62edo: Difference between revisions
→Theory: elaborate on mabon, add a factoid about 9/8 |
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. | ||
=== | === 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|##]] | [[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]] | |||
|} |