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In addition to its 11-limit, 239edo also encompasses a large variety of higher primes, and is specifically commendable in the 2.3.5.7.11.17.29.31.37.43.53.59 subgroup. Primes 23, 67, and 71 are for the most part usable as well, though one should be cautious about pitting 23 against sharp odds (like 9 or 33).
In addition to its 11-limit, 239edo also encompasses a large variety of higher primes, and is specifically commendable in the 2.3.5.7.11.17.29.31.37.43.53.59 subgroup. Primes 23, 67, and 71 are for the most part usable as well, though one should be cautious about pitting 23 against sharp odds (like 9 or 33).


The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[5120/5103]], [[10976/10935]], 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]], [[neptune]], and [[alphaquarter]]. In the 11-limit, it tempers out [[3025/3024]], [[4000/3993]], [[5632/5625]], [[12005/11979]], and [[41503/41472]], supporting [[quadrafifths]] and [[unthirds]].
The equal temperament [[tempering out|tempers out]] [[2401/2400]], [[5120/5103]], [[10976/10935]], 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]], [[Neptune (temperament)|neptune]], and [[alphaquarter]]. In the 11-limit, it tempers out [[3025/3024]], [[4000/3993]], [[5632/5625]], [[12005/11979]], and [[41503/41472]], supporting [[quadrafifths]] and [[unthirds]].


=== Prime harmonics ===
=== Prime harmonics ===
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== Intervals ==
== Intervals ==
{{Interval table}}
{{Main|Table of 239edo intervals}}


== Regular temperament properties ==
== Regular temperament properties ==
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! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
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|-
|-
| 2.3
| 2.3
| {{monzo| 379 -239 }}
| {{Monzo| 379 -239 }}
| {{mapping| 239 379 }}
| {{Mapping| 239 379 }}
| −0.307
| −0.307
| 0.307
| 0.307
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|-
|-
| 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 }}
| {{Mapping| 239 379 555 }}
| −0.247
| −0.247
| 0.265
| 0.265
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| 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 }}
| {{Mapping| 239 379 555 671 }}
| −0.204
| −0.204
| 0.241
| 0.241
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| 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 }}
| {{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
|}
|}


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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
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| 55.23
| 55.23
| 33/32
| 33/32
| [[Escapade]] / [[alphaquarter]]
| [[Escapade]] / [[alphaquarter]] (239f)
|-
|-
| 1
| 1
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| 14/11
| 14/11
| [[Unthirds]] (239f)
| [[Unthirds]] (239f)
|-
| 1
| 103\239
| 517.15
| 66/49
| [[Cutefourths]] (239f)
|-
|-
| 1
| 1
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| 582.43
| 582.43
| 7/5
| 7/5
| [[Neptune]] (7-limit)
| [[Neptune (temperament)|Neptune]] (7-limit)
|}
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
<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 ==
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