Below are listed the dyadic chords of 11-limit octacot temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.
Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the 88 cents temperament is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.
Triads
Number
|
Chord
|
Transversal
|
Type
|
Hash
|
1
|
0-2-4
|
1-10/9-11/9
|
otonal
|
2
|
0-2-5
|
1-10/9-9/7
|
sensamagic
|
3
|
0-3-5
|
1-7/6-9/7
|
sensamagic
|
4
|
0-2-7
|
1-10/9-10/7
|
utonal
|
5
|
0-3-7
|
1-7/6-10/7
|
swetismic
|
6
|
0-4-7
|
1-11/9-10/7
|
swetismic
|
7
|
0-5-7
|
1-9/7-10/7
|
otonal
|
8
|
0-3-8
|
1-7/6-3/2
|
otonal
|
9
|
0-4-8
|
1-11/9-3/2
|
rastmic
|
10
|
0-5-8
|
1-9/7-3/2
|
utonal
|
11
|
0-2-9
|
1-11/10-11/7
|
utonal
|
12
|
0-4-9
|
1-11/9-11/7
|
utonal
|
13
|
0-5-9
|
1-9/7-11/7
|
otonal
|
14
|
0-7-9
|
1-10/7-11/7
|
otonal
|
15
|
0-2-10
|
1-10/9-5/3
|
utonal
|
16
|
0-3-10
|
1-7/6-5/3
|
otonal
|
17
|
0-5-10
|
1-9/7-5/3
|
sensamagic
|
18
|
0-7-10
|
1-10/7-5/3
|
utonal
|
19
|
0-8-10
|
1-3/2-5/3
|
otonal
|
20
|
0-2-11
|
1-10/9-7/4
|
werkismic
|
21
|
0-3-11
|
1-7/6-7/4
|
utonal
|
22
|
0-4-11
|
1-11/9-7/4
|
werkismic
|
23
|
0-7-11
|
1-10/7-7/4
|
werkismic
|
24
|
0-8-11
|
1-3/2-7/4
|
otonal
|
25
|
0-9-11
|
1-11/7-7/4
|
werkismic
|
26
|
0-2-12
|
1-11/10-11/6
|
utonal
|
27
|
0-3-12
|
1-7/6-11/6
|
otonal
|
28
|
0-4-12
|
1-11/9-11/6
|
utonal
|
29
|
0-5-12
|
1-9/7-11/6
|
swetismic
|
30
|
0-7-12
|
1-10/7-11/6
|
swetismic
|
31
|
0-8-12
|
1-3/2-11/6
|
otonal
|
32
|
0-9-12
|
1-11/7-11/6
|
utonal
|
33
|
0-10-12
|
1-5/3-11/6
|
otonal
|
34
|
0-4-16
|
1-11/9-9/8
|
rastmic
|
35
|
0-5-16
|
1-9/7-9/8
|
utonal
|
36
|
0-7-16
|
1-10/7-9/8
|
werkismic
|
37
|
0-8-16
|
1-3/2-9/8
|
ambitonal
|
38
|
0-9-16
|
1-11/7-9/8
|
werkismic
|
39
|
0-11-16
|
1-7/4-9/8
|
otonal
|
40
|
0-12-16
|
1-11/6-9/8
|
rastmic
|
41
|
0-2-18
|
1-10/9-5/4
|
utonal
|
42
|
0-7-18
|
1-10/7-5/4
|
utonal
|
43
|
0-8-18
|
1-3/2-5/4
|
otonal
|
44
|
0-9-18
|
1-11/7-5/4
|
cassacot
|
45
|
0-10-18
|
1-5/3-5/4
|
utonal
|
46
|
0-11-18
|
1-7/4-5/4
|
otonal
|
47
|
