Diaschismic/Chords
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.
Chords are named with ups and downs. The comma (the actual punctuation mark) is pronounced "add", thus Cv,9 is "C down add 9". The pergen is (P8/2, P5), #2 in the notation guide for rank-2 pergens. The period is both vA4 and ^d5. The P5 generator in mingen form is reduced by one period to become both ^m2 and vA1, and hence M2/2. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period. ^1 = 6c, where c = the amount in cents the tempered fifth exceeds 700¢. For 34edo, c = 5.9¢ and ^1 = 1\34 = 35.3¢. In this notation, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5. Thus ^1 equals ~81/80 and ~64/63 and ~8192/8019 = [13 -6 0 0 -1⟩.
| 1st
genchain |
Cents (34edo) | 0 | 706 | 212 | 918 | 424 | 1129 | 635 | 141 | 847 | 353 | 1059 | 565 | 71 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ratio | 1/1 | 3/2 | 9/8 | 27/16
56/33 |
14/11 | 21/11
40/21 |
10/7 | 15/14 | 45/28 | 40/33 | 20/11 | 15/11 | 45/44 | |
| Interval | P1 | P5 | M2 | M6 | M3 | M7 | A4
^^d5 |
A1
^^m2 |
A5
^^m6 |
^^m3 | ^^m7 | ^^4 | ^^1 | |
| Genspan | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
| 2nd
genchain |
Cents (34edo) | 600 | 106 | 812 | 318 | 1024 | 529 | 35 | 741 | 247 | 953 | 459 | 1165 | 671 |
| Ratio | 45/32
64/45 |
16/15 | 8/5 | 6/5 | 9/5 | 27/20 | 81/80
64/63 |
32/21 | 8/7 | 12/7 | 9/7 | 27/14
64/33 |
16/11 | |
| Interval | vA4
^d5 |
vA1
^m2 |
vA5
^m6 |
vA2
^m3 |
^m7 | ^4 | ^1 | ^5 | ^M2 | ^M6 | ^M3 | ^M7 | ^A4 | |
5/4, 7/4 and 11/8 all occur on the fourthward half of the 2nd genchain:
| 1at
genchain |
Cents (34edo) | 0 | 494 | 988 | 282 | 776 | 71 | 565 | 1059 | 353 | 847 | 141 | 635 | 1129 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ratio | 1/1 | 4/3 | 16/9 | 32/27
33/28 |
11/7 | 22/21
21/20 |
7/5 | 28/15 | 56/45 | 33/20 | 11/10 | 22/15 | 88/45 | |
| Interval | P1 | P4 | m7 | m3 | m6 | m2 | vvA4
d5 |
vvM7
d8 |
vvM3
d4 |
vvM6 | vvM2 | vv5 | vv8 | |
| Genspan | 0 | -1 | -2 | -3 | -4 | -5 | -6 | -7 | -8 | -9 | -10 | -11 | -12 | |
| 2nd
genchain |
Cents (34edo) | 600 | 1094 | 388 | 882 | 176 | 671 | 1165 | 459 | 953 | 247 | 741 | 35 | 529 |
| Ratio | 45/32
64/45 |
15/8 | 5/4 | 5/3 | 10/9 | 40/27 | 160/81
63/32 |
21/16 | 7/4 | 7/6 | 14/9 | 2827
33/32 |
11/8 | |
| Interval | vA4
^d5 |
vM7
^d8 |
vM3
^d4 |
vM6 | vM2 | v5 | v8 | v4 | vm7 | vm3 | vm6 | vm2 | vd5 | |
| 1st genchain | Genspan | 2nd genchain | ||||
|---|---|---|---|---|---|---|
| Cents | Ratio | Interval | Cents | Ratio | Interval | |
| 282 | ^^M2 | 14 | 882 | 18/11 | ^A5 | |
| 776 | ^^5 | 13 | 176 | 12/11 | ^A1 | |
