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.

[[Category:~~Equal divisions of the octave~~]]

291edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val| 291 461 676 }} ([[patent val]]), {{val| 291 462 676 }} (291b), and {{val| 291 461 675 }} (291c).

Using the patent val, it [[tempering out|tempers out]] [[393216/390625]] and {{monzo| -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 {{monzo| 80 -46 -3 }} in the 5-limit.

Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 291 factors into {{factorization|291}}, 291edo contains [[3edo]] and [[97edo]] as its subsets.

[[Category:Hemiwürschmidt]]

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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: &lt;291 461 676| (patent val), &lt;291 462 676| (291b), and &lt;291 461 675| (291c). Using the patent val, it tempers out 393216/390625 and |-47 37 -5&gt; 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&gt; in the 5-limit. Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave]]
+edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val| 291 461 676 }} ([[patent val]]), {{val| 291 462 676 }} (291b), and {{val| 291 461 675 }} (291c).
+Using the patent val, it [[tempering out|tempers out]] [[393216/390625]] and {{monzo| -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 {{monzo| 80 -46 -3 }} in the 5-limit.
+Using the 291c val, it tempers out 390625000/387420489 and 1121008359375/1099511627776 in the 5-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|291}}
+=== Subsets and supersets ===
+Since 291 factors into {{factorization|291}}, 291edo contains [[3edo]] and [[97edo]] as its subsets.
+[[Category:Hemiwürschmidt]]