211edo
| ← 210edo | 211edo | 212edo → |
211 equal divisions of the octave (abbreviated 211edo or 211ed2), also called 211-tone equal temperament (211tet) or 211 equal temperament (211et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 211 equal parts of about 5.69 ¢ each. Each step represents a frequency ratio of 21/211, or the 211th root of 2.
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 (%) | -43 | +7 | -35 | +15 | +6 | +21 | -35 | -45 | -31 | +22 | -47 | |
| 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.