Mothwellsmic chords: Difference between revisions
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'''Mothwellsmic chords''' are [[essentially tempered chord]]s tempered by the mothwellsma, [[99/98]]. | '''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: | 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. | * 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 | * 1-7/6-11/8-3/2 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; | * 1-7/6-11/8-11/6 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. | * 1-7/6-11/8-14/9 with steps 7/6-7/6-8/7-9/7. | ||
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 | * 1-7/6-11/8-3/2-7/4 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. | * 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 | Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]]. | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit]] | ||
Revision as of 11:25, 27 October 2023
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
- 1-7/6-11/8-11/6 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.
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 chords include 22edo, 31edo, 53edo, 96edo and 127edo.