172edo
| ← 171edo | 172edo | 173edo → |
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| (patent val), <172 272 399| (172b), and <172 273 400| (172c). Using the 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, supporting the 7-limit bohpier temperament; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-limit; 169/168, 352/351, 364/363, and 1716/1715 in the 13-limit, supporting the leapweek temperament. 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; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-limit; 625/624, 975/968, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the alternative 172bdee val, it tempers out 225/224, 118098/117649, and 3176523/3125000 in the 7-limit; 243/242, 1617/1600, 2079/2048, and 117649/117128 in the 11-limit; 351/350, 625/624, 1188/1183, and 1573/1568 in the 13-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; 176/175, 896/891, and 1331/1323 in the 11-limit. Using the alternative 172cef val, it tempers out 441/440, 1344/1331, and 3388/3375 in the 11-limit; 196/195, 352/351, 832/825, 1001/1000, and 2197/2187 in the 13-limit. Using the alternative 172cf val, 196/195, 1716/1715, 2080/2079, 2197/2187, and 2200/2197 are tempered out in the 13-limit. Using the 172f val, 275/273, 640/637, 847/845, and 1575/1573 are tempered out in the 13-limit.
It is the first EDO which an approximate all intervals within the smallest commonly cited value of the just-noticeable difference (3.5 cents).