Below are listed the dyadic chords of 11-limit echidna temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 540/539 are labeled swetismic, by 896/891 pentacircle, and by 176/175 valinorsmic.
The normal mapping for echidna is ech = [<2 1 9 2 12|, <0 3 -6 5 -7|]. From this we may derive a val v = ech[1] + 100 ech[2] = <2 301 -591 502 -688| which we may use to sort and normalize the chords of echidna. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v, and the next column gives a transversal which tempers to the chord by echidnic tempering. Finally, the Graham complexity is listed in the last column.
Echidna has MOS of size 6, 8, 14, 22, 36, 58 and 80. It may be seen that a modest number of chords are available to 14 notes, but that 22 has many more, and that may be a good choice as a scale with which to explore the harmonies of echidna. If for some reason you needed pentads and hexads, 36 notes would be fine.
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-100-199
|
1-9/7-7/6
|
swetismic
|
4
|
| 2
|
0-101-199
|
1-20/11-7/6
|
swetismic
|
4
|
| 3
|
0-100-299
|
1-9/7-3/2
|
utonal
|
6
|
| 4
|
0-199-299
|
1-7/6-3/2
|
otonal
|
6
|
| 5
|
0-199-498
|
1-7/6-7/4
|
utonal
|
10
|
| 6
|
0-299-498
|
1-3/2-7/4
|
otonal
|
10
|
| 7
|
0-100-596
|
1-9/7-9/8
|
utonal
|
12
|
| 8
|
0-299-596
|
1-3/2-9/8
|
ambitonal
|
12
|
| 9
|
0-498-596
|
1-7/4-9/8
|
otonal
|
12
|
| 10
|
0-101-597
|
1-20/11-8/5
|
valinorsmic
|
12
|
| 11
|
0-498-597
|
1-7/4-8/5
|
valinorsmic
|
12
|
| 12
|
0-100-696
|
1-9/7-16/11
|
pentacircle
|
14
|
| 13
|
0-101-696
|
1-20/11-16/11
|
otonal
|
14
|
| 14
|
0-596-696
|
1-9/8-16/11
|
pentacircle
|
14
|
| 15
|
0-597-696
|
1-8/5-16/11
|
utonal
|
14
|
| 16
|
0-299-894
|
1-3/2-6/5
|
utonal
|
18
|
| 17
|
0-597-894
|
1-8/5-6/5
|
otonal
|
18
|
| 18
|
0-101-993
|
1-20/11-12/11
|
otonal
|
20
|
| 19
|
0-299-993
|
1-3/2-12/11
|
utonal
|
20
|
| 20
|
0-696-993
|
1-16/11-12/11
|
otonal
|
20
|
| 21
|
0-894-993
|
1-6/5-12/11
|
utonal
|
20
|
| 22
|
0-100-1093
|
1-9/7-7/5
|
swetismic
|
22
|
| 23
|
0-199-1093
|
1-7/6-7/5
|
utonal
|
22
|
| 24
|
0-498-1093
|
1-7/4-7/5
|
utonal
|
22
|
| 25
|
0-597-1093
|
1-8/5-7/5
|
otonal
|
22
|
| 26
|
0-894-1093
|
1-6/5-7/5
|
otonal
|
22
|
| 27
|
0-993-1093
|
1-12/11-7/5
|
swetismic
|
22
|
| 28
|
0-101-1192
|
1-20/11-14/11
|
otonal
|
24
|
| 29
|
0-199-1192
|
1-7/6-14/11
|
utonal
|
24
|
| 30
|
0-498-1192
|
1-7/4-14/11
|
utonal
|
24
|
| 31
|
0-596-1192
|
1-9/8-14/11
|
pentacircle
|
24
|
| 32
|
0-597-1192
|
1-8/5-14/11
|
valinorsmic
|
24
|
| 33
|
0-696-1192
|
1-16/11-14/11
|
otonal
|
24
|
| 34
|
0-993-1192
|
1-12/11-14/11
|
otonal
|
24
|
| 35
|
0-1093-1192
|
1-7/5-14/11
|
utonal
|
24
|
| 36
|
0-100-1193
|
1-9/7-9/5
|
utonal
|
24
|
| 37
|
0-299-1193
|
1-3/2-9/5
|
utonal
|
24
|
| 38
|
0-596-1193
|
1-9/8-9/5
|
utonal
|
24
|
| 39
|
0-597-1193
|
1-8/5-9/5
|
otonal
|
24
|
| 40
|
0-894-1193
|
1-6/5-9/5
|
otonal
|
24
|
| 41
|
0-1093-1193
|
1-7/5-9/5
|
otonal
|
