Major minthmic chords: Difference between revisions
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For triads, there are four pairs of chords in inverse relationship: | For triads, there are four pairs of chords in inverse relationship: | ||
* | * 1–16/13–3/2 with steps of 16/13, 11/9, 4/3, and its inverse | ||
* | * 1–11/9–3/2 with steps of 11/9, 16/13, 4/3; | ||
* | * 1–13/11–4/3 with steps of 13/11, 9/8, 3/2, and its inverse | ||
* | * 1–9/8–4/3 with steps of 9/8, 13/11, 3/2; | ||
* | * 1–9/8–16/13 with steps of 9/8, 12/11, 13/8, and its inverse | ||
* | * 1–12/11–16/13 with steps of 12/11, 9/8, 13/8; | ||
* | * 1–9/8–11/9 with steps of 9/8, 13/12, 18/11, and its inverse | ||
* | * 1–13/12–11/9 with steps of 13/12, 9/8, 18/11. | ||
For tetrads, there are five palindromic chords and eleven pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are five palindromic chords and eleven pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–11/9–3/2–13/8 with steps of 11/9, 16/13, 13/12, 16/13; | ||
* | * 1–11/9–4/3–13/8 with steps of 11/9, 12/11, 11/9, 16/13; | ||
* | * 1–9/8–4/3–3/2 with steps of 9/8, 13/11, 9/8, 4/3; | ||
* | * 1–9/8–16/13–18/13 with steps of 9/8, 12/11, 9/8, 13/9; | ||
* | * 1–9/8–11/9–11/8 with steps of 9/8, 13/12, 9/8, 16/11. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–11/9–11/8–13/8 with steps of 11/9, 9/8, 13/11, 16/13, and its inverse | ||
* | * 1–13/11–4/3–13/8 with steps of 13/11, 9/8, 11/9, 16/13; | ||
* | * 1–11/9–13/9–13/8 with steps of 11/9, 13/11, 9/8, 16/13, and its inverse | ||
* | * 1–9/8–4/3–13/8 with steps of 9/8, 13/11, 11/9, 16/13; | ||
* | * 1–16/13–18/13–3/2 with steps of 16/13, 9/8, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–11/9–3/2 with steps of 13/12, 9/8, 16/13, 4/3; | ||
* | * 1–16/13–4/3–3/2 with steps of 16/13, 13/12, 9/8, 4/3, and its inverse | ||
* | * 1–9/8–11/9–3/2 with steps of 9/8, 13/12, 16/13, 4/3; | ||
* | * 1–11/9–11/8–3/2 with steps of 11/9, 9/8, 12/11, 4/3, and its inverse | ||
* | * 1–12/11–16/13–3/2 with steps of 12/11, 9/8, 11/9, 4/3; | ||
* | * 1–11/9–4/3–3/2 with steps of 11/9, 12/11, 9/8, 4/3, and its inverse | ||
* | * 1–9/8–16/13–3/2 with steps of 9/8, 12/11, 11/9, 4/3; | ||
* | * 1–13/11–4/3–16/11 with steps of 13/11, 9/8, 12/11, 11/8, and its inverse | ||
* | * 1–12/11–16/13–16/11 with steps of 12/11, 9/8, 13/11, 11/8; | ||
* | * 1–13/11–4/3–13/9 with steps of 13/11, 9/8, 13/12, 18/13, and its inverse | ||
* | * 1–13/12–11/9–13/9 with steps of 13/12, 9/8, 13/11, 18/13; | ||
* | * 1–9/8–16/13–4/3 with steps of 9/8, 12/11, 13/12, 3/2, and its inverse | ||
* | * 1–13/12–13/11–4/3 with steps of 13/12, 12/11, 9/8, 3/2; | ||
* | * 1–9/8–11/9–4/3 with steps of 9/8, 13/12, 12/11, 3/2, and its inverse | ||
* | * 1–12/11–13/11–4/3 with steps of 12/11, 13/12, 9/8, 3/2; | ||
* | * 1–12/11–16/13–4/3 with steps of 12/11, 9/8, 13/12, 3/2, and its inverse | ||
* | * 1–13/12–11/9–4/3 with steps of 13/12, 9/8, 12/11, 3/2. | ||
For pentads, there are fourteen pairs of chords in inverse relationship: | For pentads, there are fourteen pairs of chords in inverse relationship: | ||
* | * 1–13/11–4/3–16/11–18/11 with steps of 13/11, 9/8, 12/11, 9/8, 11/9, and its inverse | ||
* | * 1–9/8–16/13–18/13–18/11 with steps of 9/8, 12/11, 9/8, 13/11, 11/9; | ||
* | * 1–9/8–4/3–3/2–18/11 with steps of 9/8, 13/11, 9/8, 12/11, 11/9, and its inverse | ||
* | * 1–12/11–16/13–16/11–18/11 with steps of 12/11, 9/8, 13/11, 9/8, 11/9; | ||
* | * 1–9/8–16/13–3/2–18/11 with steps of 9/8, 12/11, 11/9, 12/11, 11/9, and its inverse | ||
* | * 1–12/11–4/3–16/11–18/11 with steps of 12/11, 11/9, 12/11, 9/8, 11/9; | ||
* | * 1–11/9–11/8–3/2–13/8 with steps of 11/9, 9/8, 12/11, 13/12, 16/13, and its inverse | ||
* | * 1–13/12–13/11–4/3–13/8 with steps of 13/12, 12/11, 9/8, 11/9, 16/13; | ||
