Chords of meanpop

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Below are listed the dyadic chords of 11-limit meanpop temperament. Meanpop is one of the two extensions of septimal meantone, which itself is the main extension of 5-limit meantone; this is the temperament tempering out 81/80, 126/125 and 385/384. Typing the chords requires consideration of the fact that meanpop conflates 9/8 and 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 which employs 9/8 and 16/9.

Chords requiring tempering only by 81/80 are labeled didymic, by 126/125 starling, by 225/224 marvel, by 385/384 keenanismic and by 540/539 swetismic. Chords which require any two of 81/80, 126/125 or 225/224 are labeled erato, and any two of 225/224, 385/384 or 540/539 unimarv. A chord requiring both of 81/80 and 540/539 is labeled terpsichore, and a chord requiring any three independent commas from those discussed above is labeled meanpop.

Meanpop has MOS of size 5, 7, 12, 19, 31, 50 and 81. While 5-limit meantone has been thoroughly explored, the same is not true of meanpop. The 19 note MOS would seem to be a good place to start such explorations.

Triads

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

Tetrads

Number Chord Transversal Type
1 0-1-2-3 1-3/2-9/8-5/3 didymic
2 0-1-2-4 1-3/2-9/8-5/4 otonal
3 0-1-3-4 1-3/2-5/3-5/4 ambitonal
4 0-2-3-4 1-10/9-5/3-5/4 utonal
5 0-2-3-6 1-9/8-5/3-7/5 erato
6 0-2-4-6 1-9/8-5/4-7/5 erato
7 0-3-4-6 1-5/3-5/4-7/5 erato
8 0-2-4-8 1-9/8-5/4-14/9 erato
9 0-2-6-8 1-9/8-7/5-14/9 erato
10 0-4-6-8 1-5/4-7/5-14/9 erato
11 0-1-3-9 1-3/2-5/3-7/6 otonal
12 0-3-6-9 1-5/3-7/5-7/6 starling
13 0-6-8-9 1-7/5-14/9-7/6 utonal
14 0-1-2-10 1-3/2-9/8-7/4 otonal
15 0-1-4-10 1-3/2-5/4-7/4 otonal
16 0-2-4-10 1-9/8-5/4-7/4 otonal
17 0-2-6-10 1-9/8-7/5-7/4 marvel
18 0-4-6-10 1-5/4-7/5-7/4 marvel
19 0-2-8-10 1-9/8-14/9-7/4 didymic
20 0-4-8-10 1-5/4-14/9-7/4 marvel
21 0-6-8-10 1-7/5-14/9-7/4 utonal
22 0-1-9-10 1-3/2-7/6-7/4 ambitonal
23 0-6-9-10 1-7/5-7/6-7/4 utonal
24 0-8-9-10 1-14/9-7/6-7/4 utonal
25 0-3-4-13 1-5/3-5/4-16/11 keenanismic
26 0-3-9-13 1-5/3-7/6-16/11 keenanismic
27 0-4-10-13 1-5/4-7/4-16/11 keenanismic
28 0-9-10-13 1-7/6-7/4-16/11 keenanismic
