639edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[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 | ||
| 0.1238 | | 0.1238 | ||
| 6.59 | | 6.59 | ||
| Line 24: | Line 33: | ||
| {{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 | ||
| 0.1134 | | 0.1134 | ||
| 6.04 | | 6.04 | ||
| Line 31: | Line 40: | ||
| 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 | ||
| 0.1062 | | 0.1062 | ||
| 5.65 | | 5.65 | ||
| Line 38: | Line 47: | ||
| 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 | ||
| 0.1020 | | 0.1020 | ||
| 5.43 | | 5.43 | ||
| Line 45: | Line 54: | ||
| 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 | ||
| 0.0955 | | 0.0955 | ||
| 5.08 | | 5.08 | ||
| Line 52: | Line 61: | ||
| 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 | ||
| 0.0970 | | 0.0970 | ||
| 5.16 | | 5.16 | ||
| Line 59: | Line 68: | ||
| 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 | ||
| 0.0971 | | 0.0971 | ||
| 5.17 | | 5.17 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
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| 6/5<br />(36/35) | | 6/5<br />(36/35) | ||
| [[Ennealimmal]] / ennealimmalis | | [[Ennealimmal]] / ennealimmalis | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||