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'''Ursulismmic chords''' are [[essentially tempered chord]]s tempered by the ursulisma, [[375/374]].  
'''Ursulismic chords''' are [[dyadic chord|essentially tempered chords]] tempered by the ursulisma, [[375/374]].
 
There are 8 triads, 28 tetrads, 26 pentads and 7 hexads as 2.3.5.11.17 subgroup [[17-odd-limit]] essentially tempered chords.


The ursulismic triads include the following inversely related pairs:  
The ursulismic triads include the following inversely related pairs:  
* 1-5/4-17/10 with steps 5/4-15/11-20/17, and its inverse
* 1–5/4–22/15 with steps of 5/4, 20/17, 15/11, and its inverse  
* 1-5/4-22/15 with steps 5/4-20/17-15/11;
* 1–20/17–22/15 with steps of 20/17, 5/4, 15/11;
* 1-17/15-5/4 with steps 17/15-11/10-8/5, and its inverse
* 1–6/5–15/11 with steps of 6/5, 17/15, 22/15, and its inverse
* 1-11/10-5/4 with steps 11/10-17/15-8/5;
* 1–17/15–15/11 with steps of 17/15, 6/5, 22/15;
* 1-17/10-15/8 with steps 17/10-11/10-16/15, and its inverse
* 1–17/15–5/4 with steps of 17/15, 11/10, 8/5, and its inverse  
* 1-11/10-15/8 with steps 11/10-17/10-16/15;  
* 1–11/10–5/4 with steps of 11/10, 17/15, 8/5;
* 1-22/15-5/3 with steps 22/15-17/15-6/5, and its inverse
* 1–11/10–20/17 with steps of 11/10, 16/15, 17/10, and its inverse
* 1-17/15-5/3 with steps 17/15-22/15-6/5.  
* 1–16/15–20/17 with steps of 16/15, 11/10, 17/10.
 
For tetrads, there are eight palindromic chords and ten pairs of chords in inverse relationship. The palindromic chords are
* 1–6/5–15/11–18/11 with steps of 6/5, 17/15, 6/5, 11/9;
* 1–20/17–22/15–8/5 with steps of 20/17, 5/4, 12/11, 5/4;
* 1–20/17–5/4–22/15 with steps of 20/17, 17/16, 20/17, 15/11;
* 1–17/15–5/4–17/12 with steps of 17/15, 11/10, 17/15, 24/17;
* 1–11/10–5/4–11/8 with steps of 11/10, 17/15, 11/10, 16/11;
* 1–17/15–6/5–15/11 with steps of 17/15, 18/17, 17/15, 22/15;
* 1–11/10–20/17–22/17 with steps of 11/10, 16/15, 11/10, 17/11;
* 1–17/15–15/11–17/11 with steps of 17/15, 6/5, 17/15, 22/17.


