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Charismic chords: Difference between revisions

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The two charismic triads are in inverse relationship:  
The two charismic triads are in inverse relationship:  
* 1-5/4-24/17 with steps of 5/4-9/8-17/12;
* 1–5/4–24/17 with steps of 5/4, 9/8, 17/12;
* 1-9/8-24/17 with steps of 9/8-5/4-17/12.
* 1–9/8–24/17 with steps of 9/8, 5/4, 17/12.


For tetrads, there are five palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are  
For tetrads, there are five palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are  
* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;
* 1–5/4–24/17–30/17 with steps of 5/4, 9/8, 5/4, 17/15;
* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;
* 1–9/8–5/4–24/17 with steps of 9/8, 10/9, 9/8, 17/12;
* 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;
* 1–16/15–4/3–17/12 with steps of 16/15, 5/4, 16/15, 24/17;
* 1-16/15-5/4-4/3 with steps of 16/15-20/17-16/15-3/2;
* 1–16/15–5/4–4/3 with steps of 16/15, 20/17, 16/15, 3/2;
* 1-16/15-9/8-6/5 with steps of 16/15-18/17-16/15-5/3.
* 1–16/15–9/8–6/5 with steps of 16/15, 18/17, 16/15, 5/3.


The inversely related pairs of chords are  
The inversely related pairs of chords are  
* 1-5/4-24/17-15/8 with steps of 5/4-9/8-4/3-16/15, and its inverse  
* 1–5/4–24/17–15/8 with steps of 5/4, 9/8, 4/3, 16/15, and its inverse  
* 1-4/3-3/2-15/8 with steps of 4/3-9/8-5/4-16/15;
* 1–4/3–3/2–15/8 with steps of 4/3, 9/8, 5/4, 16/15;
* 1-5/4-24/17-3/2 with steps of 5/4-9/8-16/15-4/3, and its inverse  
* 1–5/4–24/17–3/2 with steps of 5/4, 9/8, 16/15, 4/3, and its inverse  
* 1-16/15-6/5-3/2 with steps of 16/15-9/8-5/4-4/3;
* 1–16/15–6/5–3/2 with steps of 16/15, 9/8, 5/4, 4/3;
* 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12, and its inverse  
* 1–5/4–4/3–24/17 with steps of 5/4, 16/15, 18/17, 17/12, and its inverse  
* 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;
* 1–18/17–9/8–24/17 with steps of 18/17, 16/15, 5/4, 17/12;
* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12, and its inverse  
* 1–20/17–5/4–24/17 with steps 20/17, 16/15, 9/8, 17/12, and its inverse  
* 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.
* 1–9/8–6/5–24/17 with steps of 9/8, 16/15, 20/17, 17/12.


For pentads, there are one palindromic chord and eight pairs of chords in inverse relationship. The palindromic chord is  
For pentads, there are one palindromic chord and eight pairs of chords in inverse relationship. The palindromic chord is  
* 1-5/4-24/17-30/17-15/8 with steps of 5/4-9/8-5/4-16/15-16/15.
* 1–5/4–24/17–30/17–15/8 with steps of 5/4, 9/8, 5/4, 16/15, 16/15.


