Diaschismic/Chords: Difference between revisions

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Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Diaschismic_family#Diaschismic|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.
Below are listed the [[dyadic chord]]s 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 chords|werckismic]], by [[176/175]] [[Valinorsmic chords|valinorsmic]], by [[896/891]] [[Pentacircle chords|pentacircle]], and by [[126/125]] [[Starling chords|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 dia = [<2 0 11 31 45|, <0 1 -2 -8 -12|]. From this we may derive a val v = dia[1] - 100 dia[2] = <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.
The normal mapping for diaschismic is {{nowrap|V<sub>dia</sub> {{=}} {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}}}. From this we may derive a val {{nowrap|'''V''' {{=}} V<sub>dia</sub>[0] &minus; 100 V<sub>dia</sub>[1]}} {{nowrap|{{=}} {{val| 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 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.
Diaschismic has [[mos scale]]s 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.


=Triads=
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 [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf 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 unison]] is ^^d2, thus {{nowrap|^^C {{=}} B#}}. One up is 6 mingen generators minus 1 period, which is half a pythagorean comma. {{nowrap|^1 {{=}} 6''c''}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. For 46edo, {{nowrap|''c'' {{=}} 4.3¢}} and {{nowrap|^1 {{=}} 1\46}} =&nbsp;26.1¢.


In Diaschismic, {{nowrap|5/4 {{=}} vM3}}, {{nowrap|7/4 {{=}} vm7}}, and {{nowrap|11/8 {{=}} vd5}} or vvvA4. Thus ^1 equals ~81/80 and ~64/63 and {{nowrap|~[[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 {{nowrap|A4 > d5}}. If {{nowrap|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.
{| class="wikitable"
{| class="wikitable"
|+ style="font-size: 105%;" | Diaschismic's two genchains, with cents in 46edo
|-
! colspan="3" | 1st genchain
! rowspan="2" | Genspan
! colspan="3" | 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
|-
|-
| | Number
| 1043
| | Chord
| 20/11
| | Transversal
| ^^m7
| | Type
! 10
| | Complexity
| 443
| 9/7
| ^M3
|-
|-
| | 1
| 339
| | 0-104-208
| 40/33
| | 1-4/3-16/9
| ^^m3
| | ambitonal
! 9
| | 4
| 939
| 12/7
| ^M6
|-
|-
| | 2
| 835
| | 0-104-311
| 45/28
| | 1-4/3-5/3
| A5, ^^m6
| | otonal
! 8
| | 6
| 235
| 8/7
| ^M2
|-
|-
| | 3
| 130
| | 0-207-311
| 15/14
| | 1-5/4-5/3
| A1, ^^m2
| | utonal
! 7
| | 6
| 730
| 32/21
| ^5
|-
|-
| | 4
| 626
| | 0-104-413
| 10/7
| | 1-4/3-10/9
| A4, ^^d5
| | otonal
! 6
| | 8
| 26
| 81/80, 64/63
| ^1
|-
|-
| | 5
| 1122
| | 0-207-413
| 40/21, 21/11
| | 1-5/4-10/9
| M7
| | utonal
! 5
| | 8
| 522
| 27/20
| ^4
|-
|-
| | 6
| 417
| | 0-208-413
| 14/11
| | 1-16/9-10/9
| M3
| | otonal
! 4
| | 8
| 1017
| 9/5
| ^m7
|-
|-
| | 7
| 913
| | 0-311-413
| 27/16, 56/33
| | 1-5/3-10/9
| M6
| | utonal
! 3
| | 8
| 313
| 6/5
| ^m3
|-
|-
| | 8
| 209
| | 0-207-414
| 9/8
| | 1-5/4-11/7
| M2
| | valinorsmic
! 2
| | 8
| 809
| 8/5
| vA5, ^m6
|-
|-
| | 9
| 704
| | 0-208-414
| '''3/2'''
| | 1-16/9-11/7
| P5
| | pentacircle
! 1
| | 8
| 104
| 16/15
| vA1, ^m2
|-
|-
| | 10
! 0
| | 0-207-620
! 1/1
| | 1-5/4-7/5
! P1
| | starling
! 0
| | 12
| 600
| 45/32, 64/45
| vA4, ^d5
|-
|-
| | 11
| 496
| | 0-208-620
| 4/3
| | 1-16/9-7/5
| P4
| | werckismic
! -1
| | 12
| 1096
| 15/8
| vM7, ^d8
|-
|-
| | 12
| 991
| | 0-311-620
| 16/9
| | 1-5/3-7/5
| m7
| | starling
! -2
| | 12
| 391
| '''5/4'''
| vM3, ^d4
|-
|-
| | 13
| 287
| | 0-413-620
| 32/27, 33/28
| | 1-10/9-7/5
| m3
