Kestrel chords: Difference between revisions
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For triads, there are three pairs of chords in inverse relationship: | For triads, there are three pairs of chords in inverse relationship: | ||
* | * 1–7/6–18/13 with steps of 7/6, 13/11, 13/9, and its inverse | ||
* | * 1–13/11–18/13 with steps of 13/11, 7/6, 13/9; | ||
* | * 1–14/11–18/13 with steps of 14/11, 13/12, 13/9, and its inverse | ||
* | * 1–13/12–18/13 with steps of 13/12, 14/11, 13/9; | ||
* | * 1–13/11–9/7 with steps of 13/11, 13/12, 14/9, and its inverse | ||
* | * 1–13/12–9/7 with steps of 13/12, 13/11, 14/9. | ||
For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–13/11–18/13–18/11 with steps of 13/11, 7/6, 13/11, 11/9; | ||
* | * 1–13/12–18/13–3/2 with steps of 13/12, 14/11, 13/12, 4/3; | ||
* | * 1–13/12–13/11–9/7 with steps of 13/12, 12/11, 13/12, 14/9. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–11/9–13/9–11/7 with steps of 11/9, 13/11, 13/12, 14/11, and its inverse | ||
* | * 1–13/12–9/7–11/7 with steps of 13/12, 13/11, 11/9, 14/11; | ||
* | * 1–7/6–18/13–3/2 with steps of 7/6, 13/11, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–9/7–3/2 with steps of 13/12, 13/11, 7/6, 4/3; | ||
* | * 1–13/11–9/7–18/13 with steps of 13/11, 13/12, 14/13, 13/9, and its inverse | ||
* | * 1–14/13–7/6–18/13 with steps of 14/13, 13/12, 13/11, 13/9; | ||
* | * 1–13/11–14/11–18/13 with steps of 13/11, 14/13, 13/12, 13/9, and its inverse | ||
* | * 1–13/12–7/6–18/13 with steps of 13/12, 14/13, 13/11, 13/9; | ||
* | * 1–7/6–14/11–18/13 with steps of 7/6, 12/11, 13/12, 13/9, and its inverse | ||
* | * 1–13/12–13/11–18/13 with steps of 13/12, 12/11, 7/6, 13/9; | ||
* | * 1–13/12–9/7–18/13 with steps of 13/12, 13/11, 14/13, 13/9, and its inverse | ||
* | * 1–14/13–14/11–18/13 with steps of 14/13, 13/11, 13/12, 13/9. | ||
For pentads, there are three pairs of chords in inverse relationship: | For pentads, there are three pairs of chords in inverse relationship: | ||
* | * 1–13/11–9/7–18/13–18/11 with steps of 13/11, 13/12, 14/13, 13/11, 11/9, and its inverse | ||
* | * 1–13/11–14/11–18/13–18/11 with steps of 13/11, 14/13, 13/12, 13/11, 11/9; | ||
* | * 1–13/12–7/6–18/13–3/2 with steps of 13/12, 14/13, 13/11, 13/12, 4/3, and its inverse | ||
* | * 1–13/12–9/7–18/13–3/2 with steps of 13/12, 13/11, 14/13, 13/12, 4/3; | ||
* | * 1–13/12–13/11–9/7–18/13 with steps of 13/12, 12/11, 13/12, 14/13, 13/9, and its inverse | ||
* | * 1–14/13–7/6–14/11–18/13 with steps of 14/13, 13/12, 12/11, 13/12, 13/9. | ||
Equal temperaments with kestrel chords include {{Optimal ET sequence|17, 24, 26, 41, 53, 58, 77, 94, 103, 111, 161, 205, 214 and 255}}, with 255edo giving the [[optimal patent val]]. | Equal temperaments with kestrel chords include {{Optimal ET sequence|17, 24, 26, 41, 53, 58, 77, 94, 103, 111, 161, 205, 214 and 255}}, with 255edo giving the [[optimal patent val]]. | ||
[[Category:13-odd-limit]] | [[Category:13-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||