Dakotismic chords: Difference between revisions
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For triads, there are seven pairs of chords in inverse relationship: | For triads, there are seven pairs of chords in inverse relationship: | ||
* | * 1–6/5–17/11 with steps 6/5, 9/7, 22/17, and its inverse | ||
* | * 1–22/17–5/3 with steps 22/17, 9/7, 6/5; | ||
* | * 1–7/6–22/17 with steps 7/6, 10/9, 17/11, and its inverse | ||
* | * 1–17/11–12/7 with steps 17/11, 10/9, 7/6; | ||
* | * 1–11/10–17/12 with steps 11/10, 9/7, 24/17, and its inverse | ||
* | * 1–9/7–17/12 with steps 9/7, 11/10, 24/17; | ||
* | * 1–14/11–24/17 with steps 14/11, 10/9, 17/12, and its inverse | ||
* 1–10/9–24/17 with steps 10/9, 14/11, 17/12; | |||
* 1–9/7–15/11 with steps 9/7, 18/17, 22/15, and its inverse | |||
* 1–9/7–17/9 with steps 9/7, 22/15, 18/17; | |||
* 1–11/7–5/3 with steps 11/7, 18/17, 6/5, and its inverse | |||
* 1–11/7–17/9 with steps 11/7, 6/5, 18/17; | |||
* 1–11/10–7/6 with steps 11/10, 18/17, 12/7, and its inverse | |||
* 1–11/10–17/9 with steps 11/10, 12/7, 18/17. | |||
For tetrads, there are three palindromic chords and twenty-four pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are three palindromic chords and twenty-four pairs of chords in inverse relationship. The palindromic chords are | ||
* | * 1–6/5–9/7–17/11 with steps 6/5, 15/14, 6/5, 22/17; | ||
* | * 1–18/17–9/7–15/11 with steps 18/17, 17/14, 18/17, 22/15; | ||
* | * 1–18/17–5/3–30/17 with steps 18/17, 11/7, 18/17, 17/15. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* | * 1–14/11–17/11–9/5 with steps 14/11, 17/14, 7/6, 10/9, and its inverse | ||
* | * 1–7/6–17/12–9/5 with steps 7/6, 17/14, 14/11, 10/9; | ||
* | * 1–6/5–17/11–12/7 with steps 6/5, 9/7, 10/9, 7/6, and its inverse | ||
* | * 1–7/6–22/17–5/3 with steps 7/6, 10/9, 9/7, 6/5; | ||
* | * 1–6/5–17/11–9/5 with steps 6/5, 9/7, 7/6, 10/9, and its inverse | ||
* | * 1–10/9–22/17–5/3 with steps 10/9, 7/6, 9/7, 6/5; | ||
* | * 1–9/7–17/12–11/7 with steps 9/7, 11/10, 10/9, 14/11, and its inverse | ||
* | * 1–14/11–24/17–14/9 with steps 14/11, 10/9, 11/10, 9/7; | ||
* | * 1–11/10–17/12–11/7 with steps 11/10, 9/7, 10/9, 14/11, and its inverse | ||
* | * 1–14/11–24/17–20/11 with steps 14/11, 10/9, 9/7, 11/10; | ||
* | * 1–11/10–17/12–17/10 with steps 11/10, 9/7, 6/5, 20/17, and its inverse | ||
* | * 1–6/5–17/11–17/10 with steps 6/5, 9/7, 11/10, 20/17; | ||
* | * 1–17/12–11/7–11/6 with steps 17/12, 10/9, 7/6, 12/11, and its inverse | ||
* | * 1–17/12–17/11–9/5 with steps 17/12, 12/11, 7/6, 10/9; | ||
* | * 1–22/17–5/3–11/6 with steps 22/17, 9/7, 11/10, 12/11, and its inverse | ||
* | * 1–11/10–17/12–11/6 with steps 11/10, 9/7, 22/17, 12/11; | ||