| | starling
! -3
| | 12
| 887
| 5/3
| vM6, ^d7
|-
|-
| | 14
| 783
| | 0-414-620
| 11/7
| | 1-11/7-7/5
| m6, vvA5
| | werckismic
! -4
| | 12
| 183
| 10/9
| vM2
|-
|-
| | 15
| 78
| | 0-207-827
| 22/21, 21/20
| | 1-5/4-7/4
| m2
| | otonal
! -5
| | 16
| 678
| 40/27
| v5
|-
|-
| | 16
| 574
| | 0-413-827
| 7/5
| | 1-10/9-7/4
| d5, vvA4
| | werckismic
! -6
| | 16
| 1174
| 160/81, 63/32
| v8
|-
|-
| | 17
| 1070
| | 0-414-827
| 28/15
| | 1-11/7-7/4
| d8, vvM7
| | werckismic
! -7
| | 16
| 470
| 21/16
| v4
|-
|-
| | 18
| 365
| | 0-620-827
| 56/45
| | 1-7/5-7/4
| d4, vvM3
| | utonal
! -8
| | 16
| 965
| '''7/4'''
| vm7
|-
|-
| | 19
| 861
| | 0-104-929
| 33/20
| | 1-4/3-7/6
| vvM6
| | otonal
! -9
| | 18
| 261
| 7/6
| vm3
|-
|-
| | 20
| 157
| | 0-311-929
| 11/10
| | 1-5/3-7/6
| vvM2
| | otonal
! -10
| | 18
| 757
| 14/9
| vm6
|-
|-
| | 21
| 652
| | 0-620-929
| 22/15
| | 1-7/5-7/6
| vv5
| | utonal
! -11
| | 18
| 52
| 28/27, 33/32
| vm2, vvvA1
|-
|-
| | 22
| 1148
| | 0-827-929
| 88/45
| | 1-7/4-7/6
| vv8
| | utonal
! -12
| | 18
| 548
| '''11/8'''
| vd5, vvvA4
|-
|-
| | 23
| 443
| | 0-207-1032
|  
| | 1-5/4-11/10
| vv4
| | valinorsmic
! -13
| | 20
| 1043
| 11/6
| vd8, vvvM7
|-
|-
| | 24
| 939
| | 0-414-1032
|  
| | 1-11/7-11/10
| vvm7
| | utonal
! -14
| | 20
| 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 ==
{| class="wikitable center-1"
|-
|-
| | 25
! #
| | 0-620-1032
! Chord
| | 1-7/5-11/10
! Transversal
| | otonal
! Type
| | 20
! Ratios
! As (sub)harmonics
! Genspans
! Name
! Complexity
|-
|-
| | 26
| 1
| | 0-827-1032
| 0-104-208
| | 1-7/4-11/10
| 1-4/3-16/9
| | valinorsmic
| ambitonal
| | 20
| 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
|-
|-
| | 27
| 2
| | 0-104-1033
| 0-104-311
| | 1-4/3-14/9
| 1-4/3-5/3
| | otonal
| otonal
| | 20
| 1-5/4-3/2
| 4:5:6
| 0 -2' 1
| Cv
| 6
|-
|-
| | 28
| 3
| | 0-208-1033
| 0-207-311
| | 1-16/9-14/9
| 1-5/4-5/3
| | otonal
| utonal
| | 20
| 1-6/5-3/2
| 6/5/4
| 0 3' 1
| C^m
| 6
|-
|-
| | 29
| 4
| | 0-413-1033
| 0-104-413
| | 1-10/9-14/9
| 1-4/3-10/9
| | otonal
| otonal
| | 20
| 1-6/5-9/5
| 5:6:9
| 0 3' 4'
| C^m7no5
| 8
|-
|-
| | 30
| 5
| | 0-620-1033
| 0-207-413
| | 1-7/5-14/9
| 1-5/4-10/9
| | utonal
| utonal
| | 20
| 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
|-
|-
| | 31
| 6
| | 0-827-1033
| 0-208-413
| | 1-7/4-14/9
| 1-16/9-10/9
| | utonal
| otonal
| | 20
| 1-5/4-9/4
| 4:5:9
| 0 -2' 2
| Cv,9no5
| 8
|-
|-
| | 32
| 7
| | 0-929-1033
| 0-311-413
| | 1-7/6-14/9
| 1-5/3-10/9
| | utonal
| utonal
| | 20
| 1-3/2-9/5
| 9/6/5
| 0 1 4'
| C^m7no3
| 8
|-
|-
| | 33
| 8
| | 0-207-1239
| 0-207-414
| | 1-5/4-11/8
| 1-5/4-11/7
| | otonal
| valinorsmic
| | 24
| 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
|-
|-
| | 34
| 9
| | 0-208-1239
| 0-208-414
| | 1-16/9-11/8
| 1-16/9-11/7
| | pentacircle
| pentacircle
| | 24
| 1-9/8-14/11
|  
| 0 2 4
| C,9no5
| 8
|-
|-
| | 35
| 10
| | 0-414-1239
| 0-207-620
| | 1-11/7-11/8
| 1-5/4-7/5
| | utonal
| starling
| | 24
| 1-5/4-7/5
|  
| 0 -2' -6
| Cv(b5)
| 12
|-
|-
| | 36
| 11
| | 0-827-1239
| 0-208-620
| | 1-7/4-11/8
| 1-16/9-7/5
| | otonal
| werckismic
| | 24
| 1-14/11-10/7
|  
| 0 4 6
| C(^^b5)
| 12
|-
|-
| | 37
| 12
| | 0-1032-1239
| 0-311-620
| | 1-11/10-11/8
| 1-5/3-7/5
| | utonal
| starling
| | 24
| 1-6/5-10/7
|  
| 0 3' 6
| C^m(^^d5)
| 12
|-
|-
| | 38
| 13
| | 0-1033-1239
| 0-413-620
| | 1-14/9-11/8
| 1-10/9-7/5
| | pentacircle
| starling
| | 24
| 1-10/9-7/5
|  
| 0 -4' -6
| Cv2(b5)
| 12
|-
|-
| | 39
| 14
| | 0-104-1343
| 0-414-620
| | 1-4/3-11/6
| 1-11/7-7/5
| | otonal
| werckismic
| | 26
| 1-14/11-16/9
|  
| 0 4 -2
| C7no5
| 12
|-
|-
| | 40
| 15
| | 0-311-1343
| 0-207-827
| | 1-5/3-11/6
| 1-5/4-7/4
