Mothwellsmic chords: Difference between revisions

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The '''mothwellsmic triad''' is an [[Dyadic_chord|essentially tempered chord]] which is the [[99/98|99/98]] tempering of 1-[[7/6|7/6]]-[[11/8|11/8]], with steps of 7/6-7/6-16/11. Equal divisions with mothwellsmic [[triad|triads]] include [[22edo|22]], [[31edo|31]], [[53edo|53]], [[96edo|96]] and [[127edo|127]].
'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]].
[[Category:11-limit]]
 
[[Category:mothwellsmic]]
There are one triad, six tetrads and four pentads as 2.3.7.11 subgroup [[11-odd-limit]] essentially tempered chords.
[[Category:todo:discuss_title]]
 
[[Category:triad]]
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]]

Latest revision as of 10:23, 10 October 2024

Mothwellsmic chords are essentially tempered chords 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.

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 temperaments with mothwellsmic chords include 22, 31, 53, 96, and 127.

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