Chords of meanpop

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 (undecimal marvel). 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