Catakleismic/11-limit chords: Difference between revisions

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[[Category:Chords]]
[[Category:Lists of chords]]
[[Category:Catakleismic]]
[[Category:Catakleismic]]

Latest revision as of 21:48, 22 June 2025

Below are listed the dyadic chords of 11-limit catakleismic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are labeled swetismic, by 385/384 keenanismic, and by 225/224 marvel. Chords requiring any two of 540/539, 385/384 or 225/224 are labeled unimarvel.

Catakleismic has MOS of size 7, 11, 15, 19, 34, 53 and 72. It is a complex temperament and not much attention has been paid to it, but one notable feature it has is that 11-limit marvel (unimarvel) shrinks the kleisma to a very small interval in an optimal tuning, so very little tuning damage is incurred by catakleismic over that of marvel. Hence, catakleismic can be thought of as one way of organizing the chords of marvel, which are also listed below.

Triads

# Chord Transversal Type
1 0-1-6 1-6/5-3/2 utonal
2 0-5-6 1-5/4-3/2 otonal
3 0-1-7 1-6/5-9/5 otonal
4 0-6-7 1-3/2-9/5 utonal
5 0-5-10 1-5/4-14/9 marvel
6 0-5-12 1-5/4-9/8 otonal
7 0-6-12 1-3/2-9/8 ambitonal
8 0-7-12 1-9/5-9/8 utonal
9 0-6-16 1-3/2-7/6 otonal
10 0-10-16 1-14/9-7/6 utonal
11 0-1-17 1-6/5-7/5 otonal
12 0-5-17 1-5/4-7/5 marvel
13 0-7-17 1-9/5-7/5 otonal
14 0-10-17 1-14/9-7/5 utonal
15 0-12-17 1-9/8-7/5 marvel
16 0-16-17 1-7/6-7/5 utonal
17 0-5-21 1-5/4-16/11 keenanismic
18 0-16-21 1-7/6-16/11 keenanismic
19 0-1-22 1-6/5-7/4 keenanismic
20 0-5-22 1-5/4-7/4 otonal
21 0-6-22 1-3/2-7/4 otonal
22 0-10-22 1-14/9-7/4 utonal
23 0-12-22 1-9/8-7/4 otonal
24 0-16-22 1-7/6-7/4 utonal
25 0-17-22 1-7/5-7/4 utonal
26 0-21-22 1-16/11-7/4 keenanismic
27 0-5-26 1-5/4-20/11 utonal
28 0-10-26 1-14/9-20/11 swetismic
29 0-16-26 1-7/6-20/11 swetismic
30 0-21-26 1-16/11-20/11 otonal
31 0-1-27 1-6/5-12/11 utonal
32 0-5-27 1-5/4-12/11 keenanismic
33 0-6-27 1-3/2-12/11 utonal
34 0-10-27 1-14/9-12/11 swetismic
35 0-17-27 1-7/5-12/11 swetismic
36 0-21-27 1-16/11-12/11 otonal
37 0-22-27 1-7/4-12/11 keenanismic
38 0-26-27 1-20/11-12/11 otonal
39 0-6-33 1-3/2-18/11 utonal
40 0-7-33 1-9/5-18/11 utonal
41 0-12-33 1-9/8-18/11 utonal
42 0-16-33 1-7/6-18/11 swetismic
43 0-17-33 1-7/5-18/11 swetismic
44 0-21-33 1-16/11-18/11 otonal
45 0-26-33 1-20/11-18/11 otonal
46 0-27-33 1-12/11-18/11 otonal
47 0-10-43 1-14/9-14/11 utonal
48 0-16-43 1-7/6-14/11 utonal
49 0-17-43 1-7/5-14/11 utonal
50 0-21-43 1-16/11-14/11 otonal
51 0-22-43 1-7/4-14/11 utonal
52 0-26-43 1-20/11-14/11 otonal
53 0-27-43 1-12/11-14/11 otonal
54 0-33-43 1-18/11-14/11 otonal

