Mothwellsmic chords: Difference between revisions

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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]].

[[Category:11-limit]]

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.

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

* 1–12/11–9/7–3/2 with steps 12/11, 7/6, 7/6, 4/3;

* 1–9/7–3/2–7/4 with steps 9/7, 7/6, 7/6, 8/7, and its inverse

* 1–7/6–3/2–12/7 with steps 7/6, 9/7, 8/7, 7/6.

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

* 1–9/8–9/7–3/2–7/4 with steps 9/8, 8/7, 7/6, 7/6, 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

* 1–7/6–9/7–3/2–7/4 with steps 7/6, 12/11, 7/6, 7/6, 8/7, and its inverse

* 1–7/6–9/7–3/2–12/7 with steps 7/6, 12/11, 7/6, 8/7, 7/6.

[[Equal temperament]]s with mothwellsmic chords include {{EDOs| 22, 31, 53, 96, and 127 }}.

[[Category:11-odd-limit chords]]

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Mothwellsmic]]

~~[[Category:Triad]]~~

~~[[Category:Essentially tempered chords]]~~

~~{{todo|discuss title}}~~

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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]].
-[[Category:11-limit]]
+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.
+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
+* 1–12/11–9/7–3/2 with steps 12/11, 7/6, 7/6, 4/3;
+* 1–9/7–3/2–7/4 with steps 9/7, 7/6, 7/6, 8/7, and its inverse
+* 1–7/6–3/2–12/7 with steps 7/6, 9/7, 8/7, 7/6.
+For pentads, there are two palindromic chords and a pair of chords in inverse relationship. The palindromic chords are
+* 1–9/8–9/7–3/2–7/4 with steps 9/8, 8/7, 7/6, 7/6, 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
+* 1–7/6–9/7–3/2–7/4 with steps 7/6, 12/11, 7/6, 7/6, 8/7, and its inverse
+* 1–7/6–9/7–3/2–12/7 with steps 7/6, 12/11, 7/6, 8/7, 7/6.
+[[Equal temperament]]s with mothwellsmic chords include {{EDOs| 22, 31, 53, 96, and 127 }}.
+[[Category:11-odd-limit chords]]
+[[Category:Essentially tempered chords]]
+[[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Mothwellsmic]]
-[[Category:Triad]]
-[[Category:Essentially tempered chords]]
-{{todo|discuss title}}