0-16-18
|
1-9/8-5/4
|
otonal
|
48
|
0-2-20
|
1-11/10-11/8
|
utonal
|
49
|
0-4-20
|
1-11/9-11/8
|
utonal
|
50
|
0-8-20
|
1-3/2-11/8
|
otonal
|
51
|
0-9-20
|
1-11/7-11/8
|
utonal
|
52
|
0-10-20
|
1-5/3-11/8
|
ptolemismic
|
53
|
0-11-20
|
1-7/4-11/8
|
otonal
|
54
|
0-12-20
|
1-11/6-11/8
|
utonal
|
55
|
0-16-20
|
1-9/8-11/8
|
otonal
|
56
|
0-18-20
|
1-5/4-11/8
|
otonal
|
Tetrads
Number
|
Chord
|
Transversal
|
Type
|
Hash
|
1
|
0-2-4-7
|
1-10/9-11/9-10/7
|
octarod
|
2
|
0-2-5-7
|
1-10/9-9/7-10/7
|
sensamagic
|
3
|
0-3-5-7
|
1-7/6-9/7-10/7
|
octarod
|
4
|
0-3-5-8
|
1-7/6-9/7-3/2
|
sensamagic
|
5
|
0-2-4-9
|
1-11/10-11/9-11/7
|
utonal
|
6
|
0-2-5-9
|
1-10/9-9/7-11/7
|
octarod
|
7
|
0-2-7-9
|
1-10/9-10/7-11/7
|
ptolemismic
|
8
|
0-4-7-9
|
1-11/9-10/7-11/7
|
octarod
|
9
|
0-5-7-9
|
1-9/7-10/7-11/7
|
otonal
|
10
|
0-2-5-10
|
1-10/9-9/7-5/3
|
sensamagic
|
11
|
0-3-5-10
|
1-7/6-9/7-5/3
|
sensamagic
|
12
|
0-2-7-10
|
1-10/9-10/7-5/3
|
utonal
|
13
|
0-3-7-10
|
1-7/6-10/7-5/3
|
swetismic
|
14
|
0-5-7-10
|
1-9/7-10/7-5/3
|
sensamagic
|
15
|
0-3-8-10
|
1-7/6-3/2-5/3
|
otonal
|
16
|
0-5-8-10
|
1-9/7-3/2-5/3
|
sensamagic
|
17
|
0-2-4-11
|
1-10/9-11/9-7/4
|
octagari
|
18
|
0-2-7-11
|
1-10/9-10/7-7/4
|
werkismic
|
19
|
0-3-7-11
|
1-7/6-10/7-7/4
|
jove
|
20
|
0-4-7-11
|
1-11/9-10/7-7/4
|
jove
|
21
|
0-3-8-11
|
1-7/6-3/2-7/4
|
ambitonal
|
22
|
0-4-8-11
|
1-11/9-3/2-7/4
|
jove
|
23
|
0-2-9-11
|
1-10/9-11/7-7/4
|
octagari
|
24
|
0-4-9-11
|
1-11/9-11/7-7/4
|
werkismic
|
25
|
0-7-9-11
|
1-10/7-11/7-7/4
|
octagari
|
26
|
0-2-4-12
|
1-11/10-11/9-11/6
|
utonal
|
27
|
0-2-5-12
|
1-10/9-9/7-11/6
|
octarod
|
28
|
0-3-5-12
|
1-7/6-9/7-11/6
|
octarod
|
29
|
0-2-7-12
|
1-10/9-10/7-11/6
|
octarod
|
30
|
0-3-7-12
|
1-7/6-10/7-11/6
|
swetismic
|
31
|
0-4-7-12
|
1-11/9-10/7-11/6
|
swetismic
|
32
|
0-5-7-12
|
1-9/7-10/7-11/6
|
swetismic
|
33
|
0-3-8-12
|
1-7/6-3/2-11/6
|
otonal
|
34
|
0-4-8-12
|
1-11/9-3/2-11/6
|
rastmic
|
35
|
0-5-8-12
|
1-9/7-3/2-11/6
|
swetismic
|
36
|
0-2-9-12
|
1-11/10-11/7-11/6
