Chords of hemiwur: Difference between revisions

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[[Category:Lists of chords]]
[[Category:Dyadic chords]]
[[Category:11-limit]]
[[Category:Hemiwur]]

Latest revision as of 11:02, 25 April 2023

Below are listed the dyadic chords of 11-limit hemiwur temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 121/120 are biyatismic, by 176/175 valinorsmic, and by 385/384 keenanismic. Chords requiring any two of the above are labeled zeus.

Hemiwur has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 32, and so would require the 37 note MOS, but there are many chords of much lower complexity, so that the 13-note MOS, for instance, has a couple of hexads, plus many more pentads, tetrads and triads.

Triads

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

Tetrads

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

Pentads

Number Chord Transversal Type
1 0-2-4-7-9 1-5/4-11/7-11/10-11/8 valinorsmic
2 0-2-5-7-9 1-5/4-7/4-11/10-11/8 valinorsmic
3 0-2-4-7-11 1-5/4-11/7-11/10-12/7 zeus
4 0-2-4-9-11 1-5/4-11/7-11/8-12/7 zeus
5 0-2-7-9-11 1-5/4-11/10-11/8-12/7 zeus
6 0-4-7-9-11 1-11/7-11/10-11/8-12/7 zeus
7 0-3-5-7-14 1-7/5-7/4-11/10-6/5 zeus
8 0-5-7-9-14 1-7/4-11/10-11/8-6/5 zeus
9 0-7-9-11-14 1-11/10-11/8-12/7-6/5 zeus
10 0-2-5-7-16 1-5/4-7/4-11/10-3/2 zeus
11 0-2-5-9-16 1-5/4-7/4-11/8-3/2 otonal
12 0-2-7-9-16 1-5/4-11/10-11/8-3/2 zeus
13 0-5-7-9-16 1-7/4-11/10-11/8-3/2 zeus
14 0-2-7-11-16 1-5/4-11/10-12/7-3/2 zeus
15 0-2-9-11-16 1-5/4-11/8-12/7-3/2 zeus
16 0-7-9-11-16 1-11/10-11/8-12/7-3/2 zeus
17 0-5-7-14-16 1-7/4-11/10-6/5-3/2 zeus
18 0-5-9-14-16 1-7/4-11/8-6/5-3/2 zeus
19 0-7-9-14-16 1-11/10-11/8-6/5-3/2 zeus
20 0-7-11-14-16 1-12/11-12/7-6/5-3/2 utonal
21 0-9-11-14-16 1-11/8-12/7-6/5-3/2 zeus
22 0-7-9-14-23 1-11/10-11/8-6/5-18/11 zeus
23 0-7-9-16-23 1-11/10-11/8-3/2-18/11 biyatismic
24 0-7-14-16-23 1-11/10-6/5-3/2-18/11 biyatismic
25 0-9-14-16-23 1-11/8-6/5-3/2-18/11 zeus
26 0-3-7-14-30 1-7/5-11/10-6/5-9/5 otonal
27 0-7-14-16-30 1-11/10-6/5-3/2-9/5 biyatismic
28 0-7-14-23-30 1-11/10-6/5-18/11-9/5 biyatismic
29 0-7-16-23-30 1-11/10-3/2-18/11-9/5 biyatismic
30 0-14-16-23-30 1-6/5-3/2-18/11-9/5 biyatismic
31 0-16-23-27-30 1-3/2-18/11-9/7-9/5 utonal
32 0-2-5-9-32 1-5/4-7/4-11/8-9/8 otonal
33 0-2-5-16-32 1-5/4-7/4-3/2-9/8 otonal
34 0-2-9-16-32 1-5/4-11/8-3/2-9/8 otonal
35 0-5-9-16-32 1-7/4-11/8-3/2-9/8 otonal
36 0-9-16-23-32 1-11/8-3/2-18/11-9/8 biyatismic
37 0-16-23-27-32 1-3/2-18/11-9/7-9/8 utonal
38 0-16-23-30-32 1-3/2-18/11-9/5-9/8 utonal
39 0-16-27-30-32 1-3/2-9/7-9/5-9/8 utonal
40 0-23-27-30-32 1-18/11-9/7-9/5-9/8 utonal

Hexads

Number Chord Transversal Type
1 0-2-4-7-9-11 1-5/4-11/7-11/10-11/8-12/7 zeus
2 0-2-5-7-9-16 1-5/4-7/4-11/10-11/8-3/2 zeus
3 0-2-7-9-11-16 1-5/4-11/10-11/8-12/7-3/2 zeus
4 0-5-7-9-14-16 1-7/4-11/10-11/8-6/5-3/2 zeus
5 0-7-9-11-14-16 1-11/10-11/8-12/7-6/5-3/2 zeus
6 0-7-9-14-16-23 1-11/10-11/8-6/5-3/2-18/11 zeus
7 0-7-14-16-23-30 1-11/10-6/5-3/2-18/11-9/5 biyatismic
8 0-2-5-9-16-32 1-5/4-7/4-11/8-3/2-9/8 otonal
9 0-16-23-27-30-32 1-3/2-18/11-9/7-9/5-9/8 utonal
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