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 46edo, c = 4.3¢ and ^1 = 1\46 = 26.1¢.
In Diaschismic, 5/4 = vM3, 7/4 = vm7 and 11/8 = vd5 or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and ~8192/8019 = [13 -6 0 0 -1⟩. This won't be true for most (P8, P5/2) temperaments. So although the ratios are specific to diaschismic, the chord names apply to any (P8, P5/2) temperament with A4 > d5. If A4 < d5, the arrows flip direction.
Because the list is limited to dyadic chords, certain obvious chords like C, Cm, C7 and Cm7 are omitted.
| 1st genchain | Genspan | 2nd genchain | ||||
|---|---|---|---|---|---|---|
| Cents | Ratio | Interval | Cents | Ratio | Interval | |
| 261 | ^^M2 | 14 | 861 | 18/11 | ^A5, ^^^m6 | |
| 757 | ^^5 | 13 | 157 | 12/11 | ^A1, ^^^m2 | |
| 52 | 45/44 | ^^1 | 12 | 652 | 16/11 | ^A4, ^^^d5 |
| 548 | 15/11 | ^^4 | 11 | 1148 | 27/14, 64/33 | ^M7, ^^^d8 |
| 1043 | 20/11 | ^^m7 | 10 | 443 | 9/7 | ^M3 |
| 339 | 40/33 | ^^m3 | 9 | 939 | 12/7 | ^M6 |
| 835 | 45/28 | A5, ^^m6 | 8 | 235 | 8/7 | ^M2 |
| 130 | 15/14 | A1, ^^m2 | 7 | 730 | 32/21 | ^5 |
| 626 | 10/7 | A4, ^^d5 | 6 | 26 | 81/80, 64/63 | ^1 |
| 1122 | 40/21, 21/11 | M7 | 5 | 522 | 27/20 | ^4 |
| 417 | 14/11 | M3 | 4 | 1017 | 9/5 | ^m7 |
| 913 | 27/16, 56/33 | M6 | 3 | 313 | 6/5 | ^m3 |
| 209 | 9/8 | M2 | 2 | 809 | 8/5 | vA5, ^m6 |
| 704 | 3/2 | P5 | 1 | 104 | 16/15 | vA1, ^m2 |
| 0 | 1/1 | P1 | 0 | 600 | 45/32, 64/45 | vA4, ^d5 |
| 496 | 4/3 | P4 | -1 | 1096 | 15/8 | vM7, ^d8 |
| 991 | 16/9 | m7 | -2 | 391 | 5/4 | vM3, ^d4 |
| 287 | 32/27, 33/28 | m3 | -3 | 887 | 5/3 | vM6, ^d7 |
| 783 | 11/7 | m6, vvA5 | -4 | 183 | 10/9 | vM2 |
| 78 | 22/21, 21/20 | m2 | -5 | 678 | 40/27 | v5 |
| 574 | 7/5 | d5, vvA4 | -6 | 1174 | 160/81, 63/32 | v8 |
| 1070 | 28/15 | d8, vvM7 | -7 | 470 | 21/16 | v4 |
| 365 | 56/45 | d4, vvM3 | -8 | 965 | 7/4 | vm7 |
| 861 | 33/20 | vvM6 | -9 | 261 | 7/6 | vm3 |
| 157 | 11/10 | vvM2 | -10 | 757 | 14/9 | vm6 |
| 652 | 22/15 | vv5 | -11 | 52 | 28/27, 33/32 | vm2, vvvA1 |
| 1148 | 88/45 | vv8 | -12 | 548 | 11/8 | vd5, vvvA4 |
| 443 | vv4 | -13 | 1043 | 11/6 | vd8, vvvM7 | |
| 939 | vvm7 | -14 | 339 | 11/9 | vd4, vvvM3 | |