* | * 1–11/9–4/3–3/2–13/8 with steps of 11/9, 12/11, 9/8, 13/12, 16/13 and, its inverse | ||
* | * 1–13/12–11/9–4/3–13/8 with steps of 13/12, 9/8, 12/11, 11/9, 16/13; | ||
* | * 1–11/9–4/3–13/9–13/8 with steps of 11/9, 12/11, 13/12, 9/8, 16/13, and its inverse | ||
* | * 1–9/8–11/9–4/3–13/8 with steps of 9/8, 13/12, 12/11, 11/9, 16/13; | ||
* | * 1–13/11–4/3–13/9–13/8 with steps of 13/11, 9/8, 13/12, 9/8, 16/13, and its inverse | ||
* | * 1–9/8–11/9–11/8–13/8 with steps of 9/8, 13/12, 9/8, 13/11, 16/13; | ||
* | * 1–9/8–4/3–3/2–13/8 with steps of 9/8, 13/11, 9/8, 13/12, 16/13, and its inverse | ||
* | * 1–13/12–11/9–13/9–13/8 with steps of 13/12, 9/8, 13/11, 9/8, 16/13; | ||
* | * 1–9/8–11/9–3/2–13/8 with steps of 9/8, 13/12, 16/13, 13/12, 16/13, and its inverse | ||
* | * 1–13/12–4/3–13/9–13/8 with steps of 13/12, 16/13, 13/12, 9/8, 16/13; | ||
* | * 1–9/8–16/13–4/3–3/2 with steps of 9/8, 12/11, 13/12, 9/8, 4/3, and its inverse | ||
* | * 1–9/8–11/9–4/3–3/2 with steps of 9/8, 13/12, 12/11, 9/8, 4/3; | ||
* | * 1–9/8–16/13–18/13–3/2 with steps of 9/8, 12/11, 9/8, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–11/9–4/3–3/2 with steps of 13/12, 9/8, 12/11, 9/8, 4/3; | ||
* | * 1–9/8–11/9–11/8–3/2 with steps of 9/8, 13/12, 9/8, 12/11, 4/3, and its inverse | ||
* | * 1–12/11–16/13–4/3–3/2 with steps of 12/11, 9/8, 13/12, 9/8, 4/3; | ||
* | * 1–12/11–16/13–4/3–16/11 with steps of 12/11, 9/8, 13/12, 12/11, 11/8, and its inverse | ||
* | * 1–12/11–13/11–4/3–16/11 with steps of 12/11, 13/12, 9/8, 12/11, 11/8; | ||
* | * 1–13/12–11/9–4/3–13/9 with steps of 13/12, 9/8, 12/11, 13/12, 18/13, and its inverse | ||
* | * 1–13/12–13/11–4/3–13/9 with steps of 13/12, 12/11, 9/8, 13/12, 18/13. | ||
For hexads, there are two palindromic chords and five pairs of chords in inverse relationship. The palindromic chords are | For hexads, there are two palindromic chords and five pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–12/11–16/13–4/3–3/2–18/11 with steps of 12/11, 9/8, 13/12, 9/8, 12/11, 11/9; | ||
* | * 1–13/12–11/9–4/3–3/2–13/8 with steps of 13/12, 9/8, 12/11, 9/8, 13/12, 16/13. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–9/8–16/13–4/3–3/2–22/13 with steps of 9/8, 12/11, 9/8, 13/12, 9/8, 13/11, and its inverse | ||
* | * 1–9/8–11/9–11/8–3/2–22/13 with steps of 9/8, 13/12, 9/8, 12/11, 9/8, 13/11; | ||
* | * 1–9/8–16/13–18/13–3/2–18/11 with steps of 9/8, 12/11, 9/8, 13/12, 12/11, 11/9, and its inverse | ||
* | * 1–12/11–13/11–4/3–16/11–18/11 with steps of 12/11, 13/12, 9/8, 12/11, 9/8, 11/9; | ||
* | * 1–9/8–16/13–4/3–3/2–18/11 with steps of 9/8, 12/11, 13/12, 9/8, 12/11, 11/9, and its inverse | ||
* | * 1–12/11–16/13–4/3–16/11–18/11 with steps of 12/11, 9/8, 13/12, 12/11, 9/8, 11/9; | ||
* | * 1–9/8–11/9–11/8–3/2–13/8 with steps of 9/8, 13/12, 9/8, 12/11, 13/12, 16/13, and its inverse | ||
* | * 1–13/12–13/11–4/3–13/9–13/8 with steps of 13/12, 12/11, 9/8, 13/12, 9/8, 16/13; | ||
* | * 1–9/8–11/9–4/3–3/2–13/8 with steps of 9/8, 13/12, 12/11, 9/8, 13/12, 16/13, and its inverse | ||
* | * 1–13/12–11/9–4/3–13/9–13/8 with steps of 13/12, 9/8, 12/11, 13/12, 9/8, 16/13. | ||
Finally, there is a pair of heptads in inverse relationship: | Finally, there is a pair of heptads in inverse relationship: | ||
* | * 1–9/8–16/13–4/3–3/2–18/11–24/13 with steps of 9/8, 12/11, 13/12, 9/8, 12/11, 9/8, 13/12 (→[[minthmic7a]]), and its inverse | ||
* | * 1–9/8–11/9–4/3–3/2–13/8–11/6 with steps of 9/8, 13/12, 12/11, 9/8, 13/12, 9/8, 12/11 (→[[minthmic7b]]). | ||
Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of | Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of | ||
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== Notes == | == Notes == | ||
[[Category:13-odd-limit]] | [[Category:13-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||