The inversely related pairs of chords are  
The inversely related pairs of chords are  
* 1-9/8-5/4-24/17-3/2 with steps of 9/8-10/9-9/8-16/15-4/3, and its inverse  
* 1–9/8–5/4–24/17–3/2 with steps of 9/8, 10/9, 9/8, 16/15, 4/3, and its inverse  
* 1-9/8-5/4-24/17-15/8 with steps of 9/8-10/9-9/8-4/3-16/15;
* 1–9/8–5/4–24/17–15/8 with steps of 9/8, 10/9, 9/8, 4/3, 16/15;
* 1-5/4-24/17-3/2-15/8 with steps of 5/4-9/8-16/15-5/4-16/15, and its inverse  
* 1–5/4–24/17–3/2–15/8 with steps of 5/4, 9/8, 16/15, 5/4, 16/15, and its inverse  
* 1-5/4-4/3-5/3-16/9 with steps of 5/4-16/15-5/4-16/15-9/8;
* 1–5/4–4/3–5/3–16/9 with steps of 5/4, 16/15, 5/4, 16/15, 9/8;
* 1-5/4-4/3-24/17-15/8 with steps of 5/4-16/15-18/17-4/3-16/15, and its inverse  
* 1–5/4–4/3–24/17–15/8 with steps of 5/4, 16/15, 18/17, 4/3, 16/15, and its inverse  
* 1-5/4-4/3-16/9-15/8 with steps of 5/4-16/15-4/3-18/17-16/15;
* 1–5/4–4/3–16/9–15/8 with steps of 5/4, 16/15, 4/3, 18/17, 16/15;
* 1-5/4-4/3-24/17-3/2 with steps of 5/4-16/15-18/17-16/15-4/3, and its inverse  
* 1–5/4–4/3–24/17–3/2 with steps of 5/4, 16/15, 18/17, 16/15, 4/3, and its inverse  
* 1-16/15-9/8-6/5-3/2 with steps of 16/15-18/17-16/15-5/4-4/3;
* 1–16/15–9/8–6/5–3/2 with steps of 16/15, 18/17, 16/15, 5/4, 4/3;
* 1-20/17-5/4-4/3-15/8 with steps of 20/17-16/15-16/15-24/17-16/15, and its inverse  
* 1–20/17–5/4–4/3–15/8 with steps of 20/17, 16/15, 16/15, 24/17, 16/15, and its inverse  
* 1-20/17-5/4-30/17-15/8 with steps of 20/17-16/15-24/17-16/15-16/15;
* 1–20/17–5/4–30/17–15/8 with steps of 20/17, 16/15, 24/17, 16/15, 16/15;
* 1-16/15-5/4-4/3-3/2 with steps of 16/15-20/17-16/15-9/8-4/3, and its inverse  
* 1–16/15–5/4–4/3–3/2 with steps of 16/15, 20/17, 16/15, 9/8, 4/3, and its inverse  
* 1-9/8-6/5-24/17-3/2 with steps of 9/8-16/15-20/17-16/15-4/3;
* 1–9/8–6/5–24/17–3/2 with steps of 9/8, 16/15, 20/17, 16/15, 4/3;
* 1-20/17-5/4-4/3-24/17 with steps of 20/17-16/15-16/15-18/17-17/12, and its inverse  
* 1–20/17–5/4–4/3–24/17 with steps of 20/17, 16/15, 16/15, 18/17, 17/12, and its inverse  
* 1-18/17-9/8-6/5-24/17 with steps of 18/17-16/15-16/15-20/17-17/12;
* 1–18/17–9/8–6/5–24/17 with steps of 18/17, 16/15, 16/15, 20/17, 17/12;
* 1-5/4-24/17-3/2-30/17 with steps of 5/4-9/8-16/15-20/17-17/15, and its inverse  
* 1–5/4–24/17–3/2–30/17 with steps of 5/4, 9/8, 16/15, 20/17, 17/15, and its inverse  
* 1-16/15-6/5-3/2-17/10 with steps of 16/15-9/8-5/4-17/15-20/17.
* 1–16/15–6/5–3/2–17/10 with steps of 16/15, 9/8, 5/4, 17/15, 20/17.


For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  
For hexads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are  
* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15;
* 1–9/8–5/4–24/17–3/2–15/8 with steps of 9/8, 10/9, 9/8, 16/15, 5/4, 16/15;
* 1-5/4-4/3-24/17-3/2-15/8 with steps of 5/4-16/15-18/17-16/15-5/4-16/15.
* 1–5/4–4/3–24/17–3/2–15/8 with steps of 5/4, 16/15, 18/17, 16/15, 5/4, 16/15.


The inversely related pairs of chords are  
The inversely related pairs of chords are  
* 1-16/15-5/4-4/3-17/12-3/2 with steps of 16/15-20/17-16/15-16/15-18/17-4/3, and its inverse  
* 1–16/15–5/4–4/3–17/12–3/2 with steps of 16/15, 20/17, 16/15, 16/15, 18/17, 4/3, and its inverse  
* 1-18/17-9/8-6/5-24/17-3/2 with steps of 18/17-16/15-16/15-20/17-16/15-4/3;
* 1–18/17–9/8–6/5–24/17–3/2 with steps of 18/17, 16/15, 16/15, 20/17, 16/15, 4/3;
* 1-5/4-24/17-3/2-30/17-15/8 with steps of 5/4-9/8-16/15-20/17-16/15-16/15, and its inverse  
* 1–5/4–24/17–3/2–30/17–15/8 with steps of 5/4, 9/8, 16/15, 20/17, 16/15, 16/15, and its inverse  
* 1-16/15-5/4-4/3-3/2-15/8 with steps of 16/15-20/17-16/15-9/8-5/4-16/15.
* 1–16/15–5/4–4/3–3/2–15/8 with steps of 16/15, 20/17, 16/15, 9/8, 5/4, 16/15.


Equal temperaments with charismic chords include {{Optimal ET sequence|9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}.
Equal temperaments with charismic chords include {{Optimal ET sequence| 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111 }}.


[[Category:17-odd-limit]]
[[Category:17-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Triads]]
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