31edo: Difference between revisions

31edo excels in the 2.5.7 subgroup (the JI chord 4:5:7 is represented highly [[consistent]]ly: to [[consistency #Consistency to distance d|distance]] 10.36). In 2.5.7 it tempers out the didacus comma [[3136/3125]] and the quince comma [[823543/819200]], thus also tempering out the very small [[rainy comma]], the simplest 2.5.7 comma tempered out by the 7-limit microtemperament [[171edo]]. 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 provides 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. In the 17-limit it tempers out [[120/119]], equating the otonal tetrad of 4:5:6:7 and the inversion of the 10:12:15:17 minor tetrad.

=== Commas ===