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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| -350 221 }} | | {{monzo| -350 221 }} | ||
| {{mapping| 221 350 }} | | {{mapping| 221 350 }} | ||
| 0.4740 | | +0.4740 | ||
| 0.4742 | | 0.4742 | ||
| 8.73 | | 8.73 | ||
| Line 36: | Line 37: | ||
| {{monzo| -21 3 7 }}, {{monzo| -11 26 -13 }} | | {{monzo| -21 3 7 }}, {{monzo| -11 26 -13 }} | ||
| {{mapping| 221 350 513 }} | | {{mapping| 221 350 513 }} | ||
| 0.4299 | | +0.4299 | ||
| 0.3921 | | 0.3921 | ||
| 7.22 | | 7.22 | ||
| Line 43: | Line 44: | ||
| 1029/1024, 19683/19600, 235298/234375 | | 1029/1024, 19683/19600, 235298/234375 | ||
| {{mapping| 221 350 513 620 }} | | {{mapping| 221 350 513 620 }} | ||
| 0.5282 | | +0.5282 | ||
| 0.3799 | | 0.3799 | ||
| 7.00 | | 7.00 | ||
|- | |||
| 2.3.5.7.11 | |||
| 385/384, 441/440, 19683/19600, 235298/234375 | |||
| {{mapping| 221 350 513 620 764 }} (221e) | |||
| +0.5904 | |||
| 0.3618 | |||
| 6.66 | |||
|} | |} | ||
=== 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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| 75/64 | | 75/64 | ||
| [[Orson]] | | [[Orson]] | ||
|- | |||
| 1 | |||
| 57\221 | |||
| 309.50 | |||
| 448/375 | |||
| [[Triwell]] (221e) | |||
|- | |- | ||
| 1 | | 1 | ||
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| [[Tritriple]] (221e) | | [[Tritriple]] (221e) | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||