| | otonal
| otonal
| | 26
| 1-5/4-7/4
| 4:5:7
| 0 -2' -8'
| Cv7no5
| 16
|-
|-
| | 41
| 16
| | 0-414-1343
| 0-413-827
| | 1-11/7-11/6
| 1-10/9-7/4
| | utonal
| werckismic
| | 26
| 1-10/9-7/4
1-8/7-14/11
|  
| 0 -4' -8'
0 8' 4
| Cv7v9no35
C,^9no5
| 16
|-
|-
| | 42
| 17
| | 0-929-1343
| 0-414-827
| | 1-7/6-11/6
| 1-11/7-7/4
| | otonal
| werckismic
| | 26
| 1-9/5-16/7
1-10/9-14/11
|  
| 0 4' 8'
0 -4' 4
| C^7^9no35
C,v9no5
| 16
|-
|-
| | 43
| 18
| | 0-1032-1343
| 0-620-827
| | 1-11/10-11/6
| 1-7/5-7/4
| | utonal
| utonal
| | 26
| 1-5/4-10/7
| 10/8/7
| 0 -2' 6
| Cv(^^b5)
| 16
|-
|-
| | 44
| 19
| | 0-1239-1343
| 0-104-929
| | 1-11/8-11/6
| 1-4/3-7/6
| | utonal
| otonal
| | 26
| 1-3/2-7/4
| 4:6:7
| 0 1 -8'
| Cv7no3
| 18
|-
|-
| | 45
| 20
| | 0-104-1445
| 0-311-929
| | 1-4/3-11/9
| 1-5/3-7/6
| | otonal
| otonal
| | 28
| 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
|-
|-
| | 46
| 21
| | 0-208-1445
| 0-620-929
| | 1-16/9-11/9
| 1-7/5-7/6
| | otonal
| utonal
| | 28
| 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
|-
|-
| | 47
| 22
| | 0-413-1445
| 0-827-929
| | 1-10/9-11/9
| 1-7/4-7/6
| | otonal
| utonal
| | 28
| 1-7/6-7/4
| 7/6/4
| 0 -9' -8'
| Cvm7no5
| 18
|-
|-
| | 48
| 23
| | 0-414-1445
| 0-207-1032
| | 1-11/7-11/9
| 1-5/4-11/10
| | utonal
| valinorsmic
| | 28
| 1-5/4-11/5
1-20/11-16/7
|  
| 0 -2' -10
0 10 8'
| Cv,vv9no5
C^^7^9no35
| 20
|-
|-
| | 49
| 24
| | 0-620-1445
| 0-414-1032
| | 1-7/5-11/9
| 1-11/7-11/10
| | werckismic
| utonal
| | 28
| 1-14/11-7/5
| 14/11/10
| 0 4 -6
| C(b5)
| 20
|-
|-
| | 50
| 25
| | 0-827-1445
| 0-620-1032
| | 1-7/4-11/9
| 1-7/5-11/10
| | werckismic
| otonal
| | 28
| 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
|-
|-
| | 51
| 26
| | 0-1032-1445
| 0-827-1032
| | 1-11/10-11/9
| 1-7/4-11/10
| | utonal
| valinorsmic
| | 28
| 1-7/4-11/5
1-5/4-45/28
|  
| 0 -8' -10
0 -2' 8'
| Cv7vv9no35
Cv,v9no5
| 20
|-
|-
| | 52
| 27
| | 0-1033-1445
| 0-104-1033
| | 1-14/9-11/9
| 1-4/3-14/9
| | otonal
| otonal
| | 28
| 1-7/6-3/2
| 6:7:9
| 0 -9' 1
| Cvm
| 20
|-
|-
| | 53
| 28
| | 0-1239-1445
| 0-208-1033
| | 1-11/8-11/9
| 1-16/9-14/9
| | utonal
| otonal
| | 28
| 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
|-
|-
| | 54
| 29
| | 0-1343-1445
| 0-413-1033
| | 1-11/6-11/9
| 1-10/9-14/9
| | utonal
| otonal
| | 28
| 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=
== Tetrads ==
 
{| class="wikitable center-1"
{| class="wikitable"
|-
|-
| | Number
! #
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
| | Complexity
! Ratios
! Genspans
! Name
! Complexity
|-
|-
| | 1
| 1
| | 0-104-208-413
| 0-104-208-413
| | 1-4/3-16/9-10/9
| 1-4/3-16/9-10/9
| | otonal
| otonal
| | 8
| 1-5/4-3/2-9/4
| 0 -2' 1 2
| Cv,9
| 8
|-
|-
| | 2
| 2
| | 0-104-311-413
| 0-104-311-413
| | 1-4/3-5/3-10/9
| 1-4/3-5/3-10/9
| | ambitonal
| ambitonal
| | 8
| 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
| 3
| | 0-207-311-413
| 0-207-311-413
| | 1-5/4-5/3-10/9
| 1-5/4-5/3-10/9
| | utonal
| utonal
| | 8
| 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
| 4
| | 0-207-311-620
| 0-207-311-620
| | 1-5/4-5/3-7/5
| 1-5/4-5/3-7/5
| | starling
| starling
| | 12
| 1-6/5-3/2-5/3
| 0 3' 1 -3'
| C^mv6
| 12
|-
|-
| | 5
| 5
| | 0-207-413-620
| 0-207-413-620
| | 1-5/4-10/9-7/5
| 1-5/4-10/9-7/5
| | starling
| starling
| | 12
| 1-5/4-9/5-9/4
| 0 -2' 4' 2
| Cv9(^7)no5
| 12
|-
|-
| | 6
| 6
| | 0-208-413-620
| 0-208-413-620
| | 1-16/9-10/9-7/5
| 1-16/9-10/9-7/5
| | thrush
| thrush
| | 12
| 1-5/4-8/5-9/5
| 0 -2' 2' 4'
| Cv^7(v#5)
| 12
|-
|-
| | 7
| 7
| | 0-311-413-620
| 0-311-413-620
| | 1-5/3-10/9-7/5
| 1-5/3-10/9-7/5
| | starling
| starling
| | 12
| 1-5/4-3/2-9/5
| 0 -2' 1 4'
| Cv^7
