62edo: Difference between revisions
rank-2 temperaments |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|62}} | {{EDO intro|62}} | ||
== Theory == | == Theory == | ||
62 = 2 × 31 and the [[patent val]] is a contorted [[31edo]] through the 11-limit; in the 13-limit it tempers out [[169/168]], [[1188/1183]], [[847/845]] and [[676/675]]. It provides the [[optimal patent val]] for [[31 comma temperaments #Gallium|gallium]], [[Starling temperaments #Valentine|semivalentine]] and [[Meantone_family#Hemimeantone|hemimeantone]] temperaments. | 62 = 2 × 31 and the [[patent val]] is a contorted [[31edo]] through the 11-limit; in the 13-limit it tempers out [[169/168]], [[1188/1183]], [[847/845]] and [[676/675]]. It provides the [[optimal patent val]] for [[31 comma temperaments #Gallium|gallium]], [[Starling temperaments #Valentine|semivalentine]] and [[Meantone_family#Hemimeantone|hemimeantone]] temperaments. | ||
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The 15 & 62 temperament, corresponding to the leap day cycle, is just contorted [[valentine]], order 2. | The 15 & 62 temperament, corresponding to the leap day cycle, is just contorted [[valentine]], order 2. | ||
=== Odd harmonics === | === Odd harmonics === | ||
{{harmonics in equal|62}} | {{harmonics in equal|62}} | ||
== Intervals == | == Intervals == | ||
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| | | | ||
|} | |} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods | ! Periods<br>per 8ve | ||
per | ! Generator<br>(Reduced) | ||
!Generator | ! Cents<br>(Reduced) | ||
( | ! Associated<br>Ratio | ||
!Cents | ! Temperaments | ||
( | |||
!Associated | |||
!Temperaments | |||
|- | |- | ||
|1 | | 1 | ||
|13\62 | | 13\62 | ||
|251.61 | | 251.61 | ||
|15/13 | | 15/13 | ||
|[[Hemimeantone]] | | [[Hemimeantone]] | ||
|- | |- | ||
|1 | | 1 | ||
|17\62 | | 17\62 | ||
|329.03 | | 329.03 | ||
|16/11 | | 16/11 | ||
|[[Mabon]] | | [[Mabon]] | ||
|- | |- | ||
|2 | | 2 | ||
|4\62 | | 4\62 | ||
|77.42 | | 77.42 | ||
|21/20 | | 21/20 | ||
|[[Semivalentine]] | | [[Semivalentine]] | ||
|- | |- | ||
|31 | | 31 | ||
|1\62 | | 1\62 | ||
|19.35 | | 19.35 | ||
|196/195 | | 196/195 | ||
|[[Kumhar]] | | [[Kumhar]] | ||
|- | |- | ||
|31 | | 31 | ||
|1\62 | | 1\62 | ||
|19.35 | | 19.35 | ||
|16807/16640 | | 16807/16640 | ||
|[[Gallium]] | | [[Gallium]] | ||
|} | |} | ||
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number --> | |||