Mothwellsmic chords: Difference between revisions

Revision as of 09:12, 1 June 2023

Mothwellsmic chords are essentially tempered chords tempered by the mothwellsma, 99/98.

The mothwellsmic triad consists of a stack of two 7/6's and 16/11 closing at the octave:

It can be extended to tetrads as

They can be extended to pentads as

Equal divisions with mothwellsmic triads include 22edo, 31edo, 53edo, 96edo and 127edo.

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-The '''mothwellsmic triad''' is an [[essentially tempered chord]] which is the [[99/98]] tempering of 1-[[7/6]]-[[11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad]]s include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].
+'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].
+The mothwellsmic triad consists of a stack of two [[7/6]]'s and [[16/11]] closing at the octave:
+* 1-7/6-11/8 with steps 7/6-7/6-16/11.
+It can be extended to tetrads as
+* 1-7/6-11/8-3/2 with steps 7/6-7/6-12/11-4/3, and its inverse
+* 1-7/6-11/8-11/6 with steps 7/6-7/6-4/3-12/11;
+* 1-7/6-11/8-7/4 with steps 7/6-7/6-9/7-8/7, and its inverse
+* 1-7/6-11/8-14/9 with steps 7/6-7/6-8/7-9/7.
+They can be extended to pentads as
+* 1-7/6-11/8-3/2-7/4 with steps 7/6-7/6-12/11-7/6-8/7, and its inverse
+* 1-7/6-11/8-14/9-11/6 with steps 7/6-7/6-8/7-7/6-12/11.
+Equal divisions with mothwellsmic triads include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].
 [[Category:11-odd-limit]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Mothwellsmic]]
-{{Todo| discuss title }}