Below are listed the dyadic chords of 11-limit ennealimnic temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are labeled swetismic, 441/440 werckismic, and by 243/242 rastmic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove.
The normal mapping for ennealimnic is enn = [<9 1 1 12 -2|, <0 2 3 2 5|]. From this we may derive a val v = enn[1] + 100 enn[2] = <9 201 301 212 498| which we may use to sort and normalize the chords of ennealimmic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v, and the nnextw column gives a transversal which tempers to the chord by ennealimmic tempering. Finally, the Graham complexity is listed in the last column.
Ennealimmic has MOS of size 18, 27, 45 and 72. It may be seen that the 18 note MOS has some triads and tetrads, and 27 considerably more.
Triads
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-7-96
|
1-12/7-11/9
|
swetismic
|
9
|
| 2
|
0-2-98
|
1-7/6-10/7
|
swetismic
|
9
|
| 3
|
0-7-98
|
1-12/7-10/7
|
otonal
|
9
|
| 4
|
0-96-98
|
1-11/9-10/7
|
swetismic
|
9
|
| 5
|
0-2-100
|
1-7/6-5/3
|
otonal
|
9
|
| 6
|
0-98-100
|
1-10/7-5/3
|
utonal
|
9
|
| 7
|
0-7-188
|
1-12/7-11/10
|
swetismic
|
18
|
| 8
|
0-96-188
|
1-11/9-11/10
|
utonal
|
18
|
| 9
|
0-101-188
|
1-9/5-11/10
|
otonal
|
18
|
| 10
|
0-2-190
|
1-7/6-9/7
|
swetismic
|
18
|
| 11
|
0-7-190
|
1-12/7-9/7
|
otonal
|
18
|
| 12
|
0-98-190
|
1-10/7-9/7
|
otonal
|
18
|
| 13
|
0-101-190
|
1-9/5-9/7
|
utonal
|
18
|
| 14
|
0-188-190
|
1-11/10-9/7
|
swetismic
|
18
|
| 15
|
0-2-192
|
1-7/6-3/2
|
otonal
|
18
|
| 16
|
0-7-192
|
1-12/7-3/2
|
utonal
|
18
|
| 17
|
0-96-192
|
1-11/9-3/2
|
rastmic
|
18
|
| 18
|
0-100-192
|
1-5/3-3/2
|
otonal
|
18
|
| 19
|
0-101-192
|
1-9/5-3/2
|
utonal
|
18
|
| 20
|
0-190-192
|
1-9/7-3/2
|
utonal
|
18
|
| 21
|
0-2-194
|
1-7/6-7/4
|
utonal
|
18
|
| 22
|
0-96-194
|
1-11/9-7/4
|
werckismic
|
18
|
| 23
|
0-98-194
|
1-10/7-7/4
|
werckismic
|
18
|
| 24
|
0-192-194
|
1-3/2-7/4
|
otonal
|
18
|
| 25
|
0-98-283
|
1-10/7-5/4
|
utonal
|
27
|
| 26
|
0-100-283
|
1-5/3-5/4
|
utonal
|
27
|
| 27
|
0-192-283
|
1-3/2-5/4
|
otonal
|
27
|
| 28
|
0-194-283
|
1-7/4-5/4
|
otonal
|
27
|
| 29
|
0-7-286
|
1-12/7-11/7
|
otonal
|
27
|
| 30
|
0-96-286
|
1-11/9-11/7
|
utonal
|
27
|
| 31
|
0-98-286
|
1-10/7-11/7
|
otonal
|
27
|
| 32
|
0-101-286
|
1-9/5-11/7
|
werckismic
|
27
|
| 33
|
0-188-286
|
1-11/10-11/7
|
utonal
|
27
|
| 34
|
0-190-286
|
1-9/7-11/7
|
otonal
|
27
|
| 35
|
0-194-286
|
1-7/4-11/7
|
werckismic
|
27
|
| 36
|
0-2-288
|
1-7/6-11/6
