31edo: Difference between revisions

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== As a regular temperament ==

31edo excels in the 2.5.7 subgroup, tempering out [[3136/3125]] and {{monzo|-15 0 -2 7}} ([[823543/819200]]). In the 11-limit, 31edo can be defined as the unique temperament that tempers out [[81/80]], [[~~126~~/~~125~~]], [[~~1029~~/~~1024~~]], and [[99/98]], and it supports [[orwell]], [[mohajira]], and the relatively high-accuracy temperament [[miracle]]. In the [[13-limit]] 31edo doesn't do as well, but is the [[optimal patent val]] for the rank five temperament tempering out the 13-limit comma [[66/65]], which equates [[6/5]] and [[13/11]]. It also provides the optimal patent val for mohajira, squares and casablanca in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.

31edo excels in the 2.5.7 subgroup, tempering out [[3136/3125]] and {{monzo|-15 0 -2 7}} ([[823543/819200]]). In the 11-limit, 31edo can be defined as the unique temperament that tempers out [[81/80]], [[99/98]], [[121/120]] and [[126/125]], and it supports [[orwell]], [[mohajira]], and the relatively high-accuracy temperament [[miracle]]. In the [[13-limit]] 31edo doesn't do as well, but is the [[optimal patent val]] for the rank five temperament tempering out the 13-limit comma [[66/65]], which equates [[6/5]] and [[13/11]]. It also provides the optimal patent val for mohajira, squares and casablanca in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.

=== Commas ===

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 == As a regular temperament ==
-edo excels in the 2.5.7 subgroup, tempering out [[3136/3125]] and {{monzo|-15 0 -2 7}} ([[823543/819200]]). In the 11-limit, 31edo can be defined as the unique temperament that tempers out [[81/80]], [[126/125]], [[1029/1024]], and [[99/98]], and it supports [[orwell]], [[mohajira]], and the relatively high-accuracy temperament [[miracle]]. In the [[13-limit]] 31edo doesn't do as well, but is the [[optimal patent val]] for the rank five temperament tempering out the 13-limit comma [[66/65]], which equates [[6/5]] and [[13/11]]. It also provides the optimal patent val for mohajira, squares and casablanca in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.
+edo excels in the 2.5.7 subgroup, tempering out [[3136/3125]] and {{monzo|-15 0 -2 7}} ([[823543/819200]]). In the 11-limit, 31edo can be defined as the unique temperament that tempers out [[81/80]], [[99/98]], [[121/120]] and [[126/125]], and it supports [[orwell]], [[mohajira]], and the relatively high-accuracy temperament [[miracle]]. In the [[13-limit]] 31edo doesn't do as well, but is the [[optimal patent val]] for the rank five temperament tempering out the 13-limit comma [[66/65]], which equates [[6/5]] and [[13/11]]. It also provides the optimal patent val for mohajira, squares and casablanca in the 11-limit and huygens/meantone, squares, winston, lupercalia and nightengale in the 13-limit.
 === Commas ===