Below are listed the dyadic chords of 11-limit diaschismic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 441/440 are labeled werckismic, by 176/175 valinorsmic, by 896/891 pentacircle, and by 126/125 starling. Those requiring tempering by any two of 126/125, 176/175 or 441/440 are labeled thrush, and by both 896/891 and 441/440 pele.
The normal mapping for diaschismic is Vdia = [⟨2 0 11 31 45], ⟨0 1 -2 -8 -12]]. From this we may derive a val V = Vdia[0] - 100 Vdia[1] = ⟨2 -100 211 831 1245] which we may use to sort and normalize the chords of diaschismic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by V. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.
Diaschsmic has mos scales of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.
Triads
| #
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-104-208
|
1-4/3-16/9
|
ambitonal
|
4
|
| 2
|
0-104-311
|
1-4/3-5/3
|
otonal
|
6
|
| 3
|
0-207-311
|
1-5/4-5/3
|
utonal
|
6
|
| 4
|
0-104-413
|
1-4/3-10/9
|
otonal
|
8
|
| 5
|
0-207-413
|
1-5/4-10/9
|
utonal
|
8
|
| 6
|
0-208-413
|
1-16/9-10/9
|
otonal
|
8
|
| 7
|
0-311-413
|
1-5/3-10/9
|
utonal
|
8
|
| 8
|
0-207-414
|
1-5/4-11/7
|
valinorsmic
|
8
|
| 9
|
0-208-414
|
1-16/9-11/7
|
pentacircle
|
8
|
| 10
|
0-207-620
|
1-5/4-7/5
|
starling
|
12
|
| 11
|
0-208-620
|
1-16/9-7/5
|
werckismic
|
12
|
| 12
|
0-311-620
|
1-5/3-7/5
|
starling
|
12
|
| 13
|
0-413-620
|
1-10/9-7/5
|
starling
|
12
|
| 14
|
0-414-620
|
1-11/7-7/5
|
werckismic
|
12
|
| 15
|
0-207-827
|
1-5/4-7/4
|
otonal
|
16
|
| 16
|
0-413-827
|
1-10/9-7/4
|
werckismic
|
16
|
| 17
|
0-414-827
|
1-11/7-7/4
|
werckismic
|
16
|
| 18
|
0-620-827
|
1-7/5-7/4
|
utonal
|
16
|
| 19
|
0-104-929
|
1-4/3-7/6
|
otonal
|
18
|
| 20
|
0-311-929
|
1-5/3-7/6
|
otonal
|
18
|
| 21
|
0-620-929
|
1-7/5-7/6
|
utonal
|
18
|
| 22
|
0-827-929
|
1-7/4-7/6
|
utonal
|
18
|
| 23
|
0-207-1032
|
1-5/4-11/10
|
valinorsmic
|
20
|
| 24
|
0-414-1032
|
1-11/7-11/10
|
utonal
|
20
|
| 25
|
0-620-1032
|
1-7/5-11/10
|
otonal
|
20
|
| 26
|
0-827-1032
|
1-7/4-11/10
|
valinorsmic
|
20
|
| 27
|
0-104-1033
|
1-4/3-14/9
|
otonal
|
20
|
| 28
|
0-208-1033
|
1-16/9-14/9
|
otonal
|
20
|
| 29
|
0-413-1033
|
1-10/9-14/9
|
otonal
|
20
|
| 30
|
0-620-1033
|
1-7/5-14/9
|
utonal
|
20
|
| 31
|
0-827-1033