|
otonal
|
27
|
| 37
|
0-96-288
|
1-11/9-11/6
|
utonal
|
27
|
| 38
|
0-98-288
|
1-10/7-11/6
|
swetismic
|
27
|
| 39
|
0-100-288
|
1-5/3-11/6
|
otonal
|
27
|
| 40
|
0-188-288
|
1-11/10-11/6
|
utonal
|
27
|
| 41
|
0-190-288
|
1-9/7-11/6
|
swetismic
|
27
|
| 42
|
0-192-288
|
1-3/2-11/6
|
otonal
|
27
|
| 43
|
0-286-288
|
1-11/7-11/6
|
utonal
|
27
|
| 44
|
0-96-375
|
1-11/9-9/8
|
rastmic
|
36
|
| 45
|
0-98-375
|
1-10/7-9/8
|
werckismic
|
36
|
| 46
|
0-101-375
|
1-9/5-9/8
|
utonal
|
36
|
| 47
|
0-190-375
|
1-9/7-9/8
|
utonal
|
36
|
| 48
|
0-192-375
|
1-3/2-9/8
|
ambitonal
|
36
|
| 49
|
0-194-375
|
1-7/4-9/8
|
otonal
|
36
|
| 50
|
0-283-375
|
1-5/4-9/8
|
otonal
|
36
|
| 51
|
0-286-375
|
1-11/7-9/8
|
werckismic
|
36
|
| 52
|
0-288-375
|
1-11/6-9/8
|
rastmic
|
36
|
| 53
|
0-96-471
|
1-11/9-11/8
|
utonal
|
45
|
| 54
|
0-188-471
|
1-11/10-11/8
|
utonal
|
45
|
| 55
|
0-192-471
|
1-3/2-11/8
|
otonal
|
45
|
| 56
|
0-194-471
|
1-7/4-11/8
|
otonal
|
45
|
| 57
|
0-283-471
|
1-5/4-11/8
|
otonal
|
45
|
| 58
|
0-286-471
|
1-11/7-11/8
|
utonal
|
45
|
| 59
|
0-288-471
|
1-11/6-11/8
|
utonal
|
45
|
| 60
|
0-375-471
|
1-9/8-11/8
|
otonal
|
45
|
Tetrads
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-7-96-98
|
1-12/7-11/9-10/7
|
swetismic
|
9
|
| 2
|
0-2-98-100
|
1-7/6-10/7-5/3
|
swetismic
|
9
|
| 3
|
0-7-96-188
|
1-12/7-11/9-11/10
|
swetismic
|
18
|
| 4
|
0-2-98-190
|
1-7/6-10/7-9/7
|
swetismic
|
18
|
| 5
|
0-7-98-190
|
1-12/7-10/7-9/7
|
otonal
|
18
|
| 6
|
0-7-188-190
|
1-12/7-11/10-9/7
|
swetismic
|
18
|
| 7
|
0-101-188-190
|
1-9/5-11/10-9/7
|
swetismic
|
18
|
| 8
|
0-7-96-192
|
1-12/7-11/9-3/2
|
jove
|
18
|
| 9
|
0-2-100-192
|
1-7/6-5/3-3/2
|
otonal
|
18
|
| 10
|
0-2-190-192
|
1-7/6-9/7-3/2
|
swetismic
|
18
|
| 11
|
0-7-190-192
|
1-12/7-9/7-3/2
|
ambitonal
|
18
|
| 12
|
0-101-190-192
|
1-9/5-9/7-3/2
|
utonal
|
18
|
| 13
|
0-2-98-194
|
1-7/6-10/7-7/4
|
jove
|
18
|
| 14
|
0-96-98-194
|
1-11/9-10/7-7/4
|
jove
|
18
|
| 15
|
0-2-192-194
|
1-7/6-3/2-7/4
|
ambitonal
|
18
|
| 16
|
0-96-192-194
|
1-11/9-3/2-7/4
|
jove
|
18
|
| 17
|
0-98-100-283
|
1-10/7-5/3-5/4
|
utonal
|
27
|
| 18
|
0-100-192-283
|
1-5/3-3/2-5/4
|
ambitonal
|
27
|
| 19
|
0-98-194-283
|
1-10/7-7/4-5/4
|
werckismic
|
27
|
| 20
|
0-192-194-283
|
1-3/2-7/4-5/4
|
otonal
|
27
|
| 21
|
0-7-96-286
|
1-12/7-11/9-11/7
|
swetismic
|
27
|
| 22
|
0-7-98-286
|
1-12/7-10/7-11/7
|
otonal
|
27
|
| 23
|
0-96-98-286
|
1-11/9-10/7-11/7
|
swetismic
|
27
|
| 24
|
0-7-188-286
|
1-12/7-11/10-11/7
|
swetismic
