Chords of diaschismic
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. This is literally a semi-tone, but it's better to call it a "halftone", since the term "semitone" is used much more broadly and has many other connotations. The enharmonic interval is ^^d2, thus ^^C = B#. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. ^1 = 6c, where c is 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. The "As (sub)harmonics" column describes otonal chords as harmonics and utonal chords as subharmonics.
TODO: Complete the tables
Triads
# | Chord | Transversal | Type | Ratios | As (sub)harmonics | Genspans | Name | Complexity |
---|---|---|---|---|---|---|---|---|
1 | 0-104-208 | 1-4/3-16/9 | ambitonal | 1-4/3-3/2
1-9/8-3/2 |
6:8:9 = 12/9/8
8:9:12 = 9/8/6 |
0 -1 1
0 2 1 |
C4
C2 |
4 |
2 | 0-104-311 | 1-4/3-5/3 | otonal | 1-5/4-3/2 | 4:5:6 | 0 -2' 1 | Cv | 6 |
3 | 0-207-311 | 1-5/4-5/3 | utonal | 1-6/5-3/2 | 6/5/4 | 0 3' 1 | C^m | 6 |
4 | 0-104-413 | 1-4/3-10/9 | otonal | 1-6/5-9/5 | 5:6:9 | 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 |
20/16/9
9/5/4 |
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 | 4:5:9 | 0 -2' 2 | Cv,9no5 | 8 |
7 | 0-311-413 | 1-5/3-10/9 | utonal | 1-3/2-9/5 | 9/6/5 | 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 | 4:5:7 | 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 | 10/8/7 | 0 -2' 6 | Cv(^^b5) | 16 |
19 | 0-104-929 | 1-4/3-7/6 | otonal | 1-3/2-7/4 | 4:6:7 | 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 |
6:7:10
5:6:7 |
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 |
7/6/5
12/10/7 |
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 | 7/6/4 | 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 | 14/11/10 | 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 |
10:11:14
11:14:20 |
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 | 6:7:9 | 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 |
4:7:9
7:9:16 |
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 | 7:9:10 | 0 10' 6 | C^(^^b5) | 20 |
30 | 0-620-1033 | 1-7/5-14/9 | utonal | 1-9/7-9/5 | 9/7/5 | 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 |
9/7/4
16/14/9 |
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 | 9/7/6 | 0 10' 1 | C^ | 20 |
33 | 0-207-1239 | 1-5/4-11/8 | otonal | 1-5/4-11/8 | 8:10:11 | 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 | 14/11/8 | 0 4 -8' | C,v7no5 | 24 |
36 | 0-827-1239 | 1-7/4-11/8 | otonal | 1-14/11-16/11 | 11:14:16 | 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 |
11/10/8
20/16/11 |
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 | 8:11:12 | 0 -12' 1 | C,vd5no3 | 26 |
40 | 0-311-1343 | 1-5/3-11/6 | otonal | 1-6/5-11/5 | 5:6:11 | 0 3' -10 | C^mvv9no5 | 26 |
41 | 0-414-1343 | 1-11/7-11/6 | utonal | 1-7/6-14/11 | 14/12/11 | 0 -9' 4 | C,vm10no5 | 26 |
42 | 0-929-1343 | 1-7/6-11/6 | otonal | 1-7/6-11/6 | 6:7:11 | 0 -9' -13' | CvmvvvM7 | 26 |
43 | 0-1032-1343 | 1-11/10-11/6 | utonal | 1-6/5-24/11 | 24/20/11 | 0 3' 13' | C^m,^^^m9no5 | 26 |
44 | 0-1239-1343 | 1-11/8-11/6 | utonal | 1-4/3-16/11 | 16/12/11 | 0 -1 12' | C4(^^^b5) | 26 |
45 | 0-104-1445 | 1-4/3-11/9 | otonal | 1-3/2-11/6 | 6:9:11 | 0 1 -13' | CvvvM7no3 | 28 |
46 | 0-208-1445 | 1-16/9-11/9 | otonal | 1-11/9-16/9 | 9:11:16 | 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 |
9:10:11
10:11:18 |
0 -4' -14'
0 -10 4' |
Cv2vb4no5
Cvv2,^7no5 |
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 |
11/9/7
14/11/9 18/14/11 |
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 |
11/10/9
20/11/9 |
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 | 11:14:18 | 0 4 14' | C(^#5) | 28 |
53 | 0-1239-1445 | 1-11/8-11/9 | utonal | 1-16/11-16/9 | 16/11/9 | 0 12' -2 | C^#4,7no5 | 28 |
54 | 0-1343-1445 | 1-11/6-11/9 | utonal | 1-11/9-11/6 | 11/9/6 | 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 |