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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|638}}
{{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 2 × 11 × 29, 638edo has subset edos {{EDOs| 2, 11, 22, 29, 58, and 319 }}.
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"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|-
|2.3
! rowspan="2" | [[Subgroup]]
|{{monzo|-1011 638}}
! rowspan="2" | [[Comma list]]
|{{val|638 1011}}
! rowspan="2" | [[Mapping]]
| 0.1223
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| -1011 638 }}
| {{mapping| 638 1011 }}
| +0.1223
| 0.1223
| 0.1223
| 6.50
| 6.50
|-
|-
|2.3.5
| 2.3.5
|{{monzo|-51 19 9}}, {{monzo|-16 35 -17}}
| {{monzo| -51 19 9 }}, {{monzo| -16 35 -17 }}
|{{val|638 1011 1481}}
| {{mapping| 638 1011 1481 }}
| 0.1869
| +0.1869
| 0.1353
| 0.1353
| 7.19
| 7.19
|-
|-
|2.3.5.7
| 2.3.5.7
|4375/4374, 2100875/2097152, 5250987/5242880
| 4375/4374, 2100875/2097152, {{monzo| -11 5 11 -8 }}
|{{val|638 1011 1481 1791}}
| {{mapping| 638 1011 1481 1791 }}
| 0.1556
| +0.1556
| 0.1291
| 0.1291
| 6.86
| 6.86
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|3025/3024, 4375/4374, 9801/9800, 43923/43904
| 3025/3024, 4375/4374, 825000/823543, 1265625/1261568
|{{val|638 1011 1481 1791 2207}}
| {{mapping| 638 1011 1481 1791 2207 }}
| 0.1373
| +0.1373
| 0.1212
| 0.1212
| 6.44
| 6.44
|-
|-
|2.3.5.7.11.13
| 2.3.5.7.11.13
|625/624, 729/728, 1575/1573, 4225/4224, 78975/78848
| 625/624, 729/728, 1575/1573, 2200/2197, 823680/823543
|{{val|638 1011 1481 1791 2207 2361}}
| {{mapping| 638 1011 1481 1791 2207 2361 }}
| 0.1043
| +0.1043
| 0.1330
| 0.1330
| 7.07
| 7.07
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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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|97\638
| 97\638
|182.45
| 182.45
|10/9
| 10/9
|[[Minortone]] / [[mitonic]]
| [[Mitonic]]
|-
|-
|1
| 1
|313\638
| 313\638
|588.71
| 588.71
|7/5
| 7/5
|[[Untriton]]
| [[Untriton]]
|-
|-
|2
| 2
|94\638
| 94\638
|176.80
| 176.80
|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]]
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