62edo: Difference between revisions
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{{Infobox ET | |||
| Prime factorization = 2 × 31 | |||
| Step size = 19.355¢ | |||
| Fifth = 36\62 (696.77¢) (→ [[31edo|18\31]]) | |||
| Major 2nd = 10\62 = 193.5¢ | |||
| Semitones = 4:6 | |||
}} | |||
== Theory == | |||
'''62edo''' divides the octave into 62 equal parts of 19.35484 cents each. | '''62edo''' divides the octave into 62 equal parts of 19.35484 cents each. | ||
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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. | ||
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 temperaments are 15 & 62 and 11 & 62. | |||
=== Odd harmonics === | |||
{{harmonics in equal|62}} | {{harmonics in equal|62}} | ||
== Intervals == | == Intervals == | ||
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{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! Armodue Nomenclature 8;3 Relation | ||
|- | |- | ||
| <ul><li>'''Ɨ''' = Thick (1/8-tone up)</li><li>'''‡''' = Semisharp (1/4-tone up)</li><li>'''b''' = Flat (5/8-tone down)</li><li>'''◊''' = Node (sharp/flat blindspot 1/2-tone)</li><li>'''#''' = Sharp (5/8-tone up)</li><li>'''v''' = Semiflat (1/4-tone down)</li><li>'''⌐''' = Thin (1/8-tone down)</li></ul> | | <ul><li>'''Ɨ''' = Thick (1/8-tone up)</li><li>'''‡''' = Semisharp (1/4-tone up)</li><li>'''b''' = Flat (5/8-tone down)</li><li>'''◊''' = Node (sharp/flat blindspot 1/2-tone)</li><li>'''#''' = Sharp (5/8-tone up)</li><li>'''v''' = Semiflat (1/4-tone down)</li><li>'''⌐''' = Thin (1/8-tone down)</li></ul> | ||