291edo: Difference between revisions
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'''291edo''' is the [[EDO|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c). Using the patent val, it tempers out 393216/390625 and |-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val|optimal patent val]] for the 13-limit [[Würschmidt family|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and |80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit. | '''291edo''' is the [[EDO|equal division of the octave]] into 291 parts of 4.1237 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c). Using the patent val, it tempers out 393216/390625 and |-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the [[Optimal_patent_val|optimal patent val]] for the 13-limit [[Würschmidt family|hemiwürschmidt temperament]]. Using the 291b val, it tempers out 15625/15552 and |80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit. | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
Revision as of 19:08, 3 July 2022
291edo is the equal division of the octave into 291 parts of 4.1237 cents each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <291 461 676| (patent val), <291 462 676| (291b), and <291 461 675| (291c). Using the patent val, it tempers out 393216/390625 and |-47 37 -5> in the 5-limit; 2401/2400, 3136/3125, and 1162261467/1146880000 in the 7-limit; 243/242, 441/440, 5632/5625, and 58720256/58461513 in the 11-limit; 351/350, 1001/1000, 1575/1573, 3584/3575, and 43940/43923 in the 13-limit, so that it provides the optimal patent val for the 13-limit hemiwürschmidt temperament. Using the 291b val, it tempers out 15625/15552 and |80 -46 -3> in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.