167edo: Difference between revisions
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'''167edo''' is the [[EDO|equal division of the octave]] into 167 parts of 7.18562874251 [[cent]]s each. It [[tempering_out|tempers out]] the [[Würschmidt family|würschmidt comma]], 393216/390625 and 10737418240/10460353203 in the [[5-limit]]; 2401/2400, 3136/3125, and 179200/177147 in the [[7-limit]]; 896/891, 2200/2187, and 3388/3375 in the [[11-limit]]; 325/324, 352/351, 364/363, 1001/1000, and 1716/1715 in the [[13-limit]]; 256/255, 442/441, 595/594, 715/714, and 936/935 in the [[17-limit]]. It | '''167edo''' is the [[EDO|equal division of the octave]] into 167 parts of 7.18562874251 [[cent]]s each. It [[tempering_out|tempers out]] the [[Würschmidt family|würschmidt comma]], 393216/390625 and 10737418240/10460353203 in the [[5-limit]]; 2401/2400, 3136/3125, and 179200/177147 in the [[7-limit]]; 896/891, 2200/2187, and 3388/3375 in the [[11-limit]]; 325/324, 352/351, 364/363, 1001/1000, and 1716/1715 in the [[13-limit]], providing the [[optimal patent val]] for 11- and 13-limit [[Porwell temperaments|polypyth temperament]]; 256/255, 442/441, 595/594, 715/714, and 936/935 in the [[17-limit]]. It also supports 11-limit [[Breedsmic temperaments|unthirds temperament]]. | ||
167edo is the 39th [[prime EDO]]. | 167edo is the 39th [[prime EDO]]. | ||
Revision as of 02:48, 16 December 2018
167edo is the equal division of the octave into 167 parts of 7.18562874251 cents each. It tempers out the würschmidt comma, 393216/390625 and 10737418240/10460353203 in the 5-limit; 2401/2400, 3136/3125, and 179200/177147 in the 7-limit; 896/891, 2200/2187, and 3388/3375 in the 11-limit; 325/324, 352/351, 364/363, 1001/1000, and 1716/1715 in the 13-limit, providing the optimal patent val for 11- and 13-limit polypyth temperament; 256/255, 442/441, 595/594, 715/714, and 936/935 in the 17-limit. It also supports 11-limit unthirds temperament.
167edo is the 39th prime EDO.