62edo: Difference between revisions

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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.

=== ~~Relation~~ to a calendar reform ===

=== Mabon temperament (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.

11 & 62 is best interpreted in the 2.9.7 subgroup, where it tempers out 44957696/43046721, and the three generators of 17\62 correspond to [[16/9]]. It's possible to extend this to the 11-limit, where 17\62 is mapped to [[11/9]] and two of them make a [[16/11]]. ~~[[Eliora]] proposes~~ the ~~name ''mabon'' for this temperament~~.

11 & 62 is best interpreted in the 2.9.7 subgroup, where it tempers out 44957696/43046721, and the three generators of 17\62 correspond to [[16/9]]. It's possible to extend this to the 11-limit with comma basis {896/891, 1331/1296}, where 17\62 is mapped to [[11/9]] and two of them make a [[16/11]]. In addition, three generators make the patent val 9/8, which is also created by combining the flat patent val fifth from 31edo with the sharp 37\62 fifth.

The 15 & 62 temperament, corresponding to the leap day cycle, is just contorted [[valentine]], order 2.

@@ Line 6: / Line 6: @@
 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.
-=== Relation to a calendar reform ===
+=== Mabon temperament (relation to a calendar reform) ===
 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 is best interpreted in the 2.9.7 subgroup, where it tempers out 44957696/43046721, and the three generators of 17\62 correspond to [[16/9]]. It's possible to extend this to the 11-limit, where 17\62 is mapped to [[11/9]] and two of them make a [[16/11]]. [[Eliora]] proposes the name ''mabon'' for this temperament.
+& 62 is best interpreted in the 2.9.7 subgroup, where it tempers out 44957696/43046721, and the three generators of 17\62 correspond to [[16/9]]. It's possible to extend this to the 11-limit with comma basis {896/891, 1331/1296}, where 17\62 is mapped to [[11/9]] and two of them make a [[16/11]]. In addition, three generators make the patent val 9/8, which is also created by combining the flat patent val fifth from 31edo with the sharp 37\62 fifth.
 The 15 & 62 temperament, corresponding to the leap day cycle, is just contorted [[valentine]], order 2.