257edo

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257edo is the equal division of the octave into 257 parts of 4.66926 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <257 407 597 721| (optimal patent val), <257 408 597 722| (257bd), <257 407 596 721| (257c), and <257 407 597 722| (257d). Using the optimal patent val, it tempers out Würschmidt comma, 393216/390625 and |-36, 33, -7> in the 5-limit; 1029/1024, 177147/175000, and 393216/390625 in the 7-limit. Using the 257bd val, it tempers out the kleisma, 15625/15552 and |69, -42, -1> in the 5-limit; 4000/3969, 6144/6125, and 40353607/39858075 in the 7-limit. Using the 257c val, it tempers out the ampersand comma, 34171875/33554432 and the maja comma, 762939453125/753145430616 in the 5-limit; 225/224, 1029/1024, and 854492187500/847288609443 in the 7-limit; 243/242, 385/384, 441/440, and 152587890625/148550704533 in the 11-limit, providing for the 11-limit miracle temperament. Using the 257d val, it tempers out 1728/1715, 413343/409600, and 703125/702464 in the 7-limit.

257edo is the 55th prime EDO.