|
utonal
|
37
|
0-4-9-12
|
1-11/9-11/7-11/6
|
utonal
|
38
|
0-5-9-12
|
1-9/7-11/7-11/6
|
swetismic
|
39
|
0-7-9-12
|
1-10/7-11/7-11/6
|
octarod
|
40
|
0-2-10-12
|
1-10/9-5/3-11/6
|
ptolemismic
|
41
|
0-3-10-12
|
1-7/6-5/3-11/6
|
otonal
|
42
|
0-5-10-12
|
1-9/7-5/3-11/6
|
octarod
|
43
|
0-7-10-12
|
1-10/7-5/3-11/6
|
octarod
|
44
|
0-8-10-12
|
1-3/2-5/3-11/6
|
otonal
|
45
|
0-4-7-16
|
1-11/9-10/7-9/8
|
jove
|
46
|
0-5-7-16
|
1-9/7-10/7-9/8
|
werkismic
|
47
|
0-4-8-16
|
1-11/9-3/2-9/8
|
rastmic
|
48
|
0-5-8-16
|
1-9/7-3/2-9/8
|
utonal
|
49
|
0-4-9-16
|
1-11/9-11/7-9/8
|
jove
|
50
|
0-5-9-16
|
1-9/7-11/7-9/8
|
werkismic
|
51
|
0-7-9-16
|
1-10/7-11/7-9/8
|
octagari
|
52
|
0-4-11-16
|
1-11/9-7/4-9/8
|
jove
|
53
|
0-7-11-16
|
1-10/7-7/4-9/8
|
werkismic
|
54
|
0-8-11-16
|
1-3/2-7/4-9/8
|
otonal
|
55
|
0-9-11-16
|
1-11/7-7/4-9/8
|
werkismic
|
56
|
0-4-12-16
|
1-11/9-11/6-9/8
|
rastmic
|
57
|
0-5-12-16
|
1-9/7-11/6-9/8
|
jove
|
58
|
0-7-12-16
|
1-10/7-11/6-9/8
|
jove
|
59
|
0-8-12-16
|
1-3/2-11/6-9/8
|
rastmic
|
60
|
0-9-12-16
|
1-11/7-11/6-9/8
|
jove
|
61
|
0-2-7-18
|
1-10/9-10/7-5/4
|
utonal
|
62
|
0-2-9-18
|
1-10/9-11/7-5/4
|
octagari
|
63
|
0-7-9-18
|
1-10/7-11/7-5/4
|
octagari
|
64
|
0-2-10-18
|
1-10/9-5/3-5/4
|
utonal
|
65
|
0-7-10-18
|
1-10/7-5/3-5/4
|
utonal
|
66
|
0-8-10-18
|
1-3/2-5/3-5/4
|
ambitonal
|
67
|
0-2-11-18
|
1-10/9-7/4-5/4
|
werkismic
|
68
|
0-7-11-18
|
1-10/7-7/4-5/4
|
werkismic
|
69
|
0-8-11-18
|
1-3/2-7/4-5/4
|
otonal
|
70
|
0-9-11-18
|
1-11/7-7/4-5/4
|
octagari
|
71
|
0-7-16-18
|
1-10/7-9/8-5/4
|
werkismic
|
72
|
0-8-16-18
|
1-3/2-9/8-5/4
|
otonal
|
73
|
0-9-16-18
|
1-11/7-9/8-5/4
|
octagari
|
74
|
0-11-16-18
|
1-7/4-9/8-5/4
|
otonal
|
75
|
0-2-4-20
|
1-11/10-11/9-11/8
|
utonal
|
76
|
0-4-8-20
|
1-11/9-3/2-11/8
|
rastmic
|
77
|
0-2-9-20
|
1-11/10-11/7-11/8
|
utonal
|
78
|
0-4-9-20
|
1-11/9-11/7-11/8
|
utonal
|
79
|
0-2-10-20
|
1-10/9-5/3-11/8
|
ptolemismic
|
80
|
0-8-10-20
|
1-3/2-5/3-11/8
|
ptolemismic
|
81
|
0-2-11-20
|
1-10/9-7/4-11/8
|
