361edo: Difference between revisions
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m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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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" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
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| {{monzo| -572 361 }} | | {{monzo| -572 361 }} | ||
| {{mapping| 361 572 }} | | {{mapping| 361 572 }} | ||
| 0.1798 | | +0.1798 | ||
| 0.1798 | | 0.1798 | ||
| 5.41 | | 5.41 | ||
| Line 32: | Line 33: | ||
| {{monzo| -36 11 8 }}, {{monzo| -14 -19 19 }} | | {{monzo| -36 11 8 }}, {{monzo| -14 -19 19 }} | ||
| {{mapping| 361 572 838 }} | | {{mapping| 361 572 838 }} | ||
| 0.2230 | | +0.2230 | ||
| 0.1590 | | 0.1590 | ||
| 4.78 | | 4.78 | ||
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| 4375/4374, 823543/819200, 2460375/2458624 | | 4375/4374, 823543/819200, 2460375/2458624 | ||
| {{mapping| 361 572 838 1013 }} | | {{mapping| 361 572 838 1013 }} | ||
| 0.3020 | | +0.3020 | ||
| 0.1941 | | 0.1941 | ||
| 5.84 | | 5.84 | ||
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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> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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|- | |- | ||
| 19 | | 19 | ||
| 150\361<br>(2\361) | | 150\361<br />(2\361) | ||
| 498.61<br>(6.65) | | 498.61<br />(6.65) | ||
| 4/3<br>(225/224) | | 4/3<br />(225/224) | ||
| [[Enneadecal]] | | [[Enneadecal]] | ||
|} | |} | ||
<nowiki>* | <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 | ||