210edo: Difference between revisions
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== Theory == | == Theory == | ||
210 = 3 × 70, and 210edo shares its [[3/2|fifth]] with [[70edo]]. It is [[consistent]] to the [[9-odd-limit]], but there is a sharp tendency in the lower [[harmonic]]s. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; [[3136/3125]], [[5120/5103]], and 118098/117649 in the 7-limit. | |||
Using the | Using the 210e val, which does the best, it tempers out [[540/539]], [[4000/3993]], 6912/6875, and 15488/15435 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], [[2197/2187]], and 3584/3575 in the 13-limit. Using the patent val, it tempers out [[176/175]], 1375/1372, [[8019/8000]], and 41503/41472 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 2197/2187, and 16900/16807 in the 13-limit. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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| 123\210<br>(17\210) | | 123\210<br>(17\210) | ||
| 702.86<br>(97.14) | | 702.86<br>(97.14) | ||
| 3/2<br>( | | 3/2<br>(18/17) | ||
| [[Misty]] | | [[Misty]] (210gh) | ||
|- | |- | ||
| 5 | | 5 | ||
| | | 13\210 | ||
| | | 74.29 | ||
| | | 25/24 | ||
| [[ | | [[Countdown]] (210e) | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | ||