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 |