211edo: Difference between revisions
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211edo is in[[consistent]] to the 5-limit and higher limits, with two mappings possible for the 5-limit: {{val| 211 334 490 }} ([[patent val]]) and {{val| 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 {{monzo| 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 in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val| 211 334 490 }} ([[patent val]]) and {{val| 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 {{monzo| 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. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Revision as of 10:04, 13 April 2024
| ← 210edo | 211edo | 212edo → |
211edo is inconsistent to the 5-odd-limit and higher limits, 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.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.43 | +0.42 | -2.00 | +0.83 | +0.34 | +1.18 | -2.01 | -2.59 | -1.78 | +1.26 | -2.68 |
| Relative (%) | -42.7 | +7.3 | -35.2 | +14.6 | +6.0 | +20.7 | -35.4 | -45.5 | -31.3 | +22.1 | -47.2 | |
| Steps (reduced) |
334 (123) |
490 (68) |
592 (170) |
669 (36) |
730 (97) |
781 (148) |
824 (191) |
862 (18) |
896 (52) |
927 (83) |
954 (110) | |
Subsets and supersets
211edo is the 47th prime edo.