62edo: Difference between revisions

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rank-2 temperaments
m Restore comment of the category; cleanup
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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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|  
|  
|}
|}
[[Category:Equal divisions of the octave|##]]


== 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 octave
! Generator<br>(Reduced)
!Generator
! Cents<br>(Reduced)
(reduced)
! Associated<br>Ratio
!Cents
! Temperaments
(reduced)
!Associated
ratio
!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 -->