|
1-7/4-14/9
|
utonal
|
20
|
| 32
|
0-929-1033
|
1-7/6-14/9
|
utonal
|
20
|
| 33
|
0-207-1239
|
1-5/4-11/8
|
otonal
|
24
|
| 34
|
0-208-1239
|
1-16/9-11/8
|
pentacircle
|
24
|
| 35
|
0-414-1239
|
1-11/7-11/8
|
utonal
|
24
|
| 36
|
0-827-1239
|
1-7/4-11/8
|
otonal
|
24
|
| 37
|
0-1032-1239
|
1-11/10-11/8
|
utonal
|
24
|
| 38
|
0-1033-1239
|
1-14/9-11/8
|
pentacircle
|
24
|
| 39
|
0-104-1343
|
1-4/3-11/6
|
otonal
|
26
|
| 40
|
0-311-1343
|
1-5/3-11/6
|
otonal
|
26
|
| 41
|
0-414-1343
|
1-11/7-11/6
|
utonal
|
26
|
| 42
|
0-929-1343
|
1-7/6-11/6
|
otonal
|
26
|
| 43
|
0-1032-1343
|
1-11/10-11/6
|
utonal
|
26
|
| 44
|
0-1239-1343
|
1-11/8-11/6
|
utonal
|
26
|
| 45
|
0-104-1445
|
1-4/3-11/9
|
otonal
|
28
|
| 46
|
0-208-1445
|
1-16/9-11/9
|
otonal
|
28
|
| 47
|
0-413-1445
|
1-10/9-11/9
|
otonal
|
28
|
| 48
|
0-414-1445
|
1-11/7-11/9
|
utonal
|
28
|
| 49
|
0-620-1445
|
1-7/5-11/9
|
werckismic
|
28
|
| 50
|
0-827-1445
|
1-7/4-11/9
|
werckismic
|
28
|
| 51
|
0-1032-1445
|
1-11/10-11/9
|
utonal
|
28
|
| 52
|
0-1033-1445
|
1-14/9-11/9
|
otonal
|
28
|
| 53
|
0-1239-1445
|
1-11/8-11/9
|
utonal
|
28
|
| 54
|
0-1343-1445
|
1-11/6-11/9
|
utonal
|
28
|
Tetrads
| #
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-104-208-413
|
1-4/3-16/9-10/9
|
otonal
|
8
|
| 2
|
0-104-311-413
|
1-4/3-5/3-10/9
|
ambitonal
|
8
|
| 3
|
0-207-311-413
|
1-5/4-5/3-10/9
|
utonal
|
8
|
| 4
|
0-207-311-620
|
1-5/4-5/3-7/5
|
starling
|
12
|
| 5
|
0-207-413-620
|
1-5/4-10/9-7/5
|
starling
|
12
|
| 6
|
0-208-413-620
|
1-16/9-10/9-7/5
|
thrush
|
12
|
| 7
|
0-311-413-620
|
1-5/3-10/9-7/5
|
starling
|
12
|
| 8
|
0-207-414-620
|
1-5/4-11/7-7/5
|
thrush
|
12
|
| 9
|
0-208-414-620
|
1-16/9-11/7-7/5
|
pele
|
12
|
| 10
|
0-207-413-827
|
1-5/4-10/9-7/4
|
werckismic
|
16
|
| 11
|
0-207-414-827
|
1-5/4-11/7-7/4
|
thrush
|
16
|
| 12
|
0-207-620-827
|
1-5/4-7/5-7/4
|
starling
|
16
|
| 13
|
0-413-620-827
|
1-10/9-7/5-7/4
|
thrush
|
16
|
| 14
|
0-414-620-827
|
1-11/7-7/5-7/4
|
werckismic
|
16
|
| 15
|
0-104-311-929
|
1-4/3-5/3-7/6
|
otonal
|
18
|
| 16
|
0-311-620-929
|
1-5/3-7/5-7/6
|
starling
|
18
|
| 17
|
0-620-827-929
|
1-7/5-7/4-7/6
|
utonal
|
18
|
| 18
|
0-207-414-1032
|
1-5/4-11/7-11/10
|
valinorsmic
|
20
|
| 19
|
0-207-620-1032
|
1-5/4-7/5-11/10
|
thrush
