638edo: 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" Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
The equal temperament [[tempering out|tempers out]] the minortone comma, {{monzo| -16 35 -17 }}, in the 5-limit, [[4375/4374]] in the 7-limit, [[3025/3024]], [[9801/9800]], and 43923/43904, in the 11-limit; and [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]] and [[4225/4224]] in the 13-limit. It supplies the [[optimal patent val]] for [[quatracot]], the 224 & 414 temperament. | The equal temperament [[tempering out|tempers out]] the minortone comma, {{monzo| -16 35 -17 }}, in the 5-limit, [[4375/4374]] in the 7-limit, [[3025/3024]], [[9801/9800]], and 43923/43904, in the 11-limit; and [[625/624]], [[729/728]], [[1575/1573]], [[2200/2197]] and [[4225/4224]] in the 13-limit. It supplies the [[optimal patent val]] for [[quatracot]], the {{nowrap|224 & 414}} temperament. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 638 factors as | Since 638 factors as {{factorisation|638}}, 638edo has subset edos {{EDOs| 2, 11, 22, 29, 58, and 319 }}. | ||
== 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 | ||
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| 0.1330 | | 0.1330 | ||
| 7.07 | | 7.07 | ||
|} | |||
=== 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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| 448/405 | | 448/405 | ||
| [[Quatracot]] | | [[Quatracot]] | ||
|} | |||
<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:Quatracot]] | [[Category:Quatracot]] | ||