|
27
|
| 25
|
0-96-188-286
|
1-11/9-11/10-11/7
|
utonal
|
27
|
| 26
|
0-101-188-286
|
1-9/5-11/10-11/7
|
werckismic
|
27
|
| 27
|
0-7-190-286
|
1-12/7-9/7-11/7
|
otonal
|
27
|
| 28
|
0-98-190-286
|
1-10/7-9/7-11/7
|
otonal
|
27
|
| 29
|
0-101-190-286
|
1-9/5-9/7-11/7
|
werckismic
|
27
|
| 30
|
0-188-190-286
|
1-11/10-9/7-11/7
|
swetismic
|
27
|
| 31
|
0-96-194-286
|
1-11/9-7/4-11/7
|
werckismic
|
27
|
| 32
|
0-98-194-286
|
1-10/7-7/4-11/7
|
werckismic
|
27
|
| 33
|
0-2-98-288
|
1-7/6-10/7-11/6
|
swetismic
|
27
|
| 34
|
0-96-98-288
|
1-11/9-10/7-11/6
|
swetismic
|
27
|
| 35
|
0-2-100-288
|
1-7/6-5/3-11/6
|
otonal
|
27
|
| 36
|
0-98-100-288
|
1-10/7-5/3-11/6
|
swetismic
|
27
|
| 37
|
0-96-188-288
|
1-11/9-11/10-11/6
|
utonal
|
27
|
| 38
|
0-2-190-288
|
1-7/6-9/7-11/6
|
swetismic
|
27
|
| 39
|
0-98-190-288
|
1-10/7-9/7-11/6
|
swetismic
|
27
|
| 40
|
0-188-190-288
|
1-11/10-9/7-11/6
|
swetismic
|
27
|
| 41
|
0-2-192-288
|
1-7/6-3/2-11/6
|
otonal
|
27
|
| 42
|
0-96-192-288
|
1-11/9-3/2-11/6
|
rastmic
|
27
|
| 43
|
0-100-192-288
|
1-5/3-3/2-11/6
|
otonal
|
27
|
| 44
|
0-190-192-288
|
1-9/7-3/2-11/6
|
swetismic
|
27
|
| 45
|
0-96-286-288
|
1-11/9-11/7-11/6
|
utonal
|
27
|
| 46
|
0-98-286-288
|
1-10/7-11/7-11/6
|
swetismic
|
27
|
| 47
|
0-188-286-288
|
1-11/10-11/7-11/6
|
utonal
|
27
|
| 48
|
0-190-286-288
|
1-9/7-11/7-11/6
|
swetismic
|
27
|
| 49
|
0-96-98-375
|
1-11/9-10/7-9/8
|
jove
|
36
|
| 50
|
0-98-190-375
|
1-10/7-9/7-9/8
|
werckismic
|
36
|
| 51
|
0-101-190-375
|
1-9/5-9/7-9/8
|
utonal
|
36
|
| 52
|
0-96-192-375
|
1-11/9-3/2-9/8
|
rastmic
|
36
|
| 53
|
0-101-192-375
|
1-9/5-3/2-9/8
|
utonal
|
36
|
| 54
|
0-190-192-375
|
1-9/7-3/2-9/8
|
utonal
|
36
|
| 55
|
0-96-194-375
|
1-11/9-7/4-9/8
|
jove
|
36
|
| 56
|
0-98-194-375
|
1-10/7-7/4-9/8
|
werckismic
|
36
|
| 57
|
0-192-194-375
|
1-3/2-7/4-9/8
|
otonal
|
36
|
| 58
|
0-98-283-375
|
1-10/7-5/4-9/8
|
werckismic
|
36
|
| 59
|
0-192-283-375
|
1-3/2-5/4-9/8
|
otonal
|
36
|
| 60
|
0-194-283-375
|
1-7/4-5/4-9/8
|
otonal
|
36
|
| 61
|
0-96-286-375
|
1-11/9-11/7-9/8
|
jove
|
36
|
| 62
|
0-98-286-375
|
1-10/7-11/7-9/8
|
werckismic
|
36
|
| 63
|
0-101-286-375
|
1-9/5-11/7-9/8
|
werckismic
|
36
|
| 64
|
0-190-286-375
|
1-9/7-11/7-9/8
|
werckismic
|
36
|
| 65
|
0-194-286-375
|
1-7/4-11/7-9/8
|
werckismic
|
36
|
| 66
|
0-96-288-375
|
1-11/9-11/6-9/8
|
rastmic
|
36
|
| 67
|
0-98-288-375
|
1-10/7-11/6-9/8
|
jove
|
36
|
| 68
|
0-190-288-375
|
1-9/7-11/6-9/8
|
jove
|
36
|
| 69
|
0-192-288-375
|
