291edo

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← 290edo291edo292edo →
Prime factorization 3 × 97
Step size 4.12371¢
Fifth 170\291 (701.031¢)
Semitones (A1:m2) 26:23 (107.2¢ : 94.85¢)
Consistency limit 3
Distinct consistency limit 3

291edo is the equal division of the octave into 291 parts of 4.1237 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c).

Using the patent val, it tempers out 393216/390625 and |-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the optimal patent val for the 13-limit hemiwürschmidt temperament.

Using the 291b val, it tempers out 15625/15552 and |80 -46 -3> in the 5-limit.

Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.


Approximation of prime harmonics in 291edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 -0.92 +1.32 +0.25 +1.26 +0.71 -1.86 -0.61 -1.47 +1.35 +1.36
relative (%) +0 -22 +32 +6 +31 +17 -45 -15 -36 +33 +33
Steps
(reduced)
291
(0)
461
(170)
676
(94)
817
(235)
1007
(134)
1077
(204)
1189
(25)
1236
(72)
1316
(152)
1414
(250)
1442
(278)