169edo

From Xenharmonic Wiki
Jump to: navigation, search

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| (optimal patent val) and <169 268 393| (169c). Using the optimal 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. Using the 169c val, it tempers out the valentine comma, 1990656/1953125 and the vulture comma, 10485760000/10460353203 in the 5-limit; 126/125, 1029/1024, and / in the 7-limit; 896/891, 2401/2376, 8019/8000, and 14700/14641 in the 11-limit. Using the alternative 169cd val, it tempers out 1728/1715, 5120/5103, and 235298/234375 in the 7-limit; 176/175, 540/539, 8019/8000, and 43923/43904 in the 11-limit.