| 12
|-
|-
| | 8
| 8
| | 0-207-414-620
| 0-207-414-620
| | 1-5/4-11/7-7/5
| 1-5/4-11/7-7/5
| | thrush
| thrush
| | 12
| 1-14/11-8/5-16/9
| 0 4 2' -2
| C7(v#5)
| 12
|-
|-
| | 9
| 9
| | 0-208-414-620
| 0-208-414-620
| | 1-16/9-11/7-7/5
| 1-16/9-11/7-7/5
| | pele
| pele
| | 12
| 1-14/11-16/9-9/4
| 0 4 -2 2
| C9no5
| 12
|-
|-
| | 10
| 10
| | 0-207-413-827
| 0-207-413-827
| | 1-5/4-10/9-7/4
| 1-5/4-10/9-7/4
| | werckismic
| werckismic
| | 16
| 1-5/4-7/4-20/9
| 0 -2' -8' -4'
| Cv7v9no5
| 16
|-
|-
| | 11
| 11
| | 0-207-414-827
| 0-207-414-827
| | 1-5/4-11/7-7/4
| 1-5/4-11/7-7/4
| | thrush
| thrush
| | 16
| 1-5/4-7/4-22/7
| 0 -2' -4 -8'
| Cv7b13no5
| 16
|-
|-
| | 12
| 12
| | 0-207-620-827
| 0-207-620-827
| | 1-5/4-7/5-7/4
| 1-5/4-7/5-7/4
| | starling
| starling
| | 16
| 1-5/4-7/5-7/4
| 0 -2' -6 -8'
| Cv7(b5)
| 16
|-
|-
| | 13
| 13
| | 0-413-620-827
| 0-413-620-827
| | 1-10/9-7/5-7/4
| 1-10/9-7/5-7/4
| | thrush
| thrush
| | 16
| 1-5/4-11/7-9/5
| 0 -2' -4 4'
| Cv^7(vv#5)
| 16
|-
|-
| | 14
| 14
| | 0-414-620-827
| 0-414-620-827
| | 1-11/7-7/5-7/4
| 1-11/7-7/5-7/4
| | werckismic
| werckismic
| | 16
| 1-14/11-16/9-20/9
| 0 4 -2 -4'
| C7v9no5
| 16
|-
|-
| | 15
| 15
| | 0-104-311-929
| 0-104-311-929
| | 1-4/3-5/3-7/6
| 1-4/3-5/3-7/6
| | otonal
| otonal
| | 18
| 1-5/4-3/2-7/4
| 0 -2' 1 -8'
| Cv7
| 18
|-
|-
| | 16
| 16
| | 0-311-620-929
| 0-311-620-929
| | 1-5/3-7/5-7/6
| 1-5/3-7/5-7/6
| | starling
| starling
| | 18
| 1-6/5-7/5-5/3
| 0 3' -6 -3'
| C^d7
| 18
|-
|-
| | 17
| 17
| | 0-620-827-929
| 0-620-827-929
| | 1-7/5-7/4-7/6
| 1-7/5-7/4-7/6
| | utonal
| utonal
| | 18
| 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
| 18
| | 0-207-414-1032
| 0-207-414-1032
| | 1-5/4-11/7-11/10
| 1-5/4-11/7-11/10
| | valinorsmic
| valinorsmic
| | 20
|
|  
|  
| 20
|-
|-
| | 19
| 19
| | 0-207-620-1032
| 0-207-620-1032
| | 1-5/4-7/5-11/10
| 1-5/4-7/5-11/10
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 20
| 20
| | 0-414-620-1032
| 0-414-620-1032
| | 1-11/7-7/5-11/10
| 1-11/7-7/5-11/10
| | werckismic
| werckismic
| | 20
|
|  
|  
| 20
|-
|-
| | 21
| 21
| | 0-207-827-1032
| 0-207-827-1032
| | 1-5/4-7/4-11/10
| 1-5/4-7/4-11/10
| | valinorsmic
| valinorsmic
| | 20
|
|  
|  
| 20
|-
|-
| | 22
| 22
| | 0-414-827-1032
| 0-414-827-1032
| | 1-11/7-7/4-11/10
| 1-11/7-7/4-11/10
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 23
| 23
| | 0-620-827-1032
| 0-620-827-1032
| | 1-7/5-7/4-11/10
| 1-7/5-7/4-11/10
| | valinorsmic
| valinorsmic
| | 20
|
|  
|  
| 20
|-
|-
| | 24
| 24
| | 0-104-208-1033
| 0-104-208-1033
| | 1-4/3-16/9-14/9
| 1-4/3-16/9-14/9
| | otonal
| otonal
| | 20
|
|  
|  
| 20
|-
|-
| | 25
| 25
| | 0-104-413-1033
| 0-104-413-1033
| | 1-4/3-10/9-14/9
| 1-4/3-10/9-14/9
| | otonal
| otonal
| | 20
|
|  
|  
| 20
|-
|-
| | 26
| 26
| | 0-208-413-1033
| 0-208-413-1033
| | 1-16/9-10/9-14/9
| 1-16/9-10/9-14/9
| | otonal
| otonal
| | 20
|
|  
|  
| 20
|-
|-
| | 27
| 27
| | 0-208-620-1033
| 0-208-620-1033
| | 1-16/9-7/5-14/9
| 1-16/9-7/5-14/9
| | werckismic
| werckismic
| | 20
|
|  
|  
| 20
|-
|-
| | 28
| 28
| | 0-413-620-1033
| 0-413-620-1033
| | 1-10/9-7/5-14/9
| 1-10/9-7/5-14/9
| | starling
| starling
| | 20
|
|  
|  
| 20
|-
|-
| | 29
| 29
| | 0-413-827-1033
| 0-413-827-1033
| | 1-10/9-7/4-14/9
| 1-10/9-7/4-14/9
| | werckismic
| werckismic
| | 20
|
|  
|  
| 20
|-
|-
| | 30
| 30
| | 0-620-827-1033
| 0-620-827-1033
| | 1-7/5-7/4-14/9
| 1-7/5-7/4-14/9
| | utonal
| utonal
| | 20
|
|  
|  
| 20
|-
|-
| | 31
| 31
| | 0-104-929-1033
| 0-104-929-1033
| | 1-4/3-7/6-14/9
| 1-4/3-7/6-14/9
| | ambitonal
| ambitonal
| | 20
|
|  
|  
| 20
|-
|-
| | 32
| 32
| | 0-620-929-1033
| 0-620-929-1033
| | 1-7/5-7/6-14/9
