172edo

From Xenharmonic Wiki
Jump to: navigation, search

172edo is the equal division of the octave into 172 parts of 6.9767 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <172 273 399| (optimal patent val), <172 272 399| (172b), and <172 273 400| (172c). Using the optimal patent val, it tempers out the semicomma, 2109375/2097152 and 1220703125/1162261467 in the 5-limit; 245/243, 3125/3087, and 2097152/2066715 in the 7-limit. Using the 172b val, it tempers out the unicorn comma, 1594323/1562500 and 2197265625/2147483648 in the 5-limit; 1728/1715, 3645/3584, and 390625/388962 in the 7-limit. Using the alternative 172bd val, it tempers out 225/224, 118098/117649, and 3176523/3125000 in the 7-limit. Using the 172c val, it tempers out the diaschisma, 2048/2025 and |1, 36, -25> in the 5-limit; 4375/4374, 50421/50000, and 110592/109375 in the 7-limit.