|
20
|
| 20
|
0-414-620-1032
|
1-11/7-7/5-11/10
|
werckismic
|
20
|
| 21
|
0-207-827-1032
|
1-5/4-7/4-11/10
|
valinorsmic
|
20
|
| 22
|
0-414-827-1032
|
1-11/7-7/4-11/10
|
thrush
|
20
|
| 23
|
0-620-827-1032
|
1-7/5-7/4-11/10
|
valinorsmic
|
20
|
| 24
|
0-104-208-1033
|
1-4/3-16/9-14/9
|
otonal
|
20
|
| 25
|
0-104-413-1033
|
1-4/3-10/9-14/9
|
otonal
|
20
|
| 26
|
0-208-413-1033
|
1-16/9-10/9-14/9
|
otonal
|
20
|
| 27
|
0-208-620-1033
|
1-16/9-7/5-14/9
|
werckismic
|
20
|
| 28
|
0-413-620-1033
|
1-10/9-7/5-14/9
|
starling
|
20
|
| 29
|
0-413-827-1033
|
1-10/9-7/4-14/9
|
werckismic
|
20
|
| 30
|
0-620-827-1033
|
1-7/5-7/4-14/9
|
utonal
|
20
|
| 31
|
0-104-929-1033
|
1-4/3-7/6-14/9
|
ambitonal
|
20
|
| 32
|
0-620-929-1033
|
1-7/5-7/6-14/9
|
utonal
|
20
|
| 33
|
0-827-929-1033
|
1-7/4-7/6-14/9
|
utonal
|
20
|
| 34
|
0-207-414-1239
|
1-5/4-11/7-11/8
|
valinorsmic
|
24
|
| 35
|
0-208-414-1239
|
1-16/9-11/7-11/8
|
pentacircle
|
24
|
| 36
|
0-207-827-1239
|
1-5/4-7/4-11/8
|
otonal
|
24
|
| 37
|
0-414-827-1239
|
1-11/7-7/4-11/8
|
werckismic
|
24
|
| 38
|
0-207-1032-1239
|
1-5/4-11/10-11/8
|
valinorsmic
|
24
|
| 39
|
0-414-1032-1239
|
1-11/7-11/10-11/8
|
utonal
|
24
|
| 40
|
0-827-1032-1239
|
1-7/4-11/10-11/8
|
valinorsmic
|
24
|
| 41
|
0-208-1033-1239
|
1-16/9-14/9-11/8
|
pentacircle
|
24
|
| 42
|
0-827-1033-1239
|
1-7/4-14/9-11/8
|
pentacircle
|
24
|
| 43
|
0-104-311-1343
|
1-4/3-5/3-11/6
|
otonal
|
26
|
| 44
|
0-104-929-1343
|
1-4/3-7/6-11/6
|
otonal
|
26
|
| 45
|
0-311-929-1343
|
1-5/3-7/6-11/6
|
otonal
|
26
|
| 46
|
0-414-1032-1343
|
1-11/7-11/10-11/6
|
utonal
|
26
|
| 47
|
0-414-1239-1343
|
1-11/7-11/8-11/6
|
utonal
|
26
|
| 48
|
0-1032-1239-1343
|
1-11/10-11/8-11/6
|
utonal
|
26
|
| 49
|
0-104-208-1445
|
1-4/3-16/9-11/9
|
otonal
|
28
|
| 50
|
0-104-413-1445
|
1-4/3-10/9-11/9
|
otonal
|
28
|
| 51
|
0-208-413-1445
|
1-16/9-10/9-11/9
|
otonal
|
28
|
| 52
|
0-208-414-1445
|
1-16/9-11/7-11/9
|
pentacircle
|
28
|
| 53
|
0-208-620-1445
|
1-16/9-7/5-11/9
|
werckismic
|
28
|
| 54
|
0-413-620-1445
|
1-10/9-7/5-11/9
|
thrush
|
28
|
| 55
|
0-414-620-1445
|
1-11/7-7/5-11/9
|
werckismic
|
28
|
| 56
|
0-413-827-1445
|
1-10/9-7/4-11/9
|
werckismic
|
28
|
| 57
|
0-414-827-1445
|
1-11/7-7/4-11/9
|
werckismic
|
28
|
| 58
|
0-620-827-1445