| 1-7/5-7/6-14/9
| | utonal
| utonal
| | 20
|
|  
|  
| 20
|-
|-
| | 33
| 33
| | 0-827-929-1033
| 0-827-929-1033
| | 1-7/4-7/6-14/9
| 1-7/4-7/6-14/9
| | utonal
| utonal
| | 20
|
|  
|  
| 20
|-
|-
| | 34
| 34
| | 0-207-414-1239
| 0-207-414-1239
| | 1-5/4-11/7-11/8
| 1-5/4-11/7-11/8
| | valinorsmic
| valinorsmic
| | 24
|
|  
|  
| 24
|-
|-
| | 35
| 35
| | 0-208-414-1239
| 0-208-414-1239
| | 1-16/9-11/7-11/8
| 1-16/9-11/7-11/8
| | pentacircle
| pentacircle
| | 24
|
|  
|  
| 24
|-
|-
| | 36
| 36
| | 0-207-827-1239
| 0-207-827-1239
| | 1-5/4-7/4-11/8
| 1-5/4-7/4-11/8
| | otonal
| otonal
| | 24
|
|  
|  
| 24
|-
|-
| | 37
| 37
| | 0-414-827-1239
| 0-414-827-1239
| | 1-11/7-7/4-11/8
| 1-11/7-7/4-11/8
| | werckismic
| werckismic
| | 24
|
|  
|  
| 24
|-
|-
| | 38
| 38
| | 0-207-1032-1239
| 0-207-1032-1239
| | 1-5/4-11/10-11/8
| 1-5/4-11/10-11/8
| | valinorsmic
| valinorsmic
| | 24
|
|  
|  
| 24
|-
|-
| | 39
| 39
| | 0-414-1032-1239
| 0-414-1032-1239
| | 1-11/7-11/10-11/8
| 1-11/7-11/10-11/8
| | utonal
| utonal
| | 24
|
|  
|  
| 24
|-
|-
| | 40
| 40
| | 0-827-1032-1239
| 0-827-1032-1239
| | 1-7/4-11/10-11/8
| 1-7/4-11/10-11/8
| | valinorsmic
| valinorsmic
| | 24
|
|  
|  
| 24
|-
|-
| | 41
| 41
| | 0-208-1033-1239
| 0-208-1033-1239
| | 1-16/9-14/9-11/8
| 1-16/9-14/9-11/8
| | pentacircle
| pentacircle
| | 24
|
|  
|  
| 24
|-
|-
| | 42
| 42
| | 0-827-1033-1239
| 0-827-1033-1239
| | 1-7/4-14/9-11/8
| 1-7/4-14/9-11/8
| | pentacircle
| pentacircle
| | 24
|
|  
|  
| 24
|-
|-
| | 43
| 43
| | 0-104-311-1343
| 0-104-311-1343
| | 1-4/3-5/3-11/6
| 1-4/3-5/3-11/6
| | otonal
| otonal
| | 26
|
|  
|  
| 26
|-
|-
| | 44
| 44
| | 0-104-929-1343
| 0-104-929-1343
| | 1-4/3-7/6-11/6
| 1-4/3-7/6-11/6
| | otonal
| otonal
| | 26
|
|  
|  
| 26
|-
|-
| | 45
| 45
| | 0-311-929-1343
| 0-311-929-1343
| | 1-5/3-7/6-11/6
| 1-5/3-7/6-11/6
| | otonal
| otonal
| | 26
|
|  
|  
| 26
|-
|-
| | 46
| 46
| | 0-414-1032-1343
| 0-414-1032-1343
| | 1-11/7-11/10-11/6
| 1-11/7-11/10-11/6
| | utonal
| utonal
| | 26
|
|  
|  
| 26
|-
|-
| | 47
| 47
| | 0-414-1239-1343
| 0-414-1239-1343
| | 1-11/7-11/8-11/6
| 1-11/7-11/8-11/6
| | utonal
| utonal
| | 26
|
|  
|  
| 26
|-
|-
| | 48
| 48
| | 0-1032-1239-1343
| 0-1032-1239-1343
| | 1-11/10-11/8-11/6
| 1-11/10-11/8-11/6
| | utonal
| utonal
| | 26
|
|  
|  
| 26
|-
|-
| | 49
| 49
| | 0-104-208-1445
| 0-104-208-1445
| | 1-4/3-16/9-11/9
| 1-4/3-16/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 50
| 50
| | 0-104-413-1445
| 0-104-413-1445
| | 1-4/3-10/9-11/9
| 1-4/3-10/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 51
| 51
| | 0-208-413-1445
| 0-208-413-1445
| | 1-16/9-10/9-11/9
| 1-16/9-10/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 52
| 52
| | 0-208-414-1445
| 0-208-414-1445
| | 1-16/9-11/7-11/9
| 1-16/9-11/7-11/9
| | pentacircle
| pentacircle
| | 28
|
|  
|  
| 28
|-
|-
| | 53
| 53
| | 0-208-620-1445
| 0-208-620-1445
| | 1-16/9-7/5-11/9
| 1-16/9-7/5-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 54
| 54
| | 0-413-620-1445
| 0-413-620-1445
| | 1-10/9-7/5-11/9
| 1-10/9-7/5-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 55
| 55
| | 0-414-620-1445
| 0-414-620-1445
| | 1-11/7-7/5-11/9
| 1-11/7-7/5-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 56
| 56
| | 0-413-827-1445
| 0-413-827-1445
| | 1-10/9-7/4-11/9
| 1-10/9-7/4-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 57
| 57
| | 0-414-827-1445
| 0-414-827-1445
| | 1-11/7-7/4-11/9
| 1-11/7-7/4-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 58
| 58
| | 0-620-827-1445
| 0-620-827-1445
| | 1-7/5-7/4-11/9
| 1-7/5-7/4-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 59
| 59
