62edo: Difference between revisions

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Theory: elaborate on mabon, add a factoid about 9/8
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rank-2 temperaments
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Using the 35\62 generator, which leads to the {{val| 62 97 143 173 }} val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively {{val| 62 97 143 172 }} [[support]]s hornbostel.
Using the 35\62 generator, which leads to the {{val| 62 97 143 173 }} val, 62edo is also an excellent tuning for septimal mavila temperament; alternatively {{val| 62 97 143 172 }} [[support]]s hornbostel.


=== Mabon temperament (relation to a calendar reform) ===
=== Relation to a calendar reform ===
62 years is the amount of years in a leap week calendar cycle which corresponds to a year of 365 days 5 hours 48 minutes 23 seconds, meaning it is both a simple cycle for a calendar, and 62 being a multiple of 31 makes it a harmonically useful and playable cycle. The corresponding maximal evenness scales are 15 & 62 and 11 & 62.  
62 years is the amount of years in a leap week calendar cycle which corresponds to a year of 365 days 5 hours 48 minutes 23 seconds, meaning it is both a simple cycle for a calendar, and 62 being a multiple of 31 makes it a harmonically useful and playable cycle. The corresponding maximal evenness scales are 15 & 62 and 11 & 62.  


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[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Equal divisions of the octave|##]]
 
== Regular temperament properties ==
62edo is contorted 31edo through the 11-limit.
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
!Periods
per octave
!Generator
(reduced)
!Cents
(reduced)
!Associated
ratio
!Temperaments
|-
|1
|13\62
|251.61
|15/13
|[[Hemimeantone]]
|-
|1
|17\62
|329.03
|16/11
|[[Mabon]]
|-
|2
|4\62
|77.42
|21/20
|[[Semivalentine]]
|-
|31
|1\62
|19.35
|196/195
|[[Kumhar]]
|-
|31
|1\62
|19.35
|16807/16640
|[[Gallium]]
|}