639edo: Difference between revisions

m Adopt template: Factorization; misc. cleanup
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|639}}
{{ED intro}}


== Theory ==
== Theory ==
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== 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|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
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
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| {{monzo| 1013 -639 }}
| {{monzo| 1013 -639 }}
| {{mapping| 639 1013 }}
| {{mapping| 639 1013 }}
| -0.1238
| −0.1238
| 0.1238
| 0.1238
| 6.59
| 6.59
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| {{monzo| 1 -27 18 }}, {{monzo| 55 -1 -23 }}
| {{monzo| 1 -27 18 }}, {{monzo| 55 -1 -23 }}
| {{mapping| 639 1013 1484 }}
| {{mapping| 639 1013 1484 }}
| -0.1601
| −0.1601
| 0.1134
| 0.1134
| 6.04
| 6.04
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| 2401/2400, 4375/4374, {{monzo| 58 -14 -13 -2 }}
| 2401/2400, 4375/4374, {{monzo| 58 -14 -13 -2 }}
| {{mapping| 639 1013 1484 1794 }}
| {{mapping| 639 1013 1484 1794 }}
| -0.1369
| −0.1369
| 0.1062
| 0.1062
| 5.65
| 5.65
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| 2401/2400, 4375/4374, 5632/5625, 161280/161051
| 2401/2400, 4375/4374, 5632/5625, 161280/161051
| {{mapping| 639 1013 1484 1794 2211 }}
| {{mapping| 639 1013 1484 1794 2211 }}
| -0.1554
| −0.1554
| 0.1020
| 0.1020
| 5.43
| 5.43
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| 2080/2079, 2401/2400, 4375/4374, 5632/5625, 20480/20449
| 2080/2079, 2401/2400, 4375/4374, 5632/5625, 20480/20449
| {{mapping| 639 1013 1484 1794 2211 2365 }}
| {{mapping| 639 1013 1484 1794 2211 2365 }}
| -0.1650
| −0.1650
| 0.0955
| 0.0955
| 5.08
| 5.08
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| 1156/1155, 2058/2057, 2080/2079, 2401/2400, 4375/4374, 5632/5625
| 1156/1155, 2058/2057, 2080/2079, 2401/2400, 4375/4374, 5632/5625
| {{mapping| 639 1013 1484 1794 2211 2365 2612 }}
| {{mapping| 639 1013 1484 1794 2211 2365 2612 }}
| -0.1487
| −0.1487
| 0.0970
| 0.0970
| 5.16
| 5.16
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| 1156/1155, 1216/1215, 1445/1444, 2058/2057, 2080/2079, 2376/2375, 2401/2400
| 1156/1155, 1216/1215, 1445/1444, 2058/2057, 2080/2079, 2376/2375, 2401/2400
| {{mapping| 639 1013 1484 1794 2211 2365 2612, 2715 }} (639h)
| {{mapping| 639 1013 1484 1794 2211 2365 2612, 2715 }} (639h)
| -0.1618
| −0.1618
| 0.0971
| 0.0971
| 5.17
| 5.17
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+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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|-
|-
| 9
| 9
| 168\639<br>(26\639)
| 168\639<br />(26\639)
| 315.49<br>(48.83)
| 315.49<br />(48.83)
| 6/5<br>(36/35)
| 6/5<br />(36/35)
| [[Ennealimmal]] / ennealimmalis
| [[Ennealimmal]] / ennealimmalis
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct