31edo: Difference between revisions

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* 31et is lower in relative error than any previous equal temperaments in the 7-, 11-, 13-, and 17-limit. The next equal temperaments doing better in those subgroups are 72, 72, 41, and 46, respectively.

* 31et is lower in relative error than any previous equal temperaments in the 7-, 11-, 13-, and 17-limit. The next equal temperaments doing better in those subgroups are [[72edo|72]], 72, [[41edo|41]], and [[46edo|46]], respectively.

* 31et 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]].

* 31et 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 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.

* 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.

=== Uniform maps ===

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-* 31et is lower in relative error than any previous equal temperaments in the 7-, 11-, 13-, and 17-limit. The next equal temperaments doing better in those subgroups are 72, 72, 41, and 46, respectively.
+* 31et is lower in relative error than any previous equal temperaments in the 7-, 11-, 13-, and 17-limit. The next equal temperaments doing better in those subgroups are [[72edo|72]], 72, [[41edo|41]], and [[46edo|46]], respectively.
-* 31et 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]].
+* 31et 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 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.
+* 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.
 === Uniform maps ===