| 71 | 45/44 | ^^1 | 12 | 671 | 16/11 | ^A4 |
| 565 | 15/11 | ^^4 | 11 | 1165 | 27/14, 64/33 | ^M7 |
| 1059 | 20/11 | ^^m7 | 10 | 459 | 9/7 | ^M3 |
| 353 | 40/33 | ^^m3 | 9 | 953 | 12/7 | ^M6 |
| 847 | 45/28 | A5, ^^m6 | 8 | 247 | 8/7 | ^M2 |
| 141 | 15/14 | A1, ^^m2 | 7 | 741 | 32/21 | ^5 |
| 635 | 10/7 | A4, ^^d5 | 6 | 35 | 81/80, 64/63 | ^1 |
| 1129 | 21/11, 40/21 | M7 | 5 | 529 | 27/20 | ^4 |
| 424 | 14/11 | M3 | 4 | 1024 | 9/5 | ^m7 |
| 918 | 27/16, 56/33 | M6 | 3 | 318 | 6/5 | ^m3 |
| 212 | 9/8 | M2 | 2 | 812 | 8/5 | vA5, ^m6 |
| 706 | 3/2 | P5 | 1 | 106 | 16/15 | vA1, ^m2 |
| 0 | 1/1 | P1 | 0 | 600 | 45/32, 64/45 | vA4, ^d5 |
| 494 | 4/3 | P4 | -1 | 1094 | 15/8 | vM7, vd8 |
| 988 | 16/9 | m7 | -2 | 388 | 5/4 | vM3, ^d4 |
| 282 | 32/27, 33/28 | m3 | -3 | 882 | 5/3 | vM6 |
| 776 | 11/7 | m6 | -4 | 176 | 10/9 | vM2 |
| 71 | 22/21, 21/20 | m2 | -5 | 671 | 40/27 | v5 |
| 565 | 7/5 | d5, vvA4 | -6 | 1165 | 160/81, 63/32 | v8 |
| 1059 | 28/15 | d8, vvM7 | -7 | 459 | 21/16 | v4 |
| 353 | 56/45 | d4, vvM3 | -8 | 953 | 7/4 | vm7 |
| 847 | 33/20 | vvM6 | -9 | 247 | 7/6 | vm3 |
| 141 | 11/10 | vvM2 | -10 | 741 | 14/9 | vm6 |
| 635 | 22/15 | vv5 | -11 | 35 | 28/27, 33/32 | vm2 |
| 1129 | 88/45 | vv8 | -12 | 529 | 11/8 | vd5 |
| 424 | vv4 | -13 | 1024 | 11/6 | vd8 | |
| 918 | vvm7 | -14 | 318 | 11/9 | vd4 | |
In the genspans columns below, those on the 2nd genchain are marked with an apostrophe, thus 4 = M3 and 4' = ^m7.
TODO: Complete the tables
Triads
| # | Chord | Transversal | Type | Ratios | Genspans | Name | Complexity |
|---|---|---|---|---|---|---|---|
| 1 | 0-104-208 | 1-4/3-16/9 | ambitonal | 1-4/3-3/2
1-9/8-3/2 |
0 -1 1
0 2 1 |
C4
C2 |
4 |
| 2 | 0-104-311 | 1-4/3-5/3 | otonal | 1-5/4-3/2 | 0 -2' 1 | Cv | 6 |
| 3 | 0-207-311 | 1-5/4-5/3 | utonal | 1-6/5-3/2 | 0 3' 1 | C^m | 6 |
| 4 | 0-104-413 | 1-4/3-10/9 | otonal | 1-6/5-9/5 | 0 3' 4' | C^m7no5 | 8 |
| 5 | 0-207-413 | 1-5/4-10/9 | utonal | 1-5/4-20/9
1-9/5-9/4 |
0 -2' -4'
0 4' 2 |
Cv,v9no5
C^9no35 |
8 |
| 6 | 0-208-413 | 1-16/9-10/9 | otonal | 1-5/4-9/4 | 0 -2' 2 | Cv,9no5 | 8 |
| 7 | 0-311-413 | 1-5/3-10/9 | utonal | 1-3/2-9/5 | 0 1 4' | C^m7no3 | 8 |
| 8 | 0-207-414 | 1-5/4-11/7 | valinorsmic | 1-5/4-11/7
1-5/4-8/5 1-14/11-8/5 |
0 -2' -4
0 -2' 2' 0 4 -2' |
Cv(vv#5)
Cv(v#5) C(v#5) |
8 |
| 9 | 0-208-414 | 1-16/9-11/7 | pentacircle | 1-9/8-14/11 | 0 2 4 | C,9no5 | 8 |
| 10 | 0-207-620 | 1-5/4-7/5 | starling | 1-5/4-7/5 | 0 -2' -6 | Cv(b5) | 12 |
| 11 | 0-208-620 | 1-16/9-7/5 | werckismic | 1-14/11-10/7 | 0 4 6 | C(^^b5) | 12 |
| 12 | 0-311-620 | 1-5/3-7/5 | starling | 1-6/5-10/7 | 0 3' 6 | C^m(^^d5) | 12 |
