139edo

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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 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; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit. Using the 139bd val, it tempers out Würschmidt comma, 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit. Using the 139ce val, it tempers out the small diesis, 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit; 540/539, 1331/1323, and 1815/1792 in the 11-limit. Using the 139d val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit.

139edo is the 34th prime EDO.