Tetrads

# Chord Transversal Type
1 0-1-6-7 1-6/5-3/2-9/5 ambitonal
2 0-5-6-12 1-5/4-3/2-9/8 otonal
3 0-6-7-12 1-3/2-9/5-9/8 utonal
4 0-1-7-17 1-6/5-9/5-7/5 otonal
5 0-5-10-17 1-5/4-14/9-7/5 marvel
6 0-5-12-17 1-5/4-9/8-7/5 marvel
7 0-7-12-17 1-9/5-9/8-7/5 marvel
8 0-10-16-17 1-14/9-7/6-7/5 utonal
9 0-1-6-22 1-6/5-3/2-7/4 keenanismic
10 0-5-6-22 1-5/4-3/2-7/4 otonal
11 0-5-10-22 1-5/4-14/9-7/4 marvel
12 0-5-12-22 1-5/4-9/8-7/4 otonal
13 0-6-12-22 1-3/2-9/8-7/4 otonal
14 0-6-16-22 1-3/2-7/6-7/4 ambitonal
15 0-10-16-22 1-14/9-7/6-7/4 utonal
16 0-1-17-22 1-6/5-7/5-7/4 keenanismic
17 0-5-17-22 1-5/4-7/5-7/4 marvel
18 0-10-17-22 1-14/9-7/5-7/4 utonal
19 0-12-17-22 1-9/8-7/5-7/4 marvel
20 0-16-17-22 1-7/6-7/5-7/4 utonal
21 0-5-21-22 1-5/4-16/11-7/4 keenanismic
22 0-16-21-22 1-7/6-16/11-7/4 keenanismic
23 0-5-10-26 1-5/4-14/9-20/11 unimarv
24 0-10-16-26 1-14/9-7/6-20/11 swetismic
25 0-5-21-26 1-5/4-16/11-20/11 keenanismic
26 0-16-21-26 1-7/6-16/11-20/11 unimarv
27 0-1-6-27 1-6/5-3/2-12/11 utonal
28 0-5-6-27 1-5/4-3/2-12/11 keenanismic
29 0-5-10-27 1-5/4-14/9-12/11 unimarv
30 0-1-17-27 1-6/5-7/5-12/11 swetismic
31 0-5-17-27 1-5/4-7/5-12/11 unimarv
32 0-10-17-27 1-14/9-7/5-12/11 swetismic
33 0-5-21-27 1-5/4-16/11-12/11 keenanismic
34 0-1-22-27 1-6/5-7/4-12/11 keenanismic
35 0-5-22-27 1-5/4-7/4-12/11 keenanismic
36 0-6-22-27 1-3/2-7/4-12/11 keenanismic
37 0-10-22-27 1-14/9-7/4-12/11 unimarv
38 0-17-22-27 1-7/5-7/4-12/11 unimarv
39 0-21-22-27 1-16/11-7/4-12/11 keenanismic
40 0-5-26-27 1-5/4-20/11-12/11 keenanismic
41 0-10-26-27 1-14/9-20/11-12/11 swetismic
42 0-21-26-27 1-16/11-20/11-12/11 otonal
43 0-6-7-33 1-3/2-9/5-18/11 utonal
44 0-6-12-33 1-3/2-9/8-18/11 utonal
45 0-7-12-33 1-9/5-9/8-18/11 utonal
46 0-6-16-33 1-3/2-7/6-18/11 swetismic
47 0-7-17-33 1-9/5-7/5-18/11 swetismic
48 0-12-17-33 1-9/8-7/5-18/11 unimarv
49 0-16-17-33 1-7/6-7/5-18/11 swetismic
50 0-16-21-33 1-7/6-16/11-18/11 unimarv
51 0-16-26-33 1-7/6-20/11-18/11 swetismic
52 0-21-26-33 1-16/11-20/11-18/11 otonal
53 0-6-27-33 1-3/2-12/11-18/11 ambitonal
54 0-17-27-33 1-7/5-12/11-18/11 swetismic
55 0-21-27-33 1-16/11-12/11-18/11 otonal
56 0-26-27-33 1-20/11-12/11-18/11 otonal
57 0-10-16-43 1-14/9-7/6-14/11 utonal
58 0-10-17-43 1-14/9-7/5-14/11 utonal
59 0-16-17-43 1-7/6-7/5-14/11 utonal
60 0-16-21-43 1-7/6-16/11-14/11 keenanismic
61 0-10-22-43 1-14/9-7/4-14/11 utonal
62 0-16-22-43 1-7/6-7/4-14/11 utonal
63 0-17-22-43 1-7/5-7/4-14/11 utonal
64 0-21-22-43 1-16/11-7/4-14/11 keenanismic
65 0-10-26-43 1-14/9-20/11-14/11 swetismic
66 0-16-26-43 1-7/6-20/11-14/11 swetismic
67 0-21-26-43 1-16/11-20/11-14/11 otonal
68 0-10-27-43 1-14/9-12/11-14/11 swetismic
69 0-17-27-43 1-7/5-12/11-14/11 swetismic
70 0-21-27-43 1-16/11-12/11-14/11 otonal
71 0-22-27-43 1-7/4-12/11-14/11 keenanismic
72 0-26-27-43 1-20/11-12/11-14/11 otonal
73 0-16-33-43 1-7/6-18/11-14/11 swetismic
74 0-17-33-43 1-7/5-18/11-14/11 swetismic
75 0-21-33-43 1-16/11-18/11-14/11 otonal
76 0-26-33-43 1-20/11-18/11-14/11 otonal
77 0-27-33-43 1-12/11-18/11-14/11 otonal