24
|
| 42
|
0-100-1292
|
1-9/7-18/11
|
utonal
|
26
|
| 43
|
0-101-1292
|
1-20/11-18/11
|
otonal
|
26
|
| 44
|
0-199-1292
|
1-7/6-18/11
|
swetismic
|
26
|
| 45
|
0-299-1292
|
1-3/2-18/11
|
utonal
|
26
|
| 46
|
0-596-1292
|
1-9/8-18/11
|
utonal
|
26
|
| 47
|
0-696-1292
|
1-16/11-18/11
|
otonal
|
26
|
| 48
|
0-993-1292
|
1-12/11-18/11
|
otonal
|
26
|
| 49
|
0-1093-1292
|
1-7/5-18/11
|
swetismic
|
26
|
| 50
|
0-1192-1292
|
1-14/11-18/11
|
otonal
|
26
|
| 51
|
0-1193-1292
|
1-9/5-18/11
|
utonal
|
26
|
Tetlist[edit]
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-100-199-299
|
1-9/7-7/6-3/2
|
swetismic
|
6
|
| 2
|
0-199-299-498
|
1-7/6-3/2-7/4
|
ambitonal
|
10
|
| 3
|
0-100-299-596
|
1-9/7-3/2-9/8
|
utonal
|
12
|
| 4
|
0-299-498-596
|
1-3/2-7/4-9/8
|
otonal
|
12
|
| 5
|
0-100-596-696
|
1-9/7-9/8-16/11
|
pentacircle
|
14
|
| 6
|
0-101-597-696
|
1-20/11-8/5-16/11
|
valinorsmic
|
14
|
| 7
|
0-101-696-993
|
1-20/11-16/11-12/11
|
otonal
|
20
|
| 8
|
0-299-894-993
|
1-3/2-6/5-12/11
|
utonal
|
20
|
| 9
|
0-100-199-1093
|
1-9/7-7/6-7/5
|
swetismic
|
22
|
| 10
|
0-199-498-1093
|
1-7/6-7/4-7/5
|
utonal
|
22
|
| 11
|
0-498-597-1093
|
1-7/4-8/5-7/5
|
valinorsmic
|
22
|
| 12
|
0-597-894-1093
|
1-8/5-6/5-7/5
|
otonal
|
22
|
| 13
|
0-894-993-1093
|
1-6/5-12/11-7/5
|
swetismic
|
22
|
| 14
|
0-101-199-1192
|
1-20/11-7/6-14/11
|
swetismic
|
24
|
| 15
|
0-199-498-1192
|
1-7/6-7/4-14/11
|
utonal
|
24
|
| 16
|
0-498-596-1192
|
1-7/4-9/8-14/11
|
pentacircle
|
24
|
| 17
|
0-101-597-1192
|
1-20/11-8/5-14/11
|
valinorsmic
|
24
|
| 18
|
0-498-597-1192
|
1-7/4-8/5-14/11
|
valinorsmic
|
24
|
| 19
|
0-101-696-1192
|
1-20/11-16/11-14/11
|
otonal
|
24
|
| 20
|
0-596-696-1192
|
1-9/8-16/11-14/11
|
pentacircle
|
24
|
| 21
|
0-597-696-1192
|
1-8/5-16/11-14/11
|
valinorsmic
|
24
|
| 22
|
0-101-993-1192
|
1-20/11-12/11-14/11
|
otonal
|
24
|
| 23
|
0-696-993-1192
|
1-16/11-12/11-14/11
|
otonal
|
24
|
| 24
|
0-199-1093-1192
|
1-7/6-7/5-14/11
|
utonal
|
24
|
| 25
|
0-498-1093-1192
|
1-7/4-7/5-14/11
|
utonal
|
24
|
| 26
|
0-597-1093-1192
|
1-8/5-7/5-14/11
|
valinorsmic
|
24
|
| 27
|
0-993-1093-1192
|
1-12/11-7/5-14/11
|
swetismic
|
24
|
| 28
|
0-100-299-1193
|
1-9/7-3/2-9/5
|
utonal
|
24
|
| 29
|
0-100-596-1193
|
1-9/7-9/8-9/5
|
utonal
|
24
|
| 30
|
0-299-596-1193
|
1-3/2-9/8-9/5
|
utonal
|
24
|
| 31
|
0-299-894-1193
|
1-3/2-6/5-9/5
|
ambitonal
|
24
|
| 32
|
0-597-894-1193
|
1-8/5-6/5-9/5
|
otonal
|
24
|
| 33
|
0-100-1093-1193
|
1-9/7-7/5-9/5
|
swetismic
|
24
|
| 34
|
0-597-1093-1193
|
1-8/5-7/5-9/5
|
otonal
|
24
|
| 35
|
0-894-1093-1193
|
1-6/5-7/5-9/5
|
otonal
|
24
|
| 36
|
0-100-199-1292
|
1-9/7-7/6-18/11
|
swetismic
|
26
|
| 37
|
0-101-199-1292
|
1-20/11-7/6-18/11
|
swetismic
|
26
|
| 38
|
0-100-299-1292
|
1-9/7-3/2-18/11
|
utonal
|
26
|
| 39
|
0-199-299-1292
|
1-7/6-3/2-18/11
|
swetismic
|
26
|
| 40
|
0-100-596-1292
|
1-9/7-9/8-18/11
|
utonal
|
26
|
| 41
|
0-299-596-1292
|
1-3/2-9/8-18/11
|
utonal
|