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 | 1-6/5-11/5 | 0 3' -10 | C^mvv9no5 | 26 |
| 41 | 0-414-1343 | 1-11/7-11/6 | utonal | 1-7/6-14/11 | 0 -9' 4 | C,vm10no5 | 26 |
| 42 | 0-929-1343 | 1-7/6-11/6 | otonal | 1-7/6-11/6 | 0 -9' -13' | CvmvvvM7 | 26 |
| 43 | 0-1032-1343 | 1-11/10-11/6 | utonal | 1-9/7-12/5 | 0 3' 10' | C^,^m10 | 26 |
| 44 | 0-1239-1343 | 1-11/8-11/6 | utonal | 1-4/3-16/11 | 0 -1 12' | C4^#11no5 | 26 |
| 45 | 0-104-1445 | 1-4/3-11/9 | otonal | 1-3/2-11/6 | 0 1 -13' | CvvvM7no3 | 28 |
| 46 | 0-208-1445 | 1-16/9-11/9 | otonal | 1-11/9-16/9 | 0 -14' -2 | Cvb4,7no5 | 28 |
| 47 | 0-413-1445 | 1-10/9-11/9 | otonal | 1-10/9-11/9
1-11/10-9/5 |
0 -4' -14'
0 -10 4' |
Cv2vb4no5
Cvv2,^7 |
28 |
| 48 | 0-414-1445 | 1-11/7-11/9 | utonal | 1-11/9-11/7
1-14/11-14/9 1-9/7-18/11 |
0 -14' -4
0 4 -10' 0 10' 14' |
Cvb4b6no5
C,vm6no5 C^(^#5) |
28 |
| 49 | 0-620-1445 | 1-7/5-11/9 | werckismic | 1-11/9-7/5 | 0 -14' -6 | Cvb4(b5) | 28 |
| 50 | 0-827-1445 | 1-7/4-11/9 | werckismic | 1-11/9-7/4
1-8/7-7/5 |
0 -14' -8'
0 8' -6 |
Cvb4v7no5
C^2(b5) |
28 |
| 51 | 0-1032-1445 | 1-11/10-11/9 | utonal | 1-11/10-11/9
1-20/11-20/9 |
0 -10 -14'
0 10 -4' |
Cvv2vb4no5
C^^7v9no35 |
28 |
| 52 | 0-1033-1445 | 1-14/9-11/9 | otonal | 1-14/11-18/11 | 0 4 14' | C(^#5) | 28 |
| 53 | 0-1239-1445 | 1-11/8-11/9 | utonal | 1-16/11-16/9 | 0 12' -2 | C^#4,7no5 | 28 |
| 54 | 0-1343-1445 | 1-11/6-11/9 | utonal | 1-11/9-11/6 | 0 -14' -13' | CvvvM7no5 | 28 |
Tetrads
| # | Chord | Transversal | Type | Ratios | Genspans | Name | Complexity |
|---|---|---|---|---|---|---|---|
| 1 | 0-104-208-413 | 1-4/3-16/9-10/9 | otonal | 1-5/4-3/2-9/4 | 0 -2' 1 2 | Cv,9 | 8 |
| 2 | 0-104-311-413 | 1-4/3-5/3-10/9 | ambitonal | 1-5/4-3/2-5/3
1-6/5-3/2-9/5 |
0 -2' 1 -3'
0 3' 1 4' |
Cv6
C^m7 |
8 |
| 3 | 0-207-311-413 | 1-5/4-5/3-10/9 | utonal | 1-3/2-9/5-9/4
1-6/5-4/3-3/2 |
0 1 4' 2
0 3' -1 1 |
C^9no3
C^m,4 |
8 |
| 4 | 0-207-311-620 | 1-5/4-5/3-7/5 | starling | 1-6/5-3/2-5/3 | 0 3' 1 -3' | C^mv6 | 12 |
| 5 | 0-207-413-620 | 1-5/4-10/9-7/5 | starling | 1-5/4-9/5-9/4 | 0 -2' 4' 2 | Cv9(^7)no5 | 12 |
| 6 | 0-208-413-620 | 1-16/9-10/9-7/5 | thrush | 1-5/4-8/5-9/5 | 0 -2' 2' 4' | Cv^7(v#5) | 12 |
