263edo: Difference between revisions
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'''263EDO''' is the [[EDO|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. It tempers out 393216/390625 (Würschmidt comma) and |50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit. 263EDO is acculate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo|80]] and before [[343edo|343]]. Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit. | '''263EDO''' is the [[EDO|equal division of the octave]] into 263 parts of 4.5627 [[cent]]s each. It tempers out 393216/390625 (Würschmidt comma) and |50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit. 263EDO is acculate for the 17th harmonic, as the denominator of a convergent to log<sub>2</sub>17, after [[80edo|80]] and before [[343edo|343]]. Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit. | ||
Revision as of 21:29, 4 October 2022
| ← 262edo | 263edo | 264edo → |
263EDO is the equal division of the octave into 263 parts of 4.5627 cents each. It tempers out 393216/390625 (Würschmidt comma) and |50 -33 1> in the 5-limit. Using the patent val, it tempers out 4375/4374, 50421/50000, and 458752/455625 in the 7-limit; 441/440, 3388/3375, 16384/16335, and 26411/26244 in the 11-limit; 364/363, 2080/2079, 2197/2187, and 3584/3575 in the 13-limit; 595/594, 833/832, 936/935, and 1156/1155 in the 17-limit. 263EDO is acculate for the 17th harmonic, as the denominator of a convergent to log217, after 80 and before 343. Using the 263d val, it tempers out 5120/5103, 16875/16807, and 1959552/1953125 in the 7-limit; 540/539, 1375/1372, 16384/16335, and 43923/43750 in the 11-limit; 351/350, 1001/1000, 1573/1568, 2197/2187, and 4225/4224 in the 13-limit. Using the 263df val, it tempers out 352/351, 640/637, 729/728, and 3584/3575 in the 13-limit.
263EDO is the 56th prime EDO.