210edo: Difference between revisions

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'''210edo''' is the [[EDO|equal division of the octave]] into 210 parts of 5.7143 cents each. It 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. It is consistent to the 7-limit, but there is a sharp tendency for harmonics 3, 5, and 7. 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. Using the 210e val, 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.
'''210edo''' is the [[EDO|equal division of the octave]] into 210 parts of 5.7143 cents each. It 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. It is consistent to the 7-limit, but there is a sharp tendency for harmonics 3, 5, and 7. 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. Using the 210e val, 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.


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Revision as of 21:22, 4 October 2022

← 209edo 210edo 211edo →
Prime factorization 2 × 3 × 5 × 7
Step size 5.71429 ¢ 
Fifth 123\210 (702.857 ¢) (→ 41\70)
Semitones (A1:m2) 21:15 (120 ¢ : 85.71 ¢)
Consistency limit 9
Distinct consistency limit 9

210edo is the equal division of the octave into 210 parts of 5.7143 cents each. It 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. It is consistent to the 7-limit, but there is a sharp tendency for harmonics 3, 5, and 7. 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. Using the 210e val, 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.