639edo: Difference between revisions

m Adopt template: Factorization; misc. cleanup
ArrowHead294 (talk | contribs)
mNo edit summary
Line 12: Line 12:


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| 1013 -639 }}
| {{monzo| 1013 -639 }}
| {{mapping| 639 1013 }}
| {{mapping| 639 1013 }}
| -0.1238
| &minus;0.1238
| 0.1238
| 0.1238
| 6.59
| 6.59
Line 32: Line 24:
| {{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
| &minus;0.1601
| 0.1134
| 0.1134
| 6.04
| 6.04
Line 39: Line 31:
| 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
| &minus;0.1369
| 0.1062
| 0.1062
| 5.65
| 5.65
Line 46: Line 38:
| 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
| &minus;0.1554
| 0.1020
| 0.1020
| 5.43
| 5.43
Line 53: Line 45:
| 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
| &minus;0.1650
| 0.0955
| 0.0955
| 5.08
| 5.08
Line 60: Line 52:
| 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
| &minus;0.1487
| 0.0970
| 0.0970
| 5.16
| 5.16
Line 67: Line 59:
| 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
| &minus;0.1618
| 0.0971
| 0.0971
| 5.17
| 5.17
|}
{{comma basis end}}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 94: Line 80:
|-
|-
| 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
|}
{{rank-2 end}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
{{orf}}