| | 0-414-1032-1445
| 0-414-1032-1445
| | 1-11/7-11/10-11/9
| 1-11/7-11/10-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 60
| 60
| | 0-620-1032-1445
| 0-620-1032-1445
| | 1-7/5-11/10-11/9
| 1-7/5-11/10-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 61
| 61
| | 0-827-1032-1445
| 0-827-1032-1445
| | 1-7/4-11/10-11/9
| 1-7/4-11/10-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 62
| 62
| | 0-104-1033-1445
| 0-104-1033-1445
| | 1-4/3-14/9-11/9
| 1-4/3-14/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 63
| 63
| | 0-208-1033-1445
| 0-208-1033-1445
| | 1-16/9-14/9-11/9
| 1-16/9-14/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 64
| 64
| | 0-413-1033-1445
| 0-413-1033-1445
| | 1-10/9-14/9-11/9
| 1-10/9-14/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 65
| 65
| | 0-620-1033-1445
| 0-620-1033-1445
| | 1-7/5-14/9-11/9
| 1-7/5-14/9-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 66
| 66
| | 0-827-1033-1445
| 0-827-1033-1445
| | 1-7/4-14/9-11/9
| 1-7/4-14/9-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 67
| 67
| | 0-208-1239-1445
| 0-208-1239-1445
| | 1-16/9-11/8-11/9
| 1-16/9-11/8-11/9
| | pentacircle
| pentacircle
| | 28
|
|  
|  
| 28
|-
|-
| | 68
| 68
| | 0-414-1239-1445
| 0-414-1239-1445
| | 1-11/7-11/8-11/9
| 1-11/7-11/8-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 69
| 69
| | 0-827-1239-1445
| 0-827-1239-1445
| | 1-7/4-11/8-11/9
| 1-7/4-11/8-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 70
| 70
| | 0-1032-1239-1445
| 0-1032-1239-1445
| | 1-11/10-11/8-11/9
| 1-11/10-11/8-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 71
| 71
| | 0-1033-1239-1445
| 0-1033-1239-1445
| | 1-14/9-11/8-11/9
| 1-14/9-11/8-11/9
| | pentacircle
| pentacircle
| | 28
|
|  
|  
| 28
|-
|-
| | 72
| 72
| | 0-104-1343-1445
| 0-104-1343-1445
| | 1-4/3-11/6-11/9
| 1-4/3-11/6-11/9
| | ambitonal
| ambitonal
| | 28
|
|  
|  
| 28
|-
|-
| | 73
| 73
| | 0-414-1343-1445
| 0-414-1343-1445
| | 1-11/7-11/6-11/9
| 1-11/7-11/6-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 74
| 74
| | 0-1032-1343-1445
| 0-1032-1343-1445
| | 1-11/10-11/6-11/9
| 1-11/10-11/6-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 75
| 75
| | 0-1239-1343-1445
| 0-1239-1343-1445
| | 1-11/8-11/6-11/9
| 1-11/8-11/6-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|}
|}


=Pentads=
== Pentads ==
 
{| class="wikitable center-1"
{| class="wikitable"
|-
|-
| | Number
! #
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
| | Complexity
! Ratios
! Genspans
! Name
! Complexity
|-
|-
| | 1
| 1
| | 0-207-311-413-620
| 0-207-311-413-620
| | 1-5/4-5/3-10/9-7/5
| 1-5/4-5/3-10/9-7/5
| | starling
| starling
| | 12
| 1-5/4-3/2-9/5-9/4
| 0 -2' 1 4' 2
| Cv9(^7)
| 12
|-
|-
| | 2
| 2
| | 0-207-413-620-827
| 0-207-413-620-827
| | 1-5/4-10/9-7/5-7/4
| 1-5/4-10/9-7/5-7/4
| | thrush
| thrush
| | 16
|
|  
|  
| 16
|-
|-
| | 3
| 3
| | 0-207-414-620-827
| 0-207-414-620-827
| | 1-5/4-11/7-7/5-7/4
| 1-5/4-11/7-7/5-7/4
| | thrush
| thrush
| | 16
|
|  
|  
| 16
|-
|-
| | 4
| 4
| | 0-207-414-620-1032
| 0-207-414-620-1032
| | 1-5/4-11/7-7/5-11/10
| 1-5/4-11/7-7/5-11/10
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 5
| 5
| | 0-207-414-827-1032
| 0-207-414-827-1032
| | 1-5/4-11/7-7/4-11/10
| 1-5/4-11/7-7/4-11/10
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 6
| 6
| | 0-207-620-827-1032
| 0-207-620-827-1032
| | 1-5/4-7/5-7/4-11/10
| 1-5/4-7/5-7/4-11/10
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 7
| 7
| | 0-414-620-827-1032
| 0-414-620-827-1032
| | 1-11/7-7/5-7/4-11/10
| 1-11/7-7/5-7/4-11/10
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 8
| 8
| | 0-104-208-413-1033