octagari
|
82
|
0-4-11-20
|
1-11/9-7/4-11/8
|
werkismic
|
83
|
0-8-11-20
|
1-3/2-7/4-11/8
|
otonal
|
84
|
0-9-11-20
|
1-11/7-7/4-11/8
|
werkismic
|
85
|
0-2-12-20
|
1-11/10-11/6-11/8
|
utonal
|
86
|
0-4-12-20
|
1-11/9-11/6-11/8
|
utonal
|
87
|
0-8-12-20
|
1-3/2-11/6-11/8
|
ambitonal
|
88
|
0-9-12-20
|
1-11/7-11/6-11/8
|
utonal
|
89
|
0-10-12-20
|
1-5/3-11/6-11/8
|
ptolemismic
|
90
|
0-4-16-20
|
1-11/9-9/8-11/8
|
rastmic
|
91
|
0-8-16-20
|
1-3/2-9/8-11/8
|
otonal
|
92
|
0-9-16-20
|
1-11/7-9/8-11/8
|
werkismic
|
93
|
0-11-16-20
|
1-7/4-9/8-11/8
|
otonal
|
94
|
0-12-16-20
|
1-11/6-9/8-11/8
|
rastmic
|
95
|
0-2-18-20
|
1-10/9-5/4-11/8
|
ptolemismic
|
96
|
0-8-18-20
|
1-3/2-5/4-11/8
|
otonal
|
97
|
0-9-18-20
|
1-11/7-5/4-11/8
|
octagari
|
98
|
0-10-18-20
|
1-5/3-5/4-11/8
|
ptolemismic
|
99
|
0-11-18-20
|
1-7/4-5/4-11/8
|
otonal
|
100
|
0-16-18-20
|
1-9/8-5/4-11/8
|
otonal
|
Pentads
Number
|
Chord
|
Transversal
|
Type
|
Hash
|
1
|
0-2-4-7-9
|
1-10/9-11/9-10/7-11/7
|
octarod
|
2
|
0-2-5-7-9
|
1-10/9-9/7-10/7-11/7
|
octarod
|
3
|
0-2-5-7-10
|
1-10/9-9/7-10/7-5/3
|
sensamagic
|
4
|
0-3-5-7-10
|
1-7/6-9/7-10/7-5/3
|
octarod
|
5
|
0-3-5-8-10
|
1-7/6-9/7-3/2-5/3
|
sensamagic
|
6
|
0-2-4-7-11
|
1-10/9-11/9-10/7-7/4
|
octacot
|
7
|
0-2-4-9-11
|
1-10/9-11/9-11/7-7/4
|
octagari
|
8
|
0-2-7-9-11
|
1-10/9-10/7-11/7-7/4
|
octagari
|
9
|
0-4-7-9-11
|
1-11/9-10/7-11/7-7/4
|
octacot
|
10
|
0-2-4-7-12
|
1-10/9-11/9-10/7-11/6
|
octarod
|
11
|
0-2-5-7-12
|
1-10/9-9/7-10/7-11/6
|
octarod
|
12
|
0-3-5-7-12
|
1-7/6-9/7-10/7-11/6
|
octarod
|
13
|
0-3-5-8-12
|
1-7/6-9/7-3/2-11/6
|
octarod
|
14
|
0-2-4-9-12
|
1-11/10-11/9-11/7-11/6
|
utonal
|
15
|
0-2-5-9-12
|
1-10/9-9/7-11/7-11/6
|
octarod
|
16
|
0-2-7-9-12
|
1-10/9-10/7-11/7-11/6
|
octarod
|
17
|
0-4-7-9-12
|
1-11/9-10/7-11/7-11/6
|
octarod
|
18
|
0-5-7-9-12
|
1-9/7-10/7-11/7-11/6
|
octarod
|
19
|
0-2-5-10-12
|
1-10/9-9/7-5/3-11/6
|
octarod
|
20
|
0-3-5-10-12
|
1-7/6-9/7-5/3-11/6
|
octarod
|
21
|
0-2-7-10-12
|
1-10/9-10/7-5/3-11/6
|