| 13 | 0-413-620 | 1-10/9-7/5 | starling | 1-10/9-7/5 | 0 -4' -6 | Cv2(b5) | 12 |
| 14 | 0-414-620 | 1-11/7-7/5 | werckismic | 1-14/11-16/9 | 0 4 -2 | C7no5 | 12 |
| 15 | 0-207-827 | 1-5/4-7/4 | otonal | 1-5/4-7/4 | 0 -2' -8' | Cv7no5 | 16 |
| 16 | 0-413-827 | 1-10/9-7/4 | werckismic | 1-10/9-7/4
1-8/7-14/11 |
0 -4' -8'
0 8' 4 |
Cv7v9no35
C,^9no5 |
16 |
| 17 | 0-414-827 | 1-11/7-7/4 | werckismic | 1-9/5-16/7
1-10/9-14/11 |
0 4' 8'
0 -4' 4 |
C^7^9no35
C,v9no5 |
16 |
| 18 | 0-620-827 | 1-7/5-7/4 | utonal | 1-5/4-10/7 | 0 -2' 6 | Cv(^^b5) | 16 |
| 19 | 0-104-929 | 1-4/3-7/6 | otonal | 1-3/2-7/4 | 0 1 -8' | Cv7no3 | 18 |
| 20 | 0-311-929 | 1-5/3-7/6 | otonal | 1-7/6-5/3
1-6/5-7/5 |
0 -9' -3'
0 3' -6 |
Cvm6no5
C^dim |
18 |
| 21 | 0-620-929 | 1-7/5-7/6 | utonal | 1-7/6-7/5
1-6/5-12/7 |
0 -9' -6
0 3' 9' |
Cvdim
C^m6no5 |
18 |
| 22 | 0-827-929 | 1-7/4-7/6 | utonal | 1-7/6-7/4 | 0 -9' -8' | Cvm7no5 | 18 |
| 23 | 0-207-1032 | 1-5/4-11/10 | valinorsmic | 1-5/4-11/5
1-20/11-16/7 |
0 -2' -10
0 10 8' |
Cv,vv9no5
C^^7^9no35 |
20 |
| 24 | 0-414-1032 | 1-11/7-11/10 | utonal | 1-14/11-7/5 | 0 4 -6 | C(b5) | 20 |
| 25 | 0-620-1032 | 1-7/5-11/10 | otonal | 1-11/10-7/5
1-14/11-20/11 |
0 -10 -6
0 4 10 |
Cvv2(b5)
C,^^7no5 |
20 |
| 26 | 0-827-1032 | 1-7/4-11/10 | valinorsmic | 1-7/4-11/5
1-5/4-45/28 |
0 -8' -10
0 -2' 8' |
Cv7vv9no35
Cv,v9no5 |
20 |
| 27 | 0-104-1033 | 1-4/3-14/9 | otonal | 1-7/6-3/2 | 0 -9' 1 | Cvm | 20 |
| 28 | 0-208-1033 | 1-16/9-14/9 | otonal | 1-7/4-9/4
1-9/7-16/7 |
0 -8' 2
0 10' 8' |
Cv9no35
C^,^9no5 |
20 |
| 29 | 0-413-1033 | 1-10/9-14/9 | otonal | 1-9/7-10/7 | 0 10' 6 | C^(^^b5) | 20 |
| 30 | 0-620-1033 | 1-7/5-14/9 | utonal | 1-9/7-9/5 | 0 10' 4' | C^7no5 | 20 |
| 31 | 0-827-1033 | 1-7/4-14/9 | utonal | 1-9/7-9/4
1-8/7-16/9 |
0 10' 2
0 8' -2 |
C^,9no5
C^2,7no5 |
20 |
| 32 | 0-929-1033 | 1-7/6-14/9 | utonal | 1-9/7-3/2 | 0 10' 1 | C^ | 20 |
| 33 | 0-207-1239 | 1-5/4-11/8 | otonal | 1-5/4-11/8 | 0 -2' -12' | Cv(vb5) | 24 |
| 34 | 0-208-1239 | 1-16/9-11/8 | pentacircle | 1-9/7-16/11 | 0 10' 12' | C^,^#11no5 | 24 |
| 35 | 0-414-1239 | 1-11/7-11/8 | utonal | 1-14/11-7/4 | 0 4 -8' | C,v7no5 | 24 |
| 36 | 0-827-1239 | 1-7/4-11/8 | otonal | 1-14/11-16/11 | 0 4 12' | C,^#11no5 | 24 |
| 37 | 0-1032-1239 | 1-11/10-11/8 | utonal | 1-11/10-11/8
1-5/4-20/11 |
0 -10 -12'
0 -2' 10 |
Cvv2(vb5)
Cv,^^7no5 |
24 |
| 38 | 0-1033-1239 | 1-14/9-11/8 | pentacircle | 1-9/7-16/9 | 0 10' -2 | C^,7no5 | 24 |
| 39 | 0-104-1343 | 1-4/3-11/6 | otonal | 1-11/8-3/2 | 0 -12' 1 | C,vd5no3 | 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 |