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Chords of superpyth

Revision as of 06:53, 13 December 2025 by FloraC (talk | contribs) (Replace "1/1" with "1", which I think is easier on the eyes)
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Below are listed the 11-odd-limit dyadic chords of 11-limit superpyth temperament. Typing the chords requires consideration of the fact that superpyth conflates 9/8 with 8/7, and 11/10 with 10/9. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal that employs 8/7 and 10/9.

Chords essentially tempered by 64/63 are labeled archytas, by 100/99 ptolemismic, by 176/175 valinorsmic, by 245/243 sensamagic, by 540/539 swetismic. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked ares. Chords that require any two of 100/99, 245/243 and 540/539 tempering are marked octarod. Chords that require 176/175 and 540/539 tempering are marked guanyin.

Triads

+
# Transversal Type Complexity
1 1-9/8-3/2 ambitonal 2
2 1-3/2-12/7 utonal 3
3 1-8/7-12/7 otonal 3
4 1-9/7-3/2 utonal 4
5 1-8/7-9/7 ambitonal 4
6 1-9/7-12/7 otonal 4
7 1-10/9-12/7 sensamagic 7
8 1-10/9-9/7 sensamagic 7
9 1-3/2-5/3 otonal 8
10 1-9/7-5/3 sensamagic 8
11 1-10/9-5/3 utonal 8
12 1-5/4-3/2 otonal 9
13 1-9/8-5/4 otonal 9
14 1-10/9-5/4 utonal 9
15 1-5/4-5/3 utonal 9
16 1-8/7-10/7
17 1-12/7-10/7
18 1-9/7-10/7
19 1-10/9-10/7
20 1-5/3-10/7
21 1-5/4-10/7
22 1-12/7-11/9
23 1-10/9-11/9
24 1-10/7-11/9
25 1-3/2-11/6
26 1-9/7-11/6
27 1-10/9-11/6
28 1-5/3-11/6
29 1-10/7-11/6
30 1-11/9-11/6
31 1-3/2-11/8 otonal
32 1-9/8-11/8 otonal
33 1-110-11/8 utonal
34 1-5/3-11/8 ptolemismic
35 1-5/4-11/8 otonal
36 1-11/9-11/8 utonal
37 1-11/6-11/8 utonal
38 1-8/7-11/7
39 1-12/7-11/7
40 1-9/7-11/7
41 1-10/9-11/7
42 1-5/4-11/7
43 1-10/7-11/7
44 1-11/9-11/7
45 1-11/6-11/7
46 1-11/8-11/7 }

Tetrads

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# Transversal Type Complexity
1 1-3/2-8/7-12/7
2 1-3/2-8/7-9/7
3 1-3/2-12/7-9/7
4 1-8/7-12/7-9/7
5 1-12/7-9/7-10/9
6 1-3/2-9/7-5/3
7 1-9/7-10/9-5/3
8 1-3/2-8/7-5/4
9 1-3/2-5/3-5/4
10 1-10/9-5/3-5/4
11 1-8/7-12/7-10/7
12 1-8/7-9/7-10/7
13 1-12/7-9/7-10/7
14 1-12/7-10/9-10/7
15 1-9/7-10/9-10/7
16 1-9/7-5/3-10/7
17 1-10/9-5/3-10/7
18 1-8/7-5/4-10/7
19 1-10/9-5/4-10/7
20 1-5/3-5/4-10/7
21 1-12/7-10/9-11/9
22 1-12/7-10/7-11/9
23 1-10/9-10/7-11/9
24 1-3/2-9/7-11/6
25 1-9/7-10/9-11/6
26 1-3/2-5/3-11/6
27 1-9/7-5/3-11/6
28 1-10/9-5/3-11/6
29 1-9/7-10/7-11/6
30 1-10/9-10/7-11/6
31 1-5/3-10/7-11/6
32 1-10/9-11/9-11/6
33 1-10/7-11/9-11/6
34 1-3/2-8/7-11/8
35 1-3/2-5/3-11/8
36 1-10/9-5/3-11/8
37 1-3/2-5/4-11/8
38 1-8/7-5/4-11/8
39 1-10/9-5/4-11/8
40 1-5/3-5/4-11/8
41 1-10/9-11/9-11/8
42 1-3/2-11/6-11/8
43 1-10/9-11/6-11/8
44 1-5/3-11/6-11/8
45 1-11/9-11/6-11/8
46 1-8/7-12/7-11/7
47 1-8/7-9/7-11/7
48 1-12/7-9/7-11/7
49 1-12/7-10/9-11/7
50 1-9/7-10/9-11/7
51 1-8/7-5/4-11/7
52 1-10/9-5/4-11/7
53 1-8/7-10/7-11/7
54 1-12/7-10/7-11/7
55 1-9/7-10/7-11/7
56 1-10/9-10/7-11/7
57 1-5/4-10/7-11/7
58 1-12/7-11/9-11/7
59 1-10/9-11/9-11/7
60 1-10/7-11/9-11/7
61 1-9/7-11/6-11/7
62 1-10/9-11/6-11/7
63 1-10/7-11/6-11/7
64 1-11/9-11/6-11/7
65 1-8/7-11/8-11/7
66 1-10/9-11/8-11/7
67 1-5/4-11/8-11/7
68 1-11/9-11/8-11/7
69 1-11/6-11/8-11/7 }

