Mothwellsmic chords: Difference between revisions
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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. | ||
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; | ||
* | * 1–7/6–9/7–3/2 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 | ||
* | * 1–12/11–9/7–3/2 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 | 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 | 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 | [[Equal temperament]]s with mothwellsmic chords include {{EDOs| 22, 31, 53, 96, and 127 }}. | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||
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.