29 0-1-4-14 1-3/2-5/4-12/11 keenanismic
30 0-4-6-14 1-5/4-7/5-12/11 unimarv
31 0-4-8-14 1-5/4-14/9-12/11 unimarv
32 0-6-8-14 1-7/5-14/9-12/11 terpsichore
33 0-1-10-14 1-3/2-7/4-12/11 keenanismic
34 0-4-10-14 1-5/4-7/4-12/11 keenanismic
35 0-6-10-14 1-7/5-7/4-12/11 unimarv
36 0-8-10-14 1-14/9-7/4-12/11 unimarv
37 0-4-13-14 1-5/4-16/11-12/11 keenanismic
38 0-10-13-14 1-7/4-16/11-12/11 keenanismic
39 0-1-2-15 1-3/2-9/8-18/11 utonal
40 0-2-6-15 1-9/8-7/5-18/11 unimarv
41 0-1-9-15 1-3/2-7/6-18/11 swetismic
42 0-6-9-15 1-7/5-7/6-18/11 swetismic
43 0-9-13-15 1-7/6-16/11-18/11 unimarv
44 0-1-14-15 1-3/2-12/11-18/11 ambitonal
45 0-6-14-15 1-7/5-12/11-18/11 swetismic
46 0-13-14-15 1-16/11-12/11-18/11 otonal
47 0-2-3-17 1-10/9-5/3-20/11 utonal
48 0-2-4-17 1-10/9-5/4-20/11 utonal
49 0-3-4-17 1-5/3-5/4-20/11 utonal
50 0-2-8-17 1-9/8-14/9-20/11 terpsichore
51 0-4-8-17 1-5/4-14/9-20/11 unimarv
52 0-3-9-17 1-5/3-7/6-20/11 swetismic
53 0-8-9-17 1-14/9-7/6-20/11 swetismic
54 0-3-13-17 1-5/3-16/11-20/11 keenanismic
55 0-4-13-17 1-5/4-16/11-20/11 keenanismic
56 0-9-13-17 1-7/6-16/11-20/11 unimarv
57 0-4-14-17 1-5/4-12/11-20/11 keenanismic
58 0-8-14-17 1-14/9-12/11-20/11 swetismic
59 0-13-14-17 1-16/11-12/11-20/11 otonal
60 0-2-15-17 1-9/8-18/11-20/11 didymic
61 0-9-15-17 1-7/6-18/11-20/11 terpsichore
62 0-13-15-17 1-16/11-18/11-20/11 otonal
63 0-14-15-17 1-12/11-18/11-20/11 otonal
64 0-6-8-23 1-7/5-14/9-14/11 utonal
65 0-6-9-23 1-7/5-7/6-14/11 utonal
66 0-8-9-23 1-14/9-7/6-14/11 utonal
67 0-6-10-23 1-7/5-7/4-14/11 utonal
68 0-8-10-23 1-14/9-7/4-14/11 utonal
69 0-9-10-23 1-7/6-7/4-14/11 utonal
70 0-9-13-23 1-7/6-16/11-14/11 keenanismic
71 0-10-13-23 1-7/4-16/11-14/11 keenanismic
72 0-6-14-23 1-7/5-12/11-14/11 swetismic
73 0-8-14-23 1-14/9-12/11-14/11 swetismic
74 0-10-14-23 1-7/4-12/11-14/11 keenanismic
75 0-13-14-23 1-16/11-12/11-14/11 otonal
76 0-6-15-23 1-7/5-18/11-14/11 swetismic
77 0-9-15-23 1-7/6-18/11-14/11 swetismic
78 0-13-15-23 1-16/11-18/11-14/11 otonal
79 0-14-15-23 1-12/11-18/11-14/11 otonal
80 0-8-17-23 1-14/9-20/11-14/11 swetismic
81 0-9-17-23 1-7/6-20/11-14/11 swetismic
82 0-13-17-23 1-16/11-20/11-14/11 otonal
83 0-14-17-23 1-12/11-20/11-14/11 otonal
84 0-15-17-23 1-18/11-20/11-14/11 otonal