Pentads

+
# Transversal Type Complexity
1 1-3/2-8/7-12/7-9/7
2 1-8/7-12/7-9/7-10/7
3 1-12/7-9/7-10/9-10/7
4 1-9/7-10/9-5/3-10/7
5 1-10/9-5/3-5/4-10/7
6 1-12/7-10/9-10/7-11/9
7 1-3/2-9/7-5/3-11/6
8 1-9/7-10/9-5/3-11/6
9 1-9/7-10/9-10/7-11/6
10 1-9/7-5/3-10/7-11/6
11 1-10/9-5/3-10/7-11/6
12 1-10/9-10/7-11/9-11/6
13 1-3/2-8/7-5/4-11/8
14 1-3/2-5/3-5/4-11/8
15 1-10/9-5/3-5/4-11/8
16 1-3/2-5/3-11/6-11/8
17 1-10/9-5/3-11/6-11/8
18 1-10/9-11/9-11/6-11/8
19 1-8/7-12/7-9/7-11/7
20 1-12/7-9/7-10/9-11/7
21 1-8/7-12/7-10/7-11/7
22 1-8/7-9/7-10/7-11/7
23 1-12/7-9/7-10/7-11/7
24 1-12/7-10/9-10/7-11/7
25 1-9/7-10/9-10/7-11/7
26 1-8/7-5/4-10/7-11/7
27 1-10/9-5/4-10/7-11/7
28 1-12/7-10/9-11/9-11/7
29 1-12/7-10/7-11/9-11/7
30 1-10/9-10/7-11/9-11/7
31 1-9/7-10/9-11/6-11/7
32 1-9/7-10/7-11/6-11/7
33 1-10/9-10/7-11/6-11/7
34 1-10/9-11/9-11/6-11/7
35 1-10/7-11/9-11/6-11/7
36 1-8/7-5/4-11/8-11/7
37 1-10/9-5/4-11/8-11/7
38 1-10/9-11/9-11/8-11/7
39 1-10/9-11/6-11/8-11/7
40 1-11/9-11/6-11/8-11/7 }

Hexads

+
# Transversal Type Complexity
1 1-9/7-10/9-5/3-10/7-11/6 15
2 1-8/7-9/7-10/7-11/7-12/7 otonal 18
3 1-12/7-9/7-10/9-10/7-11/7 18
4 1-12/7-10/9-10/7-11/9-11/7 18
5 1-9/7-10/9-10/7-11/6-11/7 18
6 1-10/9-10/7-11/9-11/6-11/7 18
7 1-110-11/9-11/8-11/7-11/6 utonal 18 }
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