1-3/2-11/6-9/8
|
rastmic
|
36
|
| 70
|
0-286-288-375
|
1-11/7-11/6-9/8
|
jove
|
36
|
| 71
|
0-96-188-471
|
1-11/9-11/10-11/8
|
utonal
|
45
|
| 72
|
0-96-192-471
|
1-11/9-3/2-11/8
|
rastmic
|
45
|
| 73
|
0-96-194-471
|
1-11/9-7/4-11/8
|
werckismic
|
45
|
| 74
|
0-192-194-471
|
1-3/2-7/4-11/8
|
otonal
|
45
|
| 75
|
0-192-283-471
|
1-3/2-5/4-11/8
|
otonal
|
45
|
| 76
|
0-194-283-471
|
1-7/4-5/4-11/8
|
otonal
|
45
|
| 77
|
0-96-286-471
|
1-11/9-11/7-11/8
|
utonal
|
45
|
| 78
|
0-188-286-471
|
1-11/10-11/7-11/8
|
utonal
|
45
|
| 79
|
0-194-286-471
|
1-7/4-11/7-11/8
|
werckismic
|
45
|
| 80
|
0-96-288-471
|
1-11/9-11/6-11/8
|
utonal
|
45
|
| 81
|
0-188-288-471
|
1-11/10-11/6-11/8
|
utonal
|
45
|
| 82
|
0-192-288-471
|
1-3/2-11/6-11/8
|
ambitonal
|
45
|
| 83
|
0-286-288-471
|
1-11/7-11/6-11/8
|
utonal
|
45
|
| 84
|
0-96-375-471
|
1-11/9-9/8-11/8
|
rastmic
|
45
|
| 85
|
0-192-375-471
|
1-3/2-9/8-11/8
|
otonal
|
45
|
| 86
|
0-194-375-471
|
1-7/4-9/8-11/8
|
otonal
|
45
|
| 87
|
0-283-375-471
|
1-5/4-9/8-11/8
|
otonal
|
45
|
| 88
|
0-286-375-471
|
1-11/7-9/8-11/8
|
werckismic
|
45
|
| 89
|
0-288-375-471
|
1-11/6-9/8-11/8
|
rastmic
|
45
|
Pentads
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-7-96-98-286
|
1-12/7-11/9-10/7-11/7
|
swetismic
|
27
|
| 2
|
0-7-96-188-286
|
1-12/7-11/9-11/10-11/7
|
swetismic
|
27
|
| 3
|
0-7-98-190-286
|
1-12/7-10/7-9/7-11/7
|
otonal
|
27
|
| 4
|
0-7-188-190-286
|
1-12/7-11/10-9/7-11/7
|
swetismic
|
27
|
| 5
|
0-101-188-190-286
|
1-9/5-11/10-9/7-11/7
|
jove
|
27
|
| 6
|
0-96-98-194-286
|
1-11/9-10/7-7/4-11/7
|
jove
|
27
|
| 7
|
0-2-98-100-288
|
1-7/6-10/7-5/3-11/6
|
swetismic
|
27
|
| 8
|
0-2-98-190-288
|
1-7/6-10/7-9/7-11/6
|
swetismic
|
27
|
| 9
|
0-2-100-192-288
|
1-7/6-5/3-3/2-11/6
|
otonal
|
27
|
| 10
|
0-2-190-192-288
|
1-7/6-9/7-3/2-11/6
|
swetismic
|
27
|
| 11
|
0-96-98-286-288
|
1-11/9-10/7-11/7-11/6
|
swetismic
|
27
|
| 12
|
0-96-188-286-288
|
1-11/9-11/10-11/7-11/6
|
utonal
|
27
|
| 13
|
0-98-190-286-288
|
1-10/7-9/7-11/7-11/6
|
swetismic
|
27
|
| 14
|
0-188-190-286-288
|
1-11/10-9/7-11/7-11/6
|
swetismic
|
27
|
| 15
|
0-101-190-192-375
|
1-9/5-9/7-3/2-9/8
|
utonal
|
36
|
| 16
|
0-96-98-194-375
|
1-11/9-10/7-7/4-9/8
|
jove
|
36
|
| 17
|
0-96-192-194-375
|
1-11/9-3/2-7/4-9/8
|
jove
|
36
|
| 18
|
0-98-194-283-375
|
1-10/7-7/4-5/4-9/8
|
werckismic
|
36
|
| 19
|
0-192-194-283-375
|
1-3/2-7/4-5/4-9/8
|
otonal
|
36
|
| 20
|
0-96-98-286-375
|
1-11/9-10/7-11/7-9/8
|
jove
|
36
|
| 21
|
0-98-190-286-375
|