They can be extended to the following palindromic tetrads:
The inversely related pairs of chords are
* 1-11/10-17/10-15/8 with steps 11/10-17/11-11/10-16/15;  
* 1–5/4–3/2–17/10 with steps of 5/4, 6/5, 17/15, 20/17, and its inverse
* 1-17/15-22/15-5/3 with steps 17/15-22/17-17/15-6/5.  
* 1–6/5–3/2–30/17 with steps of 6/5, 5/4, 20/17, 17/15;
* 1–20/17–24/17–8/5 with steps of 20/17, 6/5, 17/15, 5/4, and its inverse
* 1–17/15–15/11–8/5 with steps of 17/15, 6/5, 20/17, 5/4;
* 1–6/5–15/11–3/2 with steps of 6/5, 17/15, 11/10, 4/3, and its inverse
* 1–11/10–5/4–3/2 with steps of 11/10, 17/15, 6/5, 4/3;
* 1–15/11–3/2–8/5 with steps of 15/11, 11/10, 16/15, 5/4, and its inverse
* 1–11/10–3/2–15/8 with steps of 11/10, 15/11, 5/4, 16/15;
* 1–5/4–11/8–22/15 with steps of 5/4, 11/10, 16/15, 15/11, and its inverse
* 1–16/15–20/17–22/15 with steps of 16/15, 11/10, 5/4, 15/11;
* 1–20/17–22/17–22/15 with steps of 20/17, 11/10, 17/15, 15/11, and its inverse
* 1–17/15–5/4–22/15 with steps of 17/15, 11/10, 20/17, 15/11;
* 1–15/11–3/2–17/10 with steps of 15/11, 11/10, 17/15, 20/17, and its inverse
* 1–11/10–3/2–30/17 with steps of 11/10, 15/11, 20/17, 17/15;
* 1–17/15–5/4–15/11 with steps of 17/15, 11/10, 12/11, 22/15, and its inverse
* 1–12/11–6/5–15/11 with steps of 12/11, 11/10, 17/15, 22/15;
* 1–17/15–5/4–4/3 with steps of 17/15, 11/10, 16/15, 3/2, and its inverse
* 1–16/15–20/17–4/3 with steps of 16/15, 11/10, 17/15, 3/2;
* 1–11/10–20/17–5/4 with steps of 11/10, 16/15, 17/16, 8/5, and its inverse
* 1–17/16–17/15–5/4 with steps of 17/16, 16/15, 11/10, 8/5.


And the following inversely related tetrads:  
For pentads, there are thirteen pairs of chords in inverse relationship:  
* 1-5/4-3/2-17/10 with steps 5/4-6/5-17/15-20/17, and its inverse
* 1–6/5–15/11–3/2–17/10 with steps of 6/5, 17/15, 11/10, 17/15, 20/17, and its inverse
* 1-6/5-3/2-30/17 with steps 6/5-5/4-20/17-17/15;  
* 1–11/10–5/4–3/2–30/17 with steps of 11/10, 17/15, 6/5, 20/17, 17/15;
* 1-11/10-3/2-15/8 with steps 11/10-15/11-5/4-16/15, and its inverse
* 1–6/5–24/17–3/2–30/17 with steps of 6/5, 20/17, 17/16, 20/17, 17/15, and its inverse
* 1-15/11-3/2-8/5 with steps 15/11-11/10-16/15-5/4;  
* 1–17/16–5/4–3/2–17/10 with steps of 17/16, 20/17, 6/5, 17/15, 20/17;
* 1-11/10-5/4-3/2 with steps 11/10-17/15-6/5-4/3, and its inverse
* 1–6/5–15/11–3/2–30/17 with steps of 6/5, 17/15, 11/10, 20/17, 17/15, and its inverse
* 1-6/5-15/11-3/2 with steps 6/5-17/15-11/10-4/3;
* 1–11/10–5/4–3/2–17/10 with steps of 11/10, 17/15, 6/5, 17/15, 20/17;
* 1-3/2-17/10-15/8 with steps 3/2-17/15-11/10-16/15, and its inverse
* 1–6/5–15/11–3/2–18/11 with steps of 6/5, 17/15, 11/10, 12/11, 11/9, and its inverse  
* 1-3/2-8/5-30/17 with steps 3/2-16/15-11/10-17/15; 
* 1–11/10–5/4–3/2–11/6 with steps of 11/10, 17/15, 6/5, 11/9, 12/11;
* 1–5/4–3/2–17/10–15/8 with steps of 5/4, 6/5, 17/15, 11/10, 16/15, and its inverse
* 1–6/5–3/2–8/5–30/17 with steps of 6/5, 5/4, 16/15, 11/10, 17/15;
* 1–5/4–17/12–3/2–17/10 with steps of 5/4, 17/15, 18/17, 17/15, 20/17, and its inverse
* 1–18/17–6/5–3/2–30/17 with steps of 18/17, 17/15, 5/4, 20/17, 17/15;
* 1–5/4–15/11–3/2–17/10 with steps of 5/4, 12/11, 11/10, 17/15, 20/17, and its inverse
* 1–11/10–6/5–3/2–30/17 with steps of 11/10, 12/11, 5/4, 20/17, 17/15;
* 1–11/10–11/8–3/2–15/8 with steps of 11/10, 5/4, 12/11, 5/4, 16/15, and its inverse  
* 1–12/11–15/11–3/2–8/5 with steps of 12/11, 5/4, 11/10, 16/15, 5/4;
* 1–15/11–3/2–8/5–17/10 with steps of 15/11, 11/10, 16/15, 17/16, 20/17, and its inverse
* 1–11/10–3/2–30/17–15/8 with steps of 11/10, 15/11, 20/17, 17/16, 16/15;
* 1–15/11–3/2–8/5–30/17 with steps of 15/11, 11/10, 16/15, 11/10, 17/15, and its inverse  
* 1–11/10–3/2–17/10–15/8 with steps of 11/10, 15/11, 17/15, 11/10, 16/15;
* 1–15/11–3/2–17/10–15/8 with steps of 15/11, 11/10, 17/15, 11/10, 16/15, and its inverse
* 1–11/10–3/2–8/5–30/17 with steps of 11/10, 15/11, 16/15, 11/10, 17/15;
* 1–24/17–3/2–8/5–30/17 with steps of 24/17, 17/16, 16/15, 11/10, 17/15, and its inverse  
* 1–17/16–3/2–17/10–15/8 with steps of 17/16, 24/17, 17/15, 11/10, 16/15;
* 1–11/10–5/4–11/8–3/2 with steps of 11/10, 17/15, 11/10, 12/11, 4/3, and its inverse
* 1–12/11–6/5–15/11–3/2 with steps of 12/11, 11/10, 17/15, 11/10, 4/3.


