Chords of superpyth: Difference between revisions

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autopatrolled
2,790 edits
expanded tables
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! Transversal
! Transversal
! Type
! Type
!Complexity
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|ambitonal
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|sensamagic
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|sensamagic
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|otonal
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|sensamagic
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|utonal
|utonal
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|utonal
|utonal
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|1/1-5/4-5/3
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|1/1-3/2-11/8
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|otonal
|otonal
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|otonal
|otonal
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|utonal
|utonal
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|ptolemismic
|ptolemismic
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|otonal
|otonal
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|1/1-11/9-11/8
|utonal
|utonal
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Line 205: Line 252:
! Transversal
! Transversal
! Type
! Type
!Complexity
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|1/1-3/2-9/7-5/3
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Line 491: Line 608:
! Transversal
! Transversal
! Type
! Type
!Complexity
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|1
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Revision as of 18:49, 26 November 2025

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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, and chords that require any two of 100/99, 245/243 and 540/539 tempering are marked octarod.

Triads

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

Tetrads

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

Pentads

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

Hexads

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