217edo: Difference between revisions

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	~~The~~ ''~~217~~ equal division~~'' divides~~ the octave into 217 ~~equal~~ parts of 5.~~530 cents~~ each. It is a strong 19-limit system, the smallest uniquely [[~~consistent\|~~consistent]] in the 19-limit and consistent to the 21-limit. ~~In the 5-limit it~~ tempers out the parakleisma, \|8 14 -13>, and the escapade comma, \|32 -7 -9>; in the 7-limit 10976/10935, 3136/3125 and 4375/4374; in the 11-limit 441/440, 4000/3993 and 5632/5625; in the 13-limit 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079; in 17-limit 595/594, 833/832, 936/935, 1156/1155, 1225/1224, 1701/1700; in the 19-limit 343/342, 476/475, 969/968, 1216/1215, 1445/1444, 1521/1520 and 1540/1539.		'''217edo''' is the [[EDO\|equal division of the octave]] into 217 parts of 5.529954 [[cent]]s each. It is a strong 19-limit system, the smallest uniquely [[consistent]] in the 19-limit and consistent to the 21-limit. It tempers out the parakleisma, \|8 14 -13>, and the escapade comma, \|32 -7 -9> in the 5-limit; 10976/10935, 3136/3125 and 4375/4374 in the 7-limit; 441/440, 4000/3993 and 5632/5625 in the 11-limit; 364/363, 676/675, 1001/1000, 1575/1573 and 2080/2079 in the 13-limit; 595/594, 833/832, 936/935, 1156/1155, 1225/1224, 1701/1700 in the 17-limit; 343/342, 476/475, 969/968, 1216/1215, 1445/1444, 1521/1520 and 1540/1539 in the 19-limit. It is the optimal patent val for the [[Hemimean clan\|arch temperament]] in the 11 and 13 limits.