Mothwellsmic chords: Difference between revisions

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'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].

There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup [[11-odd-limit]] essentially tempered chords.

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

For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

* 1-11/8-11/7-7/4 with steps 11/8-8/7-9/8-8/7

* 1-7/6-9/7-3/2 with steps 7/6-12/11-7/6-4/3

The inversely related pairs of chords are

* 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;

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* 1-7/6-11/8-14/9 with steps 7/6-7/6-8/7-9/7.

~~They can be extended to~~ pentads as

For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are

* 1-7/6-11/8-11/7-7/4 with steps 7/6-7/6-8/7-9/8-8/7

* 1-7/6-11/8-3/2-11/6 with steps 7/6-7/6-12/11-11/9-12/11

The inversely related pair of chords is

* 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]].

Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].

[[Category:11-odd-limit]]

@@ Line 1: / Line 1: @@
 '''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].
+There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup [[11-odd-limit]] essentially tempered chords.
 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
+For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
+* 1-11/8-11/7-7/4 with steps 11/8-8/7-9/8-8/7
+* 1-7/6-9/7-3/2 with steps 7/6-12/11-7/6-4/3
+The inversely related pairs of chords are
 * 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;
@@ Line 10: / Line 16: @@
 * 1-7/6-11/8-14/9 with steps 7/6-7/6-8/7-9/7.
-They can be extended to pentads as
+For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
+* 1-7/6-11/8-11/7-7/4 with steps 7/6-7/6-8/7-9/8-8/7
+* 1-7/6-11/8-3/2-11/6 with steps 7/6-7/6-12/11-11/9-12/11
+The inversely related pair of chords is
 * 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]].
+Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]].
 [[Category:11-odd-limit]]