|
1-7/5-7/4-11/9
|
werckismic
|
28
|
| 59
|
0-414-1032-1445
|
1-11/7-11/10-11/9
|
utonal
|
28
|
| 60
|
0-620-1032-1445
|
1-7/5-11/10-11/9
|
werckismic
|
28
|
| 61
|
0-827-1032-1445
|
1-7/4-11/10-11/9
|
thrush
|
28
|
| 62
|
0-104-1033-1445
|
1-4/3-14/9-11/9
|
otonal
|
28
|
| 63
|
0-208-1033-1445
|
1-16/9-14/9-11/9
|
otonal
|
28
|
| 64
|
0-413-1033-1445
|
1-10/9-14/9-11/9
|
otonal
|
28
|
| 65
|
0-620-1033-1445
|
1-7/5-14/9-11/9
|
werckismic
|
28
|
| 66
|
0-827-1033-1445
|
1-7/4-14/9-11/9
|
werckismic
|
28
|
| 67
|
0-208-1239-1445
|
1-16/9-11/8-11/9
|
pentacircle
|
28
|
| 68
|
0-414-1239-1445
|
1-11/7-11/8-11/9
|
utonal
|
28
|
| 69
|
0-827-1239-1445
|
1-7/4-11/8-11/9
|
werckismic
|
28
|
| 70
|
0-1032-1239-1445
|
1-11/10-11/8-11/9
|
utonal
|
28
|
| 71
|
0-1033-1239-1445
|
1-14/9-11/8-11/9
|
pentacircle
|
28
|
| 72
|
0-104-1343-1445
|
1-4/3-11/6-11/9
|
ambitonal
|
28
|
| 73
|
0-414-1343-1445
|
1-11/7-11/6-11/9
|
utonal
|
28
|
| 74
|
0-1032-1343-1445
|
1-11/10-11/6-11/9
|
utonal
|
28
|
| 75
|
0-1239-1343-1445
|
1-11/8-11/6-11/9
|
utonal
|
28
|
Pentads
| #
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-207-311-413-620
|
1-5/4-5/3-10/9-7/5
|
starling
|
12
|
| 2
|
0-207-413-620-827
|
1-5/4-10/9-7/5-7/4
|
thrush
|
16
|
| 3
|
0-207-414-620-827
|
1-5/4-11/7-7/5-7/4
|
thrush
|
16
|
| 4
|
0-207-414-620-1032
|
1-5/4-11/7-7/5-11/10
|
thrush
|
20
|
| 5
|
0-207-414-827-1032
|
1-5/4-11/7-7/4-11/10
|
thrush
|
20
|
| 6
|
0-207-620-827-1032
|
1-5/4-7/5-7/4-11/10
|
thrush
|
20
|
| 7
|
0-414-620-827-1032
|
1-11/7-7/5-7/4-11/10
|
thrush
|
20
|
| 8
|
0-104-208-413-1033
|
1-4/3-16/9-10/9-14/9
|
otonal
|
20
|
| 9
|
0-208-413-620-1033
|
1-16/9-10/9-7/5-14/9
|
thrush
|
20
|
| 10
|
0-413-620-827-1033
|
1-10/9-7/5-7/4-14/9
|
thrush
|
20
|
| 11
|
0-620-827-929-1033
|
1-7/5-7/4-7/6-14/9
|
utonal
|
20
|
| 12
|
0-207-414-827-1239
|
1-5/4-11/7-7/4-11/8
|
thrush
|
24
|
| 13
|
0-207-414-1032-1239
|
1-5/4-11/7-11/10-11/8
|
valinorsmic
|
24
|
| 14
|
0-207-827-1032-1239
|
1-5/4-7/4-11/10-11/8
|
valinorsmic
|
24
|
| 15
|
0-414-827-1032-1239
|
1-11/7-7/4-11/10-11/8
|
thrush
|
24
|
| 16
|
0-104-311-929-1343
|
1-4/3-5/3-7/6-11/6
|
otonal
|
26
|
| 17
|
0-414-1032-1239-1343
|
1-11/7-11/10-11/8-11/6
|
utonal
|
26
|
| 18
|
0-104-208-413-1445
|