| 7 | 0-311-413-620 | 1-5/3-10/9-7/5 | starling | 1-5/4-3/2-9/5 | 0 -2' 1 4' | Cv^7 | 12 |
| 8 | 0-207-414-620 | 1-5/4-11/7-7/5 | thrush | 1-14/11-8/5-16/9 | 0 4 2' -2 | C7(v#5) | 12 |
| 9 | 0-208-414-620 | 1-16/9-11/7-7/5 | pele | 1-14/11-16/9-9/4 | 0 4 -2 2 | C9no5 | 12 |
| 10 | 0-207-413-827 | 1-5/4-10/9-7/4 | werckismic | 1-5/4-7/4-20/9 | 0 -2' -8' -4' | Cv7v9no5 | 16 |
| 11 | 0-207-414-827 | 1-5/4-11/7-7/4 | thrush | 1-5/4-7/4-22/7 | 0 -2' -4 -8' | Cv7b13no5 | 16 |
| 12 | 0-207-620-827 | 1-5/4-7/5-7/4 | starling | 1-5/4-7/5-7/4 | 0 -2' -6 -8' | Cv7(b5) | 16 |
| 13 | 0-413-620-827 | 1-10/9-7/5-7/4 | thrush | 1-5/4-11/7-9/5 | 0 -2' -4 4' | Cv^7(vv#5) | 16 |
| 14 | 0-414-620-827 | 1-11/7-7/5-7/4 | werckismic | 1-14/11-16/9-20/9 | 0 4 -2 -4' | C7v9no5 | 16 |
| 15 | 0-104-311-929 | 1-4/3-5/3-7/6 | otonal | 1-5/4-3/2-7/4 | 0 -2' 1 -8' | Cv7 | 18 |
| 16 | 0-311-620-929 | 1-5/3-7/5-7/6 | starling | 1-6/5-7/5-5/3 | 0 3' -6 -3' | C^d7 | 18 |
| 17 | 0-620-827-929 | 1-7/5-7/4-7/6 | utonal | 1-7/6-7/5-7/4
1-6/5-3/2-12/7 |
0 -9' -6 -8'
0 3' 1 9' |
Cvdv7
C^m6 |
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 | Ratios | Genspans | Name | Complexity |
|---|---|---|---|---|---|---|---|
| 1 | 0-207-311-413-620 | 1-5/4-5/3-10/9-7/5 | starling | 1-5/4-3/2-9/5-9/4 | 0 -2' 1 4' 2 | Cv9(^7) | 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 | 1-5/4-3/2-7/4-9/4 | 0 -2' 1 -8' 2 | Cv9 | 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 | 1-9/7-3/2-9/5-9/4 | 0 10' 1 4' 2 | C^9 | 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 | Ratios | Genspans | Name | Complexity |
|---|---|---|---|---|---|---|---|
| 1 | 0-207-414-620-827-1032 | 1-5/4-11/7-7/5-7/4-11/10 | thrush | 1-5/4-7/5-7/4-11/5-22/7 | 0 -2' -6 -8' -10 -4 | v7vv9b13(b5) | 20 |
| 2 | 0-207-414-827-1032-1239 | 1-5/4-11/7-7/4-11/10-11/8 | thrush | 1-5/4-11/8-7/4-11/5-22/7 | 0 -2' -12' -8' -10 -4 | v7vv9b13(vb5) | 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 | 1-5/4-3/2-7/4-9/4-11/4 | 0 -2' 1 -8' 2 -12' | Cv9vvv#11 | 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 | 1-9/7-3/2-9/5-9/4-18/11 | 0 10' 1 4' 2 14' | C^9^^^b6 | 28 |