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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 == | ||
| Line 12: | Line 12: | ||
== 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| -404 255 }} | ||
| {{ | | {{Mapping| 255 404 }} | ||
| +0.246 | | +0.246 | ||
| 0.246 | | 0.246 | ||
| Line 22: | Line 31: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| 8 14 -13 }}, {{monzo| -36 11 8 }} | ||
| {{ | | {{Mapping| 255 404 592 }} | ||
| +0.226 | | +0.226 | ||
| 0.203 | | 0.203 | ||
| Line 30: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 16875/16807, 19683/19600, 65625/65536 | | 16875/16807, 19683/19600, 65625/65536 | ||
| {{ | | {{Mapping| 255 404 592 716 }} | ||
| +0.117 | | +0.117 | ||
| 0.257 | | 0.257 | ||
| Line 37: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 540/539, 1375/1372, 8019/8000, 65625/65536 | | 540/539, 1375/1372, 8019/8000, 65625/65536 | ||
| {{ | | {{Mapping| 255 404 592 716 882 }} | ||
| +0.136 | | +0.136 | ||
| 0.233 | | 0.233 | ||
| 4.95 | | 4.95 | ||
|} | |||
=== 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 | ||
| Line 71: | Line 87: | ||
|- | |- | ||
| 3 | | 3 | ||
| 82\255<br | | 82\255<br>(3\255) | ||
| 385.88<br | | 385.88<br>(14.12) | ||
| 5/4<br | | 5/4<br>(126/125) | ||
| [[Mutt]] (7-limit) | | [[Mutt]] (7-limit) | ||
|- | |- | ||
| 5 | | 5 | ||
| 53\255<br | | 53\255<br>(2\255) | ||
| 249.41<br | | 249.41<br>(9.41) | ||
| 81/70<br | | 81/70<br>(176/175) | ||
| [[ | | [[Hemiquintile]] / hemiquint (255) / hemiquintilis (255f) | ||
|- | |- | ||
| 5 | | 5 | ||
| 106\255<br | | 106\255<br>(4\255) | ||
| 498.82<br | | 498.82<br>(18.82) | ||
| 4/3<br | | 4/3<br>(81/80) | ||
| [[ | | [[Quintile]] | ||
|- | |- | ||
| 17 | | 17 | ||
| 53\255<br | | 53\255<br>(7\255) | ||
| 249.41<br | | 249.41<br>(32.94) | ||
| {{ | | {{Monzo| -25 -9 17 }}<br>(1990656/1953125) | ||
| [[Chlorine]] (5-limit) | | [[Chlorine]] (5-limit) | ||
|} | |||
<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 | |||
[[Category:Mirkat]] | [[Category:Mirkat]] | ||