* 1-17/15-5/4-22/15 with steps 17/15-11/10-20/17-15/11, and its inverse
For hexads, there are three palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
* 1-11/10-5/4-17/10 with steps 11/10-17/15-15/11-20/17.  
* 1–17/16–5/4–17/12–3/2–17/10 with steps of 17/16, 20/17, 17/15, 18/17, 17/15, 20/17;
* 1–11/10–5/4–3/2–17/10–15/8 with steps of 11/10, 17/15, 6/5, 17/15, 11/10, 16/15;
* 1–11/10–5/4–11/8–3/2–11/6 with steps of 11/10, 17/15, 11/10, 12/11, 11/9, 12/11.


For pentads, there are
The inversely related pairs of chords are  
* 1-11/10-5/4-3/2-15/8 with steps 11/10-17/15-6/5-5/4-16/15, and its inverse
* 1–6/5–24/17–3/2–8/5–30/17 with steps of 6/5, 20/17, 17/16, 16/15, 11/10, 17/15, and its inverse  
* 1-6/5-15/11-3/2-8/5 with steps 1-6/5-17/15-11/10-16/15-5/4;
* 1–17/16–5/4–3/2–17/10–15/8 with steps of 17/16, 20/17, 6/5, 17/15, 11/10, 16/15;
* 1-11/10-5/4-3/2-17/10 with steps 11/10-17/15-6/5-17/15-20/17, and its inverse
* 1–5/4–15/11–3/2–17/10–15/8 with steps of 5/4, 12/11, 11/10, 17/15, 11/10, 16/15, and its inverse  
* 1-6/5-15/11-3/2-30/17 with steps 6/5-17/15-11/10-20/17-17/15;  
* 1–11/10–6/5–3/2–8/5–30/17 with steps of 11/10, 12/11, 5/4, 16/15, 11/10, 17/15.
* 1-11/10-3/2-17/10-15/8 with steps 11/10-15/11-17/15-11/10-16/15, and its inverse
* 1-15/11-3/2-8/5-30/17 with steps 15/11-11/10-16/15-11/10-17/15;


Finally, there is a palindromic hexad:
Equal temperaments with ursulismic chords include {{Optimal ET sequence| 9, 12, 16, 22, 31, 34, 38, 65, 72, 87, 94, 137 and 159 }}.
* 1-11/10-5/4-3/2-17/10-15/8 with steps 11/10-17/15-6/5-17/15-11/10-16/15.  


[[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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