
| 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 | ||
| 4.34 | | 4.34 | ||
|- | |||
| 2.3.5.7.11.17 | |||
| 595/594, 1156/1155, 2058/2057, 2401/2400, 5120/5103 | |||
| {{Mapping| 239 379 555 671 827 977 }} | |||
| −0.203 | |||
| 0.203 | |||
| 4.03 | |||
|- style="border-top: double;" | |||
| 2.3.5.7.11.13 | |||
| 352/351, 625/624, 847/845, 1575/1573, 2401/2400 | |||
| {{Mapping| 239 379 555 671 827 885 }} (239f) | |||
| −0.318 | |||
| 0.296 | |||
| 5.89 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 352/351, 595/594, 625/624, 833/832, 1156/1155, 1575/1573 | |||
| {{Mapping| 239 379 555 671 827 885 977 }} (239f) | |||
| −0.290 | |||
| 0.282 | |||
| 5.63 | |||
|} | |} | ||
| Line 70: | Line 91: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 98: | Line 119: | ||
| 55.23 | | 55.23 | ||
| 33/32 | | 33/32 | ||
| [[Escapade]] / [[alphaquarter]] | | [[Escapade]] / [[alphaquarter]] (239f) | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 129: | Line 150: | ||
| 14/11 | | 14/11 | ||
| [[Unthirds]] (239f) | | [[Unthirds]] (239f) | ||
|- | |||
| 1 | |||
| 103\239 | |||
| 517.15 | |||
| 66/49 | |||
| [[Cutefourths]] (239f) | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 136: | Line 163: | ||
| [[Neptune]] (7-limit) | | [[Neptune]] (7-limit) | ||
|} | |} | ||
<nowiki />* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||