Chords of hemiwürschmidt

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Below are listed the dyadic chords of 11-limit hemiwürschmidt temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are swetismic, by 441/440 werckismic, and by 243/242 rastmic. Chords requiring any two of the above are labeled jove.

Hemiwürschmidt has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 40, and so would require the 68 note MOS. However, it will be observed that much smaller MOS still have quite a few chords.

Triads

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

Tetrads

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

Pentads

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

Hexads

Number Chord Transversal Type
1 0-3-8-11-35-38 1-7/5-11/9-12/7-11/7-11/10 jove
2 0-3-11-27-35-38 1-7/5-12/7-9/7-11/7-11/10 jove
3 0-3-27-30-35-38 1-7/5-9/7-9/5-11/7-11/10 jove
4 0-2-5-16-32-40 1-5/4-7/4-3/2-9/8-11/8 otonal
5 0-5-8-16-32-40 1-7/4-11/9-3/2-9/8-11/8 jove
6 0-8-16-24-32-40 1-11/9-3/2-11/6-9/8-11/8 rastmic
7 0-5-8-32-35-40 1-7/4-11/9-9/8-11/7-11/8 jove
8 0-8-24-32-35-40 1-11/9-11/6-9/8-11/7-11/8 jove
9 0-8-24-35-38-40 1-11/9-11/6-11/7-11/10-11/8 utonal