Pentads

# Chord Transversal Type
1 0-5-6-12-22 1-5/4-3/2-9/8-7/4 otonal
2 0-5-10-17-22 1-5/4-14/9-7/5-7/4 marvel
3 0-5-12-17-22 1-5/4-9/8-7/5-7/4 marvel
4 0-10-16-17-22 1-14/9-7/6-7/5-7/4 utonal
5 0-5-10-17-27 1-5/4-14/9-7/5-12/11 unimarv
6 0-1-6-22-27 1-6/5-3/2-7/4-12/11 keenanismic
7 0-5-6-22-27 1-5/4-3/2-7/4-12/11 keenanismic
8 0-5-10-22-27 1-5/4-14/9-7/4-12/11 unimarv
9 0-1-17-22-27 1-6/5-7/5-7/4-12/11 unimarv
10 0-5-17-22-27 1-5/4-7/5-7/4-12/11 unimarv
11 0-10-17-22-27 1-14/9-7/5-7/4-12/11 unimarv
12 0-5-21-22-27 1-5/4-16/11-7/4-12/11 keenanismic
13 0-5-10-26-27 1-5/4-14/9-20/11-12/11 unimarv
14 0-5-21-26-27 1-5/4-16/11-20/11-12/11 keenanismic
15 0-6-7-12-33 1-3/2-9/5-9/8-18/11 utonal
16 0-7-12-17-33 1-9/5-9/8-7/5-18/11 unimarv
17 0-16-21-26-33 1-7/6-16/11-20/11-18/11 unimarv
18 0-21-26-27-33 1-16/11-20/11-12/11-18/11 otonal
19 0-10-16-17-43 1-14/9-7/6-7/5-14/11 utonal
20 0-10-16-22-43 1-14/9-7/6-7/4-14/11 utonal
21 0-10-17-22-43 1-14/9-7/5-7/4-14/11 utonal
22 0-16-17-22-43 1-7/6-7/5-7/4-14/11 utonal
23 0-16-21-22-43 1-7/6-16/11-7/4-14/11 keenanismic
24 0-10-16-26-43 1-14/9-7/6-20/11-14/11 swetismic
25 0-16-21-26-43 1-7/6-16/11-20/11-14/11 unimarv
26 0-10-17-27-43 1-14/9-7/5-12/11-14/11 swetismic
27 0-10-22-27-43 1-14/9-7/4-12/11-14/11 unimarv
28 0-17-22-27-43 1-7/5-7/4-12/11-14/11 unimarv
29 0-21-22-27-43 1-16/11-7/4-12/11-14/11 keenanismic
30 0-10-26-27-43 1-14/9-20/11-12/11-14/11 swetismic
31 0-21-26-27-43 1-16/11-20/11-12/11-14/11 otonal
32 0-16-17-33-43 1-7/6-7/5-18/11-14/11 swetismic
33 0-16-21-33-43 1-7/6-16/11-18/11-14/11 unimarv
34 0-16-26-33-43 1-7/6-20/11-18/11-14/11 swetismic
35 0-21-26-33-43 1-16/11-20/11-18/11-14/11 otonal
36 0-17-27-33-43 1-7/5-12/11-18/11-14/11 swetismic
37 0-21-27-33-43 1-16/11-12/11-18/11-14/11 otonal
38 0-26-27-33-43 1-20/11-12/11-18/11-14/11 otonal

Hexads

# Chord Transversal Type
1 0-5-10-17-22-27 1-5/4-14/9-7/5-7/4-12/11 unimarv
2 0-10-16-17-22-43 1-14/9-7/6-7/5-7/4-14/11 utonal
3 0-10-17-22-27-43 1-14/9-7/5-7/4-12/11-14/11 unimarv
4 0-16-21-26-33-43 1-7/6-16/11-20/11-18/11-14/11 unimarv
5 0-21-26-27-33-43 1-16/11-20/11-12/11-18/11-14/11 otonal
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