169edo

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169 equal divisions per octave

169edo is the equal division of the octave into 169 parts of 7.1006 cents each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <169 268 392| (patent val) and <169 268 393| (169c). Using the patent val, it tempers out the sycamore comma, 48828125/47775744 and the rodan comma, 131072000/129140163 in the 5-limit; 245/243, 1029/1024, and 9765625/9633792 in the 7-limit; 385/384, 441/440, 896/891, and 312500/307461 in the 11-limit; 676/675, 975/968, and 1625/1617 in the 13-limit. Using the 169cdf val, it tempers out the valentine comma, 1990656/1953125 and the vulture comma, 10485760000/10460353203 in the 5-limit; 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit; 351/350, 352/351, 640/637, and 676/675 in the 13-limit, supporting the buzzard temperament. Using the 169d val, it tempers out 225/224, 51200/50421, and 1071875/1062882 in the 7-limit; 2200/2187, 2420/2401, 2560/2541, and 6000/5929 in the 11-limit; 169/168, 364/363, 640/637, and 676/675 in the 13-limit.