octarod
|
22
|
0-3-7-10-12
|
1-7/6-10/7-5/3-11/6
|
octarod
|
23
|
0-5-7-10-12
|
1-9/7-10/7-5/3-11/6
|
octarod
|
24
|
0-3-8-10-12
|
1-7/6-3/2-5/3-11/6
|
otonal
|
25
|
0-5-8-10-12
|
1-9/7-3/2-5/3-11/6
|
octarod
|
26
|
0-4-7-9-16
|
1-11/9-10/7-11/7-9/8
|
octacot
|
27
|
0-5-7-9-16
|
1-9/7-10/7-11/7-9/8
|
octagari
|
28
|
0-4-7-11-16
|
1-11/9-10/7-7/4-9/8
|
jove
|
29
|
0-4-8-11-16
|
1-11/9-3/2-7/4-9/8
|
jove
|
30
|
0-4-9-11-16
|
1-11/9-11/7-7/4-9/8
|
jove
|
31
|
0-7-9-11-16
|
1-10/7-11/7-7/4-9/8
|
octagari
|
32
|
0-4-7-12-16
|
1-11/9-10/7-11/6-9/8
|
jove
|
33
|
0-5-7-12-16
|
1-9/7-10/7-11/6-9/8
|
jove
|
34
|
0-4-8-12-16
|
1-11/9-3/2-11/6-9/8
|
rastmic
|
35
|
0-5-8-12-16
|
1-9/7-3/2-11/6-9/8
|
jove-
|
36
|
0-4-9-12-16
|
1-11/9-11/7-11/6-9/8
|
jove
|
37
|
0-5-9-12-16
|
1-9/7-11/7-11/6-9/8
|
jove
|
38
|
0-7-9-12-16
|
1-10/7-11/7-11/6-9/8
|
octacot
|
39
|
0-2-7-9-18
|
1-10/9-10/7-11/7-5/4
|
octagari
|
40
|
0-2-7-10-18
|
1-10/9-10/7-5/3-5/4
|
utonal
|
41
|
0-2-7-11-18
|
1-10/9-10/7-7/4-5/4
|
werkismic
|
42
|
0-2-9-11-18
|
1-10/9-11/7-7/4-5/4
|
octagari
|
43
|
0-7-9-11-18
|
1-10/7-11/7-7/4-5/4
|
octagari
|
44
|
0-7-9-16-18
|
1-10/7-11/7-9/8-5/4
|
octagari
|
45
|
0-7-11-16-18
|
1-10/7-7/4-9/8-5/4
|
werkismic
|
46
|
0-8-11-16-18
|
1-3/2-7/4-9/8-5/4
|
otonal
|
47
|
0-9-11-16-18
|
1-11/7-7/4-9/8-5/4
|
octagari
|
48
|
0-2-4-9-20
|
1-11/10-11/9-11/7-11/8
|
utonal
|
49
|
0-2-4-11-20
|
1-10/9-11/9-7/4-11/8
|
octagari
|
50
|
0-4-8-11-20
|
1-11/9-3/2-7/4-11/8
|
jove
|
51
|
0-2-9-11-20
|
1-10/9-11/7-7/4-11/8
|
octagari
|
52
|
0-4-9-11-20
|
1-11/9-11/7-7/4-11/8
|
werkismic
|
53
|
0-2-4-12-20
|
1-11/10-11/9-11/6-11/8
|
utonal
|
54
|
0-4-8-12-20
|
1-11/9-3/2-11/6-11/8
|
rastmic
|
55
|
0-2-9-12-20
|
1-11/10-11/7-11/6-11/8
|
utonal
|
56
|
0-4-9-12-20
|
1-11/9-11/7-11/6-11/8
|
utonal
|
57
|
0-2-10-12-20
|
1-10/9-5/3-11/6-11/8
|
ptolemismic
|
58
|
0-8-10-12-20
|
1-3/2-5/3-11/6-11/8
|
ptolemismic
|
59
|
0-4-8-16-20
|
1-11/9-3/2-9/8-11/8
|
rastmic
|
60
|
0-4-9-16-20
|
1-11/9-11/7-9/8-11/8
|
