62edo: Difference between revisions
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{{Infobox ET}} | {{EDO intro|62}}{{Infobox ET}} | ||
== 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 | 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 === | |||
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. | |||
62 | 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}} | ||