170edo

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170edo is the equal division of the octave into 170 parts of 7.0588 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: <170 269 395 477| (patent val), <170 270 395 477| (170b), <170 270 395 478| (170bd), and <170 269 394 477| (170c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit valentine temperament; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit. Using the 170b val, it tempers out the diaschisma, 2048/2025 and the kleisma, 15625/15552 in the 5-limit; 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit. Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit. Using the 170c val, it tempers out the lalagu comma, 43046721/41943040 and the sycamore comma, 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit unidec temperament; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.