139edo

139edo is the equal division of the octave into 139 parts of 8.6331 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323| (optimal patent val), <139 221 323| (139b), and <139 220 322| (139c). Using the optimal patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit. Using the 139b val, it tempers out Würschmidt comma, 393216/390625 and 409600000/387420489 in the 5-limit; 686/675 and 2240/2187 in the 7-limit. Using the 139c val, it tempers out small diesis, 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit.

139edo is the 34th prime EDO.