Catadictmic 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: | ||
* | * 1–16/13–11/8 with steps of 16/13, 10/9, 16/11, and its inverse | ||
* | * 1–16/11–13/8 with steps of 16/11, 10/9, 16/13; | ||
* | * 1–13/10–16/11 with steps of 13/10, 9/8, 11/8, and its inverse | ||
* | * 1–11/8–20/13 with steps of 11/8, 9/8, 13/10; | ||
* | * 1–11/10–16/13 with steps of 11/10, 9/8, 13/8, and its inverse | ||
* | * 1–9/8–16/13 with steps of 9/8, 11/10, 13/8. | ||
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 | ||
* | * 1–16/13–16/11–9/5 with steps of 16/13, 13/11, 16/13, 10/9; | ||
* | * 1–9/8–11/8–20/13 with steps of 9/8, 11/9, 9/8, 13/10; | ||
* | * 1–9/8–16/13–18/13 with steps of 9/8, 11/10, 9/8, 13/9. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–13/10–16/11–9/5 with steps of 13/10, 9/8, 16/13, 10/9, and its inverse | ||
* | * 1–16/13–18/13–9/5 with steps of 16/13, 9/8, 13/10, 10/9; | ||
* | * 1–9/8–16/11–9/5 with steps of 9/8, 13/10, 16/13, 10/9, and its inverse | ||
* | * 1–16/13–8/5–9/5 with steps of 16/13, 13/10, 9/8, 10/9; | ||
* | * 1–13/11–13/10–16/11 with steps of 13/11, 11/10, 9/8, 11/8, and its inverse | ||
* | * 1–9/8–16/13–16/11 with steps of 9/8, 11/10, 13/11, 11/8; | ||
* | * 1–13/10–16/11–8/5 with steps of 13/10, 9/8, 11/10, 5/4, and its inverse | ||
* | * 1–11/10–16/13–8/5 with steps of 11/10, 9/8, 13/10, 5/4; | ||
* | * 1–11/10–16/13–11/8 with steps of 11/10, 9/8, 10/9, 16/11, and its inverse | ||
* | * 1–10/9–5/4–11/8 with steps of 10/9, 9/8, 11/10, 16/11; | ||
* | * 1–11/10–16/13–9/5 with steps of 11/10, 9/8, 16/11, 10/9, and its inverse | ||
* | * 1–16/11–18/11–9/5 with steps of 16/11, 9/8, 11/10, 10/9. | ||
For pentads, there are three pairs of chords in inverse relationship: | For pentads, there are three pairs of chords in inverse relationship: | ||
* | * 1–16/13–16/11–8/5–9/5 with steps of 16/13, 13/11, 11/10, 9/8, 10/9, and its inverse | ||
* | * 1–9/8–16/13–16/11–9/5 with steps of 9/8, 11/10, 13/11, 16/13, 10/9; | ||
* | * 1–9/8–16/11–18/11–9/5 with steps of 9/8, 13/10, 9/8, 11/10, 10/9, and its inverse | ||
* | * 1–11/10–16/13–8/5–9/5 with steps of 11/10, 9/8, 13/10, 9/8, 10/9; | ||
* | * 1–13/10–16/11–8/5–9/5 with steps of 13/10, 9/8, 11/10, 9/8, 10/9, and its inverse | ||
* | * 1–9/8–16/13–18/13–9/5 with steps of 9/8, 11/10, 9/8, 13/10, 10/9. | ||
Equal temperaments with catadictmic chords include {{Optimal ET sequence| 7, 12, 19, 22, 24, 26, 29, 31, 43, 46, 50, 53, 72 and 96 }}. | Equal temperaments with catadictmic chords include {{Optimal ET sequence| 7, 12, 19, 22, 24, 26, 29, 31, 43, 46, 50, 53, 72 and 96 }}. | ||
[[Category:13-odd-limit]] | [[Category:13-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||