26
|
| 42
|
0-100-696-1292
|
1-9/7-16/11-18/11
|
pentacircle
|
26
|
| 43
|
0-101-696-1292
|
1-20/11-16/11-18/11
|
otonal
|
26
|
| 44
|
0-596-696-1292
|
1-9/8-16/11-18/11
|
pentacircle
|
26
|
| 45
|
0-101-993-1292
|
1-20/11-12/11-18/11
|
otonal
|
26
|
| 46
|
0-299-993-1292
|
1-3/2-12/11-18/11
|
ambitonal
|
26
|
| 47
|
0-696-993-1292
|
1-16/11-12/11-18/11
|
otonal
|
26
|
| 48
|
0-100-1093-1292
|
1-9/7-7/5-18/11
|
swetismic
|
26
|
| 49
|
0-199-1093-1292
|
1-7/6-7/5-18/11
|
swetismic
|
26
|
| 50
|
0-993-1093-1292
|
1-12/11-7/5-18/11
|
swetismic
|
26
|
| 51
|
0-101-1192-1292
|
1-20/11-14/11-18/11
|
otonal
|
26
|
| 52
|
0-199-1192-1292
|
1-7/6-14/11-18/11
|
swetismic
|
26
|
| 53
|
0-596-1192-1292
|
1-9/8-14/11-18/11
|
pentacircle
|
26
|
| 54
|
0-696-1192-1292
|
1-16/11-14/11-18/11
|
otonal
|
26
|
| 55
|
0-993-1192-1292
|
1-12/11-14/11-18/11
|
otonal
|
26
|
| 56
|
0-1093-1192-1292
|
1-7/5-14/11-18/11
|
swetismic
|
26
|
| 57
|
0-100-1193-1292
|
1-9/7-9/5-18/11
|
utonal
|
26
|
| 58
|
0-299-1193-1292
|
1-3/2-9/5-18/11
|
utonal
|
26
|
| 59
|
0-596-1193-1292
|
1-9/8-9/5-18/11
|
utonal
|
26
|
| 60
|
0-1093-1193-1292
|
1-7/5-9/5-18/11
|
swetismic
|
26
|
Pentlist[edit]
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-101-597-696-1192
|
1-20/11-8/5-16/11-14/11
|
valinorsmic
|
24
|
| 2
|
0-101-696-993-1192
|
1-20/11-16/11-12/11-14/11
|
otonal
|
24
|
| 3
|
0-199-498-1093-1192
|
1-7/6-7/4-7/5-14/11
|
utonal
|
24
|
| 4
|
0-498-597-1093-1192
|
1-7/4-8/5-7/5-14/11
|
valinorsmic
|
24
|
| 5
|
0-100-299-596-1193
|
1-9/7-3/2-9/8-9/5
|
utonal
|
24
|
| 6
|
0-597-894-1093-1193
|
1-8/5-6/5-7/5-9/5
|
otonal
|
24
|
| 7
|
0-100-199-299-1292
|
1-9/7-7/6-3/2-18/11
|
swetismic
|
26
|
| 8
|
0-100-299-596-1292
|
1-9/7-3/2-9/8-18/11
|
utonal
|
26
|
| 9
|
0-100-596-696-1292
|
1-9/7-9/8-16/11-18/11
|
pentacircle
|
26
|
| 10
|
0-101-696-993-1292
|
1-20/11-16/11-12/11-18/11
|
otonal
|
26
|
| 11
|
0-100-199-1093-1292
|
1-9/7-7/6-7/5-18/11
|
swetismic
|
26
|
| 12
|
0-101-199-1192-1292
|
1-20/11-7/6-14/11-18/11
|
swetismic
|
26
|
| 13
|
0-101-696-1192-1292
|
1-20/11-16/11-14/11-18/11
|
otonal
|
26
|
| 14
|
0-596-696-1192-1292
|
1-9/8-16/11-14/11-18/11
|
pentacircle
|
26
|
| 15
|
0-101-993-1192-1292
|
1-20/11-12/11-14/11-18/11
|
otonal
|
26
|
| 16
|
0-696-993-1192-1292
|
1-16/11-12/11-14/11-18/11
|
otonal
|
26
|
| 17
|
0-199-1093-1192-1292
|
1-7/6-7/5-14/11-18/11
|
swetismic
|
26
|
| 18
|
0-993-1093-1192-1292
|
1-12/11-7/5-14/11-18/11
|
swetismic
|
26
|
| 19
|
0-100-299-1193-1292
|
1-9/7-3/2-9/5-18/11
|
utonal
|
26
|
| 20
|
0-100-596-1193-1292
|
1-9/7-9/8-9/5-18/11
|
utonal
|
26
|
| 21
|
0-299-596-1193-1292
|
1-3/2-9/8-9/5-18/11
|
utonal
|
26
|
| 22
|
0-100-1093-1193-1292
|
1-9/7-7/5-9/5-18/11
|
swetismic
|
26
|
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-101-696-993-1192-1292
|
1-20/11-16/11-12/11-14/11-18/11
|
otonal
|
26
|
| 2
|
0-100-299-596-1193-1292
|
1-9/7-3/2-9/8-9/5-18/11
|
utonal
|
26
|