211edo

← 210edo

211edo

212edo →

Prime factorization	211 (prime)
Step size	5.6872¢
Fifth	123\211 (699.526¢)
Semitones (A1:m2)	17:18 (96.68¢ : 102.4¢)
Dual sharp fifth	124\211 (705.213¢)
Dual flat fifth	123\211 (699.526¢)
Dual major 2nd	36\211 (204.739¢)
Consistency limit	3
Distinct consistency limit	3

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 2^1/211, 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

Approximation of odd harmonics in 211edo

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.