172edo: Difference between revisions
Created page with "'''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 possi..." Tags: Mobile edit Mobile web edit |
No edit summary Tags: Mobile edit Mobile web edit |
||
| Line 1: | Line 1: | ||
'''172edo''' is the [[EDO|equal division of the octave]] into 172 parts of 6.9767 [[cent]]s 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 | '''172edo''' is the [[EDO|equal division of the octave]] into 172 parts of 6.9767 [[cent]]s 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 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; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-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; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-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. Using the 172c val, it tempers out the [[Diaschismic family|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. | ||
[[Category:Edo]] | [[Category:Edo]] | ||
Revision as of 13:24, 13 December 2018
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 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; 385/384, 896/891, 1331/1323, and 9375/9317 in the 11-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; 441/440, 1944/1925, 4000/3993, and 4125/4096 in the 11-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. 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.