Pentads

Number Chord Transversal Type
1 0-1-2-3-4 1-3/2-9/8-5/3-5/4 didymic
2 0-2-3-4-6 1-9/8-5/3-5/4-7/5 erato
3 0-2-4-6-8 1-9/8-5/4-7/5-14/9 erato
4 0-1-2-4-10 1-3/2-9/8-5/4-7/4 otonal
5 0-2-4-6-10 1-9/8-5/4-7/5-7/4 erato
6 0-2-4-8-10 1-9/8-5/4-14/9-7/4 erato
7 0-2-6-8-10 1-9/8-7/5-14/9-7/4 erato
8 0-4-6-8-10 1-5/4-7/5-14/9-7/4 erato
9 0-6-8-9-10 1-7/5-14/9-7/6-7/4 utonal
10 0-4-6-8-14 1-5/4-7/5-14/9-12/11 meanpop
11 0-1-4-10-14 1-3/2-5/4-7/4-12/11 keenanismic
12 0-4-6-10-14 1-5/4-7/5-7/4-12/11 unimarv
13 0-4-8-10-14 1-5/4-14/9-7/4-12/11 unimarv
14 0-6-8-10-14 1-7/5-14/9-7/4-12/11 meanpop
15 0-4-10-13-14 1-5/4-7/4-16/11-12/11 keenanismic
16 0-2-3-4-17 1-10/9-5/3-5/4-20/11 utonal
17 0-2-4-8-17 1-9/8-5/4-14/9-20/11 meanpop
18 0-3-4-13-17 1-5/3-5/4-16/11-20/11 keenanismic
19 0-3-9-13-17 1-5/3-7/6-16/11-20/11 unimarv
20 0-4-8-14-17 1-5/4-14/9-12/11-20/11 unimarv
21 0-4-13-14-17 1-5/4-16/11-12/11-20/11 keenanismic
22 0-9-13-15-17 1-7/6-16/11-18/11-20/11 meanpop
23 0-13-14-15-17 1-16/11-12/11-18/11-20/11 otonal
24 0-6-8-9-23 1-7/5-14/9-7/6-14/11 utonal
25 0-6-8-10-23 1-7/5-14/9-7/4-14/11 utonal
26 0-6-9-10-23 1-7/5-7/6-7/4-14/11 utonal
27 0-8-9-10-23 1-14/9-7/6-7/4-14/11 utonal
28 0-9-10-13-23 1-7/6-7/4-16/11-14/11 keenanismic
29 0-6-8-14-23 1-7/5-14/9-12/11-14/11 terpsichore
30 0-6-10-14-23 1-7/5-7/4-12/11-14/11 unimarv
31 0-8-10-14-23 1-14/9-7/4-12/11-14/11 unimarv
32 0-10-13-14-23 1-7/4-16/11-12/11-14/11 keenanismic
33 0-6-9-15-23 1-7/5-7/6-18/11-14/11 swetismic
34 0-9-13-15-23 1-7/6-16/11-18/11-14/11 unimarv
35 0-6-14-15-23 1-7/5-12/11-18/11-14/11 swetismic
36 0-13-14-15-23 1-16/11-12/11-18/11-14/11 otonal
37 0-8-9-17-23 1-14/9-7/6-20/11-14/11 swetismic
38 0-9-13-17-23 1-7/6-16/11-20/11-14/11 unimarv
39 0-8-14-17-23 1-14/9-12/11-20/11-14/11 swetismic
40 0-13-14-17-23 1-16/11-12/11-20/11-14/11 otonal
41 0-9-15-17-23 1-7/6-18/11-20/11-14/11 terpsichore
42 0-13-15-17-23 1-16/11-18/11-20/11-14/11 otonal
43 0-14-15-17-23 1-12/11-18/11-20/11-14/11 otonal

Hexads

Number Chord Transversal Type
1 0-2-4-6-8-10 1-9/8-5/4-7/5-14/9-7/4 erato
2 0-4-6-8-10-14 1-5/4-7/5-14/9-7/4-12/11 meanpop
3 0-6-8-9-10-23 1-7/5-14/9-7/6-7/4-14/11 utonal
4 0-6-8-10-14-23 1-7/5-14/9-7/4-12/11-14/11 meanpop
5 0-9-13-15-17-23 1-7/6-16/11-18/11-20/11-14/11 meanpop
6 0-13-14-15-17-23 1-16/11-12/11-18/11-20/11-14/11 otonal