| 0-104-208-413-1033
| | 1-4/3-16/9-10/9-14/9
| 1-4/3-16/9-10/9-14/9
| | otonal
| otonal
| | 20
| 1-5/4-3/2-7/4-9/4
| 0 -2' 1 -8' 2
| Cv9
| 20
|-
|-
| | 9
| 9
| | 0-208-413-620-1033
| 0-208-413-620-1033
| | 1-16/9-10/9-7/5-14/9
| 1-16/9-10/9-7/5-14/9
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 10
| 10
| | 0-413-620-827-1033
| 0-413-620-827-1033
| | 1-10/9-7/5-7/4-14/9
| 1-10/9-7/5-7/4-14/9
| | thrush
| thrush
| | 20
|
|  
|  
| 20
|-
|-
| | 11
| 11
| | 0-620-827-929-1033
| 0-620-827-929-1033
| | 1-7/5-7/4-7/6-14/9
| 1-7/5-7/4-7/6-14/9
| | utonal
| utonal
| | 20
| 1-9/7-3/2-9/5-9/4
| 0 10' 1 4' 2
| C^9
| 20
|-
|-
| | 12
| 12
| | 0-207-414-827-1239
| 0-207-414-827-1239
| | 1-5/4-11/7-7/4-11/8
| 1-5/4-11/7-7/4-11/8
| | thrush
| thrush
| | 24
|
|  
|  
| 24
|-
|-
| | 13
| 13
| | 0-207-414-1032-1239
| 0-207-414-1032-1239
| | 1-5/4-11/7-11/10-11/8
| 1-5/4-11/7-11/10-11/8
| | valinorsmic
| valinorsmic
| | 24
|
|  
|  
| 24
|-
|-
| | 14
| 14
| | 0-207-827-1032-1239
| 0-207-827-1032-1239
| | 1-5/4-7/4-11/10-11/8
| 1-5/4-7/4-11/10-11/8
| | valinorsmic
| valinorsmic
| | 24
|
|  
|  
| 24
|-
|-
| | 15
| 15
| | 0-414-827-1032-1239
| 0-414-827-1032-1239
| | 1-11/7-7/4-11/10-11/8
| 1-11/7-7/4-11/10-11/8
| | thrush
| thrush
| | 24
|
|  
|  
| 24
|-
|-
| | 16
| 16
| | 0-104-311-929-1343
| 0-104-311-929-1343
| | 1-4/3-5/3-7/6-11/6
| 1-4/3-5/3-7/6-11/6
| | otonal
| otonal
| | 26
|
|  
|  
| 26
|-
|-
| | 17
| 17
| | 0-414-1032-1239-1343
| 0-414-1032-1239-1343
| | 1-11/7-11/10-11/8-11/6
| 1-11/7-11/10-11/8-11/6
| | utonal
| utonal
| | 26
|
|  
|  
| 26
|-
|-
| | 18
| 18
| | 0-104-208-413-1445
| 0-104-208-413-1445
| | 1-4/3-16/9-10/9-11/9
| 1-4/3-16/9-10/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 19
| 19
| | 0-208-413-620-1445
| 0-208-413-620-1445
| | 1-16/9-10/9-7/5-11/9
| 1-16/9-10/9-7/5-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 20
| 20
| | 0-208-414-620-1445
| 0-208-414-620-1445
| | 1-16/9-11/7-7/5-11/9
| 1-16/9-11/7-7/5-11/9
| | pele
| pele
| | 28
|
|  
|  
| 28
|-
|-
| | 21
| 21
| | 0-413-620-827-1445
| 0-413-620-827-1445
| | 1-10/9-7/5-7/4-11/9
| 1-10/9-7/5-7/4-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 22
| 22
| | 0-414-620-827-1445
| 0-414-620-827-1445
| | 1-11/7-7/5-7/4-11/9
| 1-11/7-7/5-7/4-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 23
| 23
| | 0-414-620-1032-1445
| 0-414-620-1032-1445
| | 1-11/7-7/5-11/10-11/9
| 1-11/7-7/5-11/10-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 24
| 24
| | 0-414-827-1032-1445
| 0-414-827-1032-1445
| | 1-11/7-7/4-11/10-11/9
| 1-11/7-7/4-11/10-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 25
| 25
| | 0-620-827-1032-1445
| 0-620-827-1032-1445
| | 1-7/5-7/4-11/10-11/9
| 1-7/5-7/4-11/10-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 26
| 26
| | 0-104-208-1033-1445
| 0-104-208-1033-1445
| | 1-4/3-16/9-14/9-11/9
| 1-4/3-16/9-14/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 27
| 27
| | 0-104-413-1033-1445
| 0-104-413-1033-1445
| | 1-4/3-10/9-14/9-11/9
| 1-4/3-10/9-14/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 28
| 28
| | 0-208-413-1033-1445
| 0-208-413-1033-1445
| | 1-16/9-10/9-14/9-11/9
| 1-16/9-10/9-14/9-11/9
| | otonal
| otonal
| | 28
|
|  
|  
| 28
|-
|-
| | 29
| 29
| | 0-208-620-1033-1445
| 0-208-620-1033-1445
| | 1-16/9-7/5-14/9-11/9
| 1-16/9-7/5-14/9-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 30
| 30
| | 0-413-620-1033-1445
| 0-413-620-1033-1445
| | 1-10/9-7/5-14/9-11/9
| 1-10/9-7/5-14/9-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 31
| 31
| | 0-413-827-1033-1445
| 0-413-827-1033-1445
| | 1-10/9-7/4-14/9-11/9