jove
|
61
|
0-4-11-16-20
|
1-11/9-7/4-9/8-11/8
|
jove
|
62
|
0-8-11-16-20
|
1-3/2-7/4-9/8-11/8
|
otonal
|
63
|
0-9-11-16-20
|
1-11/7-7/4-9/8-11/8
|
werkismic
|
64
|
0-4-12-16-20
|
1-11/9-11/6-9/8-11/8
|
rastmic
|
65
|
0-8-12-16-20
|
1-3/2-11/6-9/8-11/8
|
rastmic
|
66
|
0-9-12-16-20
|
1-11/7-11/6-9/8-11/8
|
jove
|
67
|
0-2-9-18-20
|
1-10/9-11/7-5/4-11/8
|
octagari
|
68
|
0-2-10-18-20
|
1-10/9-5/3-5/4-11/8
|
ptolemismic
|
69
|
0-8-10-18-20
|
1-3/2-5/3-5/4-11/8
|
ptolemismic
|
70
|
0-2-11-18-20
|
1-10/9-7/4-5/4-11/8
|
octagari
|
71
|
0-8-11-18-20
|
1-3/2-7/4-5/4-11/8
|
otonal
|
72
|
0-9-11-18-20
|
1-11/7-7/4-5/4-11/8
|
octagari
|
73
|
0-8-16-18-20
|
1-3/2-9/8-5/4-11/8
|
otonal
|
74
|
0-9-16-18-20
|
1-11/7-9/8-5/4-11/8
|
octagari
|
75
|
0-11-16-18-20
|
1-7/4-9/8-5/4-11/8
|
otonal
|
Hexads
Number
|
Chord
|
Transversal
|
Type
|
Hash
|
1
|
0-2-4-7-9-11
|
1-10/9-11/9-10/7-11/7-7/4
|
octacot
|
2
|
0-2-4-7-9-12
|
1-10/9-11/9-10/7-11/7-11/6
|
octarod
|
3
|
0-2-5-7-9-12
|
1-10/9-9/7-10/7-11/7-11/6
|
octarod
|
4
|
0-2-5-7-10-12
|
1-10/9-9/7-10/7-5/3-11/6
|
octarod
|
5
|
0-3-5-7-10-12
|
1-7/6-9/7-10/7-5/3-11/6
|
octarod
|
6
|
0-3-5-8-10-12
|
1-7/6-9/7-3/2-5/3-11/6
|
octarod
|
7
|
0-4-7-9-11-16
|
1-11/9-10/7-11/7-7/4-9/8
|
octacot
|
8
|
0-4-7-9-12-16
|
1-11/9-10/7-11/7-11/6-9/8
|
octacot
|
9
|
0-5-7-9-12-16
|
1-9/7-10/7-11/7-11/6-9/8
|
octacot
|
10
|
0-2-7-9-11-18
|
1-10/9-10/7-11/7-7/4-5/4
|
octagari
|
11
|
0-7-9-11-16-18
|
1-10/7-11/7-7/4-9/8-5/4
|
octagari
|
12
|
0-2-4-9-11-20
|
1-10/9-11/9-11/7-7/4-11/8
|
octagari
|
13
|
0-2-4-9-12-20
|
1-11/10-11/9-11/7-11/6-11/8
|
utonal
|
14
|
0-4-8-11-16-20
|
1-11/9-3/2-7/4-9/8-11/8
|
jove
|
15
|
0-4-9-11-16-20
|
1-11/9-11/7-7/4-9/8-11/8
|
jove
|
16
|
0-4-8-12-16-20
|
1-11/9-3/2-11/6-9/8-11/8
|
rastmic
|
17
|
0-4-9-12-16-20
|
1-11/9-11/7-11/6-9/8-11/8
|
jove
|
18
|
0-2-9-11-18-20
|
1-10/9-11/7-7/4-5/4-11/8
|
octagari
|
19
|
0-8-11-16-18-20
|
1-3/2-7/4-9/8-5/4-11/8
|
otonal
|
20
|
0-9-11-16-18-20
|
1-11/7-7/4-9/8-5/4-11/8
|
octagari
|