211edo: Difference between revisions
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'''211edo''' is the [[EDO|equal division of the octave]] into 211 parts of 5.6872 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <211 334 490| (patent val) and <211 335 490| (211b). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Luna family|luna comma]], 274877906944/274658203125 in the 5-limit; 1029/1024, 3136/3125, and 1594323/1568000 in the 7-limit; 540/539, 2835/2816, 6912/6875, and 12005/11979 in the 11-limit; 351/350, 847/845, and 1001/1000 in the 13-limit. Using the 211b val, it tempers out [[Tetracot family|tetracot comma]], 20000/19683 and |55 -1 -23> in the 5-limit; 3136/3125, 84035/82944, and 100352/98415 in the 7-limit; 385/384, 2401/2376, 3773/3750, and 6655/6561 in the 11-limit; 196/195, 364/363, 625/624, and 1001/1000 in the 13-limit. Using the 211bd val, it tempers out 6144/6125, 16875/16807, and 327680/321489 in the 7-limit; 896/891, 2420/2401, 3388/3375, and 6655/6561 in the 11-limit; 572/567, 625/624, 640/637, 1573/1568, and 1625/1617 in the 13-limit. Using the 211f val, 364/363, 676/675, 1287/1280, and 1716/1715 are tempered out in the 13-limit. 211edo is quite accurate on the 2.5.7/3.11 subgroup. | '''211edo''' is the [[EDO|equal division of the octave]] into 211 parts of 5.6872 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <211 334 490| (patent val) and <211 335 490| (211b). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the [[Luna family|luna comma]], 274877906944/274658203125 in the 5-limit; 1029/1024, 3136/3125, and 1594323/1568000 in the 7-limit; 540/539, 2835/2816, 6912/6875, and 12005/11979 in the 11-limit; 351/350, 847/845, and 1001/1000 in the 13-limit. Using the 211b val, it tempers out [[Tetracot family|tetracot comma]], 20000/19683 and |55 -1 -23> in the 5-limit; 3136/3125, 84035/82944, and 100352/98415 in the 7-limit; 385/384, 2401/2376, 3773/3750, and 6655/6561 in the 11-limit; 196/195, 364/363, 625/624, and 1001/1000 in the 13-limit. Using the 211bd val, it tempers out 6144/6125, 16875/16807, and 327680/321489 in the 7-limit; 896/891, 2420/2401, 3388/3375, and 6655/6561 in the 11-limit; 572/567, 625/624, 640/637, 1573/1568, and 1625/1617 in the 13-limit. Using the 211f val, 364/363, 676/675, 1287/1280, and 1716/1715 are tempered out in the 13-limit. 211edo is quite accurate on the 2.5.7/3.11 subgroup. | ||
Revision as of 21:22, 4 October 2022
| ← 210edo | 211edo | 212edo → |
211edo is the equal division of the octave into 211 parts of 5.6872 cents each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <211 334 490| (patent val) and <211 335 490| (211b). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the luna comma, 274877906944/274658203125 in the 5-limit; 1029/1024, 3136/3125, and 1594323/1568000 in the 7-limit; 540/539, 2835/2816, 6912/6875, and 12005/11979 in the 11-limit; 351/350, 847/845, and 1001/1000 in the 13-limit. Using the 211b val, it tempers out tetracot comma, 20000/19683 and |55 -1 -23> in the 5-limit; 3136/3125, 84035/82944, and 100352/98415 in the 7-limit; 385/384, 2401/2376, 3773/3750, and 6655/6561 in the 11-limit; 196/195, 364/363, 625/624, and 1001/1000 in the 13-limit. Using the 211bd val, it tempers out 6144/6125, 16875/16807, and 327680/321489 in the 7-limit; 896/891, 2420/2401, 3388/3375, and 6655/6561 in the 11-limit; 572/567, 625/624, 640/637, 1573/1568, and 1625/1617 in the 13-limit. Using the 211f val, 364/363, 676/675, 1287/1280, and 1716/1715 are tempered out in the 13-limit. 211edo is quite accurate on the 2.5.7/3.11 subgroup.
211edo is the 47th prime EDO.