Chords of echidna
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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.
Triads
| 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
| 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
| 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 |
Hexad
| 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 |