173edo

173edo is the equal division of the octave into 173 parts of 6.9364 cents each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <173 274 402| (patent val) and <173 274 401| (173c). Using the patent val, it tempers out the unicorn comma, 1594323/1562500 and the escapade comma, 4294967296/4271484375 in the 5-limit; 1728/1715, 3136/3125, and 413343/409600 in the 7-limit; 176/175, 540/539, 1331/1323, and 264627/262144 in the 11-limit, supporting the 11-limit semisept temperament; 676/675, 847/845, 1188/1183, and 1287/1280 in the 13-limit. Using the 173c val, it tempers out the amity comma, 1600000/1594323 and 35595703125/34359738368 in the 5-limit; 2430/2401, 4000/3969, and 234375/229376 in the 7-limit, supporting the 7-limit hamity temperament. Using the alternative 173cd val, it tempers out 225/224, 84035/82944, and 1250000/1240029 in the 7-limit, supporting the 7-limit septimin temperament; 441/440, 1375/1372, 4000/3993, and 26411/26244 in the 11-limit; 325/324, 729/728, 847/845, and 1875/1859 in the 13-limit. Using the 173d val, it tempers out 126/125, 10976/10935, and 28824005/28311552 in the 7-limit; 385/384, 1617/1600, 12005/11979, and 14641/14580 in the 11-limit; 196/195, 351/350, 676/675, 1287/1280, and 10648/10647 in the 13-limit, supporting the camahueto temperament. Using the 173e val, it tempers out 441/440, 1944/1925, 4000/3993, and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, and 3159/3125 in the 13-limit. Using the 173ef val, 144/143, 351/350, 640/637, and 847/845 are tempered out in the 13-limit.

173edo is the 40th prime EDO.