123edo

123edo is the equal division of the octave into 123 parts of 9.7561 cents each. It tempers out the valentine comma, 1990656/1953125 and the misty comma, 67108864/66430125 in the 5-limit; 126/125, 1029/1024 and 537824/531441 in the 7-limit, providing the optimal patent val for the gravid temperament; 243/242, 896/891, 2401/2376, and 3388/3375 in the 11-limit; 196/195, 351/350, 832/825, 1575/1573, and 2197/2178 in the 13-limit. As its inconsistency to the 7-limit and higher limit, the mapping <123 195 286 346| (123d) is also possible for the 7-limit. Using the 123d val, it tempers out 2430/2401, 3136/3125, and 5120/5103 in the 7-limit; 176/175, 243/242, 1375/1372, and 2560/2541 in the 11-limit; 169/168, 364/363, 640/637, 729/728, and 832/825 in the 13-limit. Using the 123ce val, it tempers out 1331/1323 in the 11-limit, as well as 225/224, 245/243, and 1029/1024; 275/273, 352/351, 847/845, 1573/1568, and 3185/3168 in the 13-limit. Using the 123e val, it tempers out 121/120, 176/175, and 441/440 in the 11-limit; 196/195, 351/350, 352/351, 1287/1280, and 2197/2187 in the 13-limit. Using the 123df val, it tempers out 144/143, 351/350, 352/351, and 847/845 in the 13-limit.