| 1-10/9-7/4-14/9-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 32
| 32
| | 0-620-827-1033-1445
| 0-620-827-1033-1445
| | 1-7/5-7/4-14/9-11/9
| 1-7/5-7/4-14/9-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 33
| 33
| | 0-208-414-1239-1445
| 0-208-414-1239-1445
| | 1-16/9-11/7-11/8-11/9
| 1-16/9-11/7-11/8-11/9
| | pentacircle
| pentacircle
| | 28
|
|  
|  
| 28
|-
|-
| | 34
| 34
| | 0-414-827-1239-1445
| 0-414-827-1239-1445
| | 1-11/7-7/4-11/8-11/9
| 1-11/7-7/4-11/8-11/9
| | werckismic
| werckismic
| | 28
|
|  
|  
| 28
|-
|-
| | 35
| 35
| | 0-414-1032-1239-1445
| 0-414-1032-1239-1445
| | 1-11/7-11/10-11/8-11/9
| 1-11/7-11/10-11/8-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 36
| 36
| | 0-827-1032-1239-1445
| 0-827-1032-1239-1445
| | 1-7/4-11/10-11/8-11/9
| 1-7/4-11/10-11/8-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 37
| 37
| | 0-208-1033-1239-1445
| 0-208-1033-1239-1445
| | 1-16/9-14/9-11/8-11/9
| 1-16/9-14/9-11/8-11/9
| | pentacircle
| pentacircle
| | 28
|
|  
|  
| 28
|-
|-
| | 38
| 38
| | 0-827-1033-1239-1445
| 0-827-1033-1239-1445
| | 1-7/4-14/9-11/8-11/9
| 1-7/4-14/9-11/8-11/9
| | pele
| pele
| | 28
|
|  
|  
| 28
|-
|-
| | 39
| 39
| | 0-414-1032-1343-1445
| 0-414-1032-1343-1445
| | 1-11/7-11/10-11/6-11/9
| 1-11/7-11/10-11/6-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 40
| 40
| | 0-414-1239-1343-1445
| 0-414-1239-1343-1445
| | 1-11/7-11/8-11/6-11/9
| 1-11/7-11/8-11/6-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|-
|-
| | 41
| 41
| | 0-1032-1239-1343-1445
| 0-1032-1239-1343-1445
| | 1-11/10-11/8-11/6-11/9
| 1-11/10-11/8-11/6-11/9
| | utonal
| utonal
| | 28
|
|  
|  
| 28
|}
|}


=Hexads=
== Hexads ==
 
{| class="wikitable center-1"
{| class="wikitable"
|-
|-
| | Number
! #
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
| | Complexity
! Ratios
! Genspans
! Name
! Complexity
|-
|-
| | 1
| 1
| | 0-207-414-620-827-1032
| 0-207-414-620-827-1032
| | 1-5/4-11/7-7/5-7/4-11/10
| 1-5/4-11/7-7/5-7/4-11/10
| | thrush
| thrush
| | 20
| 1-5/4-7/5-7/4-11/5-22/7
| 0 -2' -6 -8' -10 -4
| v7vv9b13(b5)
| 20
|-
|-
| | 2
| 2
| | 0-207-414-827-1032-1239
| 0-207-414-827-1032-1239
| | 1-5/4-11/7-7/4-11/10-11/8
| 1-5/4-11/7-7/4-11/10-11/8
| | thrush
| thrush
| | 24
| 1-5/4-11/8-7/4-11/5-22/7
| 0 -2' -12' -8' -10 -4
| v7vv9b13(vb5)
| 24
|-
|-
| | 3
| 3
| | 0-414-620-827-1032-1445
| 0-414-620-827-1032-1445
| | 1-11/7-7/5-7/4-11/10-11/9
| 1-11/7-7/5-7/4-11/10-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 4
| 4
| | 0-104-208-413-1033-1445
| 0-104-208-413-1033-1445
| | 1-4/3-16/9-10/9-14/9-11/9
| 1-4/3-16/9-10/9-14/9-11/9
| | otonal
| otonal
| | 28
| 1-5/4-3/2-7/4-9/4-11/4
| 0 -2' 1 -8' 2 -12'
| Cv9vvv#11
| 28
|-
|-
| | 5
| 5
| | 0-208-413-620-1033-1445
| 0-208-413-620-1033-1445
| | 1-16/9-10/9-7/5-14/9-11/9
| 1-16/9-10/9-7/5-14/9-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 6
| 6
| | 0-413-620-827-1033-1445
| 0-413-620-827-1033-1445
| | 1-10/9-7/5-7/4-14/9-11/9
| 1-10/9-7/5-7/4-14/9-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 7
| 7
| | 0-414-827-1032-1239-1445
| 0-414-827-1032-1239-1445
| | 1-11/7-7/4-11/10-11/8-11/9
| 1-11/7-7/4-11/10-11/8-11/9
| | thrush
| thrush
| | 28
|
|  
|  
| 28
|-
|-
| | 8
| 8
| | 0-414-1032-1239-1343-1445
| 0-414-1032-1239-1343-1445
| | 1-11/7-11/10-11/8-11/6-11/9
| 1-11/7-11/10-11/8-11/6-11/9
| | utonal
| utonal
| | 28
| 1-9/7-3/2-9/5-9/4-18/11
| 0 10' 1 4' 2 14'
| C^9^^^b6
| 28
|}
|}
[[Category:Lists of chords]]
[[Category:Lists of chords]]
[[Category:Dyadic chords]]
[[Category:Dyadic chords]]
[[Category:11-limit]]
[[Category:Diaschismic]]
[[Category:Diaschismic]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]