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. | 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 | 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 | * 1-11/8-11/7-7/4 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 | * 1-7/6-9/7-3/2 with steps 7/6-12/11-7/6-4/3. | ||
The inversely related pairs of chords are | 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; | ||
* 1-7/6-11/8-7/4 with steps 7/6-7/6-9/7-8/7, and its inverse | * 1-7/6-11/8-7/4 with steps 7/6-7/6-9/7-8/7, and its inverse | ||
* 1-7/6-11/8- | * 1-7/6-11/8-11/7 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 | 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 | * 1-7/6-11/8-11/7-7/4 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 | * 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 | 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- | * 1-7/6-11/8-11/7-11/6 with steps 7/6-7/6-8/7-7/6-12/11. | ||
Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]]. | Equal divisions with mothwellsmic chords include [[22edo]], [[31edo]], [[53edo]], [[96edo]] and [[127edo]]. | ||