1-4/3-16/9-10/9-11/9
|
otonal
|
28
|
| 19
|
0-208-413-620-1445
|
1-16/9-10/9-7/5-11/9
|
thrush
|
28
|
| 20
|
0-208-414-620-1445
|
1-16/9-11/7-7/5-11/9
|
pele
|
28
|
| 21
|
0-413-620-827-1445
|
1-10/9-7/5-7/4-11/9
|
thrush
|
28
|
| 22
|
0-414-620-827-1445
|
1-11/7-7/5-7/4-11/9
|
werckismic
|
28
|
| 23
|
0-414-620-1032-1445
|
1-11/7-7/5-11/10-11/9
|
werckismic
|
28
|
| 24
|
0-414-827-1032-1445
|
1-11/7-7/4-11/10-11/9
|
thrush
|
28
|
| 25
|
0-620-827-1032-1445
|
1-7/5-7/4-11/10-11/9
|
thrush
|
28
|
| 26
|
0-104-208-1033-1445
|
1-4/3-16/9-14/9-11/9
|
otonal
|
28
|
| 27
|
0-104-413-1033-1445
|
1-4/3-10/9-14/9-11/9
|
otonal
|
28
|
| 28
|
0-208-413-1033-1445
|
1-16/9-10/9-14/9-11/9
|
otonal
|
28
|
| 29
|
0-208-620-1033-1445
|
1-16/9-7/5-14/9-11/9
|
werckismic
|
28
|
| 30
|
0-413-620-1033-1445
|
1-10/9-7/5-14/9-11/9
|
thrush
|
28
|
| 31
|
0-413-827-1033-1445
|
1-10/9-7/4-14/9-11/9
|
werckismic
|
28
|
| 32
|
0-620-827-1033-1445
|
1-7/5-7/4-14/9-11/9
|
werckismic
|
28
|
| 33
|
0-208-414-1239-1445
|
1-16/9-11/7-11/8-11/9
|
pentacircle
|
28
|
| 34
|
0-414-827-1239-1445
|
1-11/7-7/4-11/8-11/9
|
werckismic
|
28
|
| 35
|
0-414-1032-1239-1445
|
1-11/7-11/10-11/8-11/9
|
utonal
|
28
|
| 36
|
0-827-1032-1239-1445
|
1-7/4-11/10-11/8-11/9
|
thrush
|
28
|
| 37
|
0-208-1033-1239-1445
|
1-16/9-14/9-11/8-11/9
|
pentacircle
|
28
|
| 38
|
0-827-1033-1239-1445
|
1-7/4-14/9-11/8-11/9
|
pele
|
28
|
| 39
|
0-414-1032-1343-1445
|
1-11/7-11/10-11/6-11/9
|
utonal
|
28
|
| 40
|
0-414-1239-1343-1445
|
1-11/7-11/8-11/6-11/9
|
utonal
|
28
|
| 41
|
0-1032-1239-1343-1445
|
1-11/10-11/8-11/6-11/9
|
utonal
|
28
|
Hexads
| #
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-207-414-620-827-1032
|
1-5/4-11/7-7/5-7/4-11/10
|
thrush
|
20
|
| 2
|
0-207-414-827-1032-1239
|
1-5/4-11/7-7/4-11/10-11/8
|
thrush
|
24
|
| 3
|
0-414-620-827-1032-1445
|
1-11/7-7/5-7/4-11/10-11/9
|
thrush
|
28
|
| 4
|
0-104-208-413-1033-1445
|
1-4/3-16/9-10/9-14/9-11/9
|
otonal
|
28
|
| 5
|
0-208-413-620-1033-1445
|
1-16/9-10/9-7/5-14/9-11/9
|
thrush
|
28
|
| 6
|
0-413-620-827-1033-1445
|
1-10/9-7/5-7/4-14/9-11/9
|
thrush
|
28
|
| 7
|
0-414-827-1032-1239-1445
|
1-11/7-7/4-11/10-11/8-11/9
|
thrush
|
28
|
| 8
|
0-414-1032-1239-1343-1445
|
1-11/7-11/10-11/8-11/6-11/9
|
utonal
|
28
|