31edo: Difference between revisions

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31edo represents a record in [[Pepper ambiguity]] in the 7-, 9- and [[11-odd-limit]], which it is [[consistent]] through. In the [[13-limit]] it 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's 5\31 neutral third generator generates [[mosh]] and [[dicoid]] MOSes. Its 12\31 generator generates an [[oneirotonic]] scale, similar to the 5L 3s scale in [[13edo]] but with the 9/8 and 5/4 better in tune.

~~31edo is the 11th [[prime numbers|prime]] edo, following [[29edo]] and coming before [[37edo]].~~

== Commas ==

31 EDO [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 31 49 72 87 107 115 }}, comma values rounded to 5 significant digits.)

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 edo represents a record in [[Pepper ambiguity]] in the 7-, 9- and [[11-odd-limit]], which it is [[consistent]] through. In the [[13-limit]] it 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's 5\31 neutral third generator generates [[mosh]] and [[dicoid]] MOSes. Its 12\31 generator generates an [[oneirotonic]] scale, similar to the 5L 3s scale in [[13edo]] but with the 9/8 and 5/4 better in tune.
-edo is the 11th [[prime numbers|prime]] edo, following [[29edo]] and coming before [[37edo]].
 == Commas ==
 EDO [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 31 49 72 87 107 115 }}, comma values rounded to 5 significant digits.)