1-10/7-9/7-11/7-9/8
|
werckismic
|
36
|
| 22
|
0-101-190-286-375
|
1-9/5-9/7-11/7-9/8
|
werckismic
|
36
|
| 23
|
0-96-194-286-375
|
1-11/9-7/4-11/7-9/8
|
jove
|
36
|
| 24
|
0-98-194-286-375
|
1-10/7-7/4-11/7-9/8
|
werckismic
|
36
|
| 25
|
0-96-98-288-375
|
1-11/9-10/7-11/6-9/8
|
jove
|
36
|
| 26
|
0-98-190-288-375
|
1-10/7-9/7-11/6-9/8
|
jove
|
36
|
| 27
|
0-96-192-288-375
|
1-11/9-3/2-11/6-9/8
|
rastmic
|
36
|
| 28
|
0-190-192-288-375
|
1-9/7-3/2-11/6-9/8
|
jove
|
36
|
| 29
|
0-96-286-288-375
|
1-11/9-11/7-11/6-9/8
|
jove
|
36
|
| 30
|
0-98-286-288-375
|
1-10/7-11/7-11/6-9/8
|
jove
|
36
|
| 31
|
0-190-286-288-375
|
1-9/7-11/7-11/6-9/8
|
jove
|
36
|
| 32
|
0-96-192-194-471
|
1-11/9-3/2-7/4-11/8
|
jove
|
45
|
| 33
|
0-192-194-283-471
|
1-3/2-7/4-5/4-11/8
|
otonal
|
45
|
| 34
|
0-96-188-286-471
|
1-11/9-11/10-11/7-11/8
|
utonal
|
45
|
| 35
|
0-96-194-286-471
|
1-11/9-7/4-11/7-11/8
|
werckismic
|
45
|
| 36
|
0-96-188-288-471
|
1-11/9-11/10-11/6-11/8
|
utonal
|
45
|
| 37
|
0-96-192-288-471
|
1-11/9-3/2-11/6-11/8
|
rastmic
|
45
|
| 38
|
0-96-286-288-471
|
1-11/9-11/7-11/6-11/8
|
utonal
|
45
|
| 39
|
0-188-286-288-471
|
1-11/10-11/7-11/6-11/8
|
utonal
|
45
|
| 40
|
0-96-192-375-471
|
1-11/9-3/2-9/8-11/8
|
rastmic
|
45
|
| 41
|
0-96-194-375-471
|
1-11/9-7/4-9/8-11/8
|
jove
|
45
|
| 42
|
0-192-194-375-471
|
1-3/2-7/4-9/8-11/8
|
otonal
|
45
|
| 43
|
0-192-283-375-471
|
1-3/2-5/4-9/8-11/8
|
otonal
|
45
|
| 44
|
0-194-283-375-471
|
1-7/4-5/4-9/8-11/8
|
otonal
|
45
|
| 45
|
0-96-286-375-471
|
1-11/9-11/7-9/8-11/8
|
jove
|
45
|
| 46
|
0-194-286-375-471
|
1-7/4-11/7-9/8-11/8
|
werckismic
|
45
|
| 47
|
0-96-288-375-471
|
1-11/9-11/6-9/8-11/8
|
rastmic
|
45
|
| 48
|
0-192-288-375-471
|
1-3/2-11/6-9/8-11/8
|
rastmic
|
45
|
| 49
|
0-286-288-375-471
|
1-11/7-11/6-9/8-11/8
|
jove
|
45
|
Hexads
| Number
|
Chord
|
Transversal
|
Type
|
Complexity
|
| 1
|
0-96-98-194-286-375
|
1-11/9-10/7-7/4-11/7-9/8
|
jove
|
36
|
| 2
|
0-96-98-286-288-375
|
1-11/9-10/7-11/7-11/6-9/8
|
jove
|
36
|
| 3
|
0-98-190-286-288-375
|
1-10/7-9/7-11/7-11/6-9/8
|
jove
|
36
|
| 4
|
0-96-188-286-288-471
|
1-11/9-11/10-11/7-11/6-11/8
|
utonal
|
45
|
| 5
|
0-96-192-194-375-471
|
1-11/9-3/2-7/4-9/8-11/8
|
jove
|
45
|
| 6
|
0-192-194-283-375-471
|
1-3/2-7/4-5/4-9/8-11/8
|
otonal
|
45
|
| 7
|
0-96-194-286-375-471
|
1-11/9-7/4-11/7-9/8-11/8
|
jove
|
45
|
| 8
|
0-96-192-288-375-471
|
1-11/9-3/2-11/6-9/8-11/8
|
rastmic
|
45
|
| 9
|
0-96-286-288-375-471
|
1-11/9-11/7-11/6-9/8-11/8
|
jove
|
45
|