239edo: Difference between revisions

Lériendil (talk | contribs)
m Text replacement - "rgent temperament" to "rgent tuning"
Overthink (talk | contribs)
Intervals: move to separate page to reduce lag
 
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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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| [[Neptune]] (7-limit)
| [[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 ==