* | * 1–17/12–3/2–9/5 with steps 17/12, 18/17, 6/5, 10/9, and its inverse | ||
* | * 1–18/17–3/2–5/3 with steps 18/17, 17/12, 10/9, 6/5; | ||
* | * 1–9/7–15/11–3/2 with steps 9/7, 18/17, 11/10, 4/3, and its inverse | ||
* | * 1–11/10–7/6–3/2 with steps 11/10, 18/17, 9/7, 4/3; | ||
* | * 1–9/7–17/12–3/2 with steps 9/7, 11/10, 18/17, 4/3, and its inverse | ||
* | * 1–18/17–7/6–3/2 with steps 18/17, 11/10, 9/7, 4/3; | ||
* | * 1–11/10–17/12–3/2 with steps 11/10, 9/7, 18/17, 4/3, and its inverse | ||
* | * 1–18/17–15/11–3/2 with steps 18/17, 9/7, 11/10, 4/3; | ||
* 1–9/7–15/11–5/3 with steps 9/7, 18/17, 11/9, 6/5, and its inverse | |||
* 1–9/7–17/11–17/9 with steps 9/7, 6/5, 11/9, 18/17; | |||
* 1–9/7–15/11–18/11 with steps 9/7, 18/17, 6/5, 11/9, and its inverse | |||
* 1–9/7–11/7–17/9 with steps 9/7, 11/9, 6/5, 18/17; | |||
* 1–9/7–17/11–18/11 with steps 9/7, 6/5, 18/17, 11/9, and its inverse | |||
* 1–6/5–17/11–17/9 with steps 6/5, 9/7, 11/9, 18/17; | |||
* 1–6/5–14/9–17/9 with steps 6/5, 22/17, 17/14, 18/17, and its inverse | |||
* 1–17/14–11/7–17/9 with steps 17/14, 22/17, 6/5, 18/17; | |||
* 1–9/7–5/3–17/9 with steps 9/7, 22/17, 17/15, 18/17, and its inverse | |||
* 1–17/15–22/15–17/9 with steps 17/15, 22/17, 9/7, 18/17; | |||
* 1–6/5–17/10–17/9 with steps 6/5, 17/12, 10/9, 18/17, and its inverse | |||
* 1–10/9–11/7–17/9 with steps 10/9, 17/12, 6/5, 18/17; | |||
* 1–17/14–9/7–17/12 with steps 17/14, 18/17, 11/10, 24/17, and its inverse | |||
* 1–11/10–7/6–17/12 with steps 11/10, 18/17, 17/14, 24/17; | |||
* 1–10/7–11/7–5/3 with steps 10/7, 11/10, 18/17, 6/5, and its inverse | |||
* 1–10/7–12/7–20/11 with steps 10/7, 6/5, 18/17, 11/10; | |||
* 1–11/10–11/9–17/9 with steps 11/10, 10/9, 17/11, 18/17, and its inverse | |||
* 1–17/11–12/7–17/9 with steps 17/11, 10/9, 11/10, 18/17; | |||
* 1–10/9–12/7–17/9 with steps 10/9, 17/11, 11/10, 18/17, and its inverse | |||
* 1–11/10–17/10–17/9 with steps 11/10, 17/11, 10/9, 18/17; | |||
* 1–11/10–6/5–17/9 with steps 11/10, 12/11, 11/7, 18/17, and its inverse | |||
* 1–11/7–12/7–17/9 with steps 11/7, 12/11, 11/10, 18/17; | |||
* 1–15/14–9/7–15/11 with steps 15/14, 6/5, 18/17, 22/15, and its inverse | |||
* 1–18/17–14/11–15/11 with steps 18/17, 6/5, 15/14, 22/15. | |||
Equal temperaments with dakotismic chords include {{Optimal ET sequence|12, 14c, 15g, 19eg, 22, 26, 27eg, 31g, 41, 46, 50, 58, 72, 94, 118, 121, 140, 239 and 311}}. | Equal temperaments with dakotismic chords include {{Optimal ET sequence| 12, 14c, 15g, 19eg, 22, 26, 27eg, 31g, 41, 46, 50, 58, 72, 94, 118, 121, 140, 239 and 311 }}. | ||
[[Category:17-odd-limit]] | [[Category:17-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||
[[Category:Tetrads]] | [[Category:Tetrads]] | ||
[[Category:Dakotismic]] | [[Category:Dakotismic]] | ||