Diaschismic/Chords: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Cleanup; linking; categories; start bracketed indices with 0
TallKite (talk | contribs)
autopatrolled, Sysops
4,223 edits
started adding chord names
Line 4: Line 4:


Diaschsmic 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.
Diaschsmic 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.
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. 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⟩.
{| class="wikitable"
|+Diaschismic's two genchains, fifthward halves
! rowspan="3" |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
|-
! colspan="2" |Genspan
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
|-
! rowspan="3" |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:
{| class="wikitable"
|+Diaschismic's two genchains, fourthward halves
! rowspan="3" |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
|-
! colspan="2" |Genspan
!0
!-1
!-2
!-3
!-4
!-5
!-6
!-7
!-8
!-9
!-10
!-11
!-12
|-
! rowspan="3" |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
|}
{| class="wikitable"
|+Diaschismic's two genchains, with cents in 34edo
! colspan="3" |1st genchain
! rowspan="2" |Genspan
! colspan="3" |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 ==
== Triads ==
Line 13: Line 510:
! Transversal
! Transversal
! Type
! Type
!Ratios
!Genspans
!Name
! Complexity
! Complexity
|-
|-
Line 19: Line 519:
| 1-4/3-16/9
| 1-4/3-16/9
| ambitonal
| ambitonal
|1-4/3-3/2
1-9/8-3/2
|0 -1 1
0 2 1
|C4
C2
| 4
| 4
|-
|-
Line 25: Line 531:
| 1-4/3-5/3
| 1-4/3-5/3
| otonal
| otonal
|1-5/4-3/2
|0 -2' 1
|Cv
| 6
| 6
|-
|-
Line 31: Line 540:
| 1-5/4-5/3
| 1-5/4-5/3
| utonal
| utonal
|1-6/5-3/2
|0 3' 1
|C^m
| 6
| 6
|-
|-
Line 37: Line 549:
| 1-4/3-10/9
| 1-4/3-10/9
| otonal
| otonal
|1-6/5-9/5
|0 3' 4'
|C^m7no5
| 8
| 8
|-
|-
Line 43: Line 558:
| 1-5/4-10/9
| 1-5/4-10/9
| utonal
| utonal
|1-5/4-20/9
1-9/5-9/4
|0 -2' -4'
0 4' 2
|Cv,v9no5
C^9no35
| 8
| 8
|-
|-
Line 49: Line 570:
| 1-16/9-10/9
| 1-16/9-10/9
| otonal
| otonal
|1-5/4-9/4
|0 -2' 2
|Cv,9no5
| 8
| 8
|-
|-
Line 55: Line 579:
| 1-5/3-10/9
| 1-5/3-10/9
| utonal
| utonal
|1-3/2-9/5
|0 1 4'
|C^m7no3
| 8
| 8
|-
|-
Line 61: Line 588:
| 1-5/4-11/7
| 1-5/4-11/7
| valinorsmic
| 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
| 8
|-
|-
Line 67: Line 606:
| 1-16/9-11/7
| 1-16/9-11/7
| pentacircle
| pentacircle
|1-9/8-14/11
|0 2 4
|C,9no5
| 8
| 8
|-
|-
Line 73: Line 615:
| 1-5/4-7/5
| 1-5/4-7/5
| starling
| starling
|1-5/4-7/5
|0 -2' -6
|Cv(b5)
| 12
| 12
|-
|-
Line 79: Line 624:
| 1-16/9-7/5
| 1-16/9-7/5
| werckismic
| werckismic
|1-14/11-10/7
|0 4 6
|C(^^b5)
| 12
| 12
|-
|-
Line 85: Line 633:
| 1-5/3-7/5
| 1-5/3-7/5
| starling
| starling
|1-6/5-10/7
|0 3' 6
|C^m(^^d5)
| 12
| 12
|-
|-
Line 91: Line 642:
| 1-10/9-7/5
| 1-10/9-7/5
| starling
| starling
|1-10/9-7/5
|0 -4' -6
|Cv2(b5)
| 12
| 12
|-
|-
Line 97: Line 651:
| 1-11/7-7/5
| 1-11/7-7/5
| werckismic
| werckismic
|1-14/11-16/9
|0 4 -2
|C7no5
| 12
| 12
|-
|-
Line 103: Line 660:
| 1-5/4-7/4
| 1-5/4-7/4
| otonal
| otonal
|1-5/4-7/4
|0 -2' -8'
|Cv7no5
| 16
| 16
|-
|-
Line 109: Line 669:
| 1-10/9-7/4
| 1-10/9-7/4
| werckismic
| werckismic
|1-10/9-7/4
1-8/7-14/11
|0 -4' -8'
0 8' 4
|Cv7v9no35
C,^9no5
| 16
| 16
|-
|-
Line 115: Line 681:
| 1-11/7-7/4
| 1-11/7-7/4
| werckismic
| werckismic
|1-9/5-16/7
1-10/9-14/11
|0 4' 8'
0 -4' 4
|C^7^9no35
C,v9no5
| 16
| 16
|-
|-
Line 121: Line 693:
| 1-7/5-7/4
| 1-7/5-7/4
| utonal
| utonal
|1-5/4-10/7
|0 -2' 6
|Cv(^^b5)
| 16
| 16
|-
|-
Line 127: Line 702:
| 1-4/3-7/6
| 1-4/3-7/6
| otonal
| otonal
|1-3/2-7/4
|0 1 -8'
|Cv7no3
| 18
| 18
|-
|-
Line 133: Line 711:
| 1-5/3-7/6
| 1-5/3-7/6
| otonal
| otonal
|1-7/6-5/3
1-6/5-7/5
|0 -9' -3'
0 3' -6
|Cvm6no5
C^dim
| 18
| 18
|-
|-
Line 139: Line 723:
| 1-7/5-7/6
| 1-7/5-7/6
| utonal
| utonal
|1-7/6-7/5
1-6/5-12/7
|0 -9' -6
0 3' 9'
|Cvdim
C^m6no5
| 18
| 18
|-
|-
Line 145: Line 735:
| 1-7/4-7/6
| 1-7/4-7/6
| utonal
| utonal
|1-7/6-7/4
|0 -9' -8'
|Cvm7no5
| 18
| 18
|-
|-
Line 151: Line 744:
| 1-5/4-11/10
| 1-5/4-11/10
| valinorsmic
| valinorsmic
|1-5/4-11/5
1-20/11-16/7
|0 -2' -10
0 10 8'
|Cv,vv9no5
C^^7^9no35
| 20
| 20
|-
|-
Line 157: Line 756:
| 1-11/7-11/10
| 1-11/7-11/10
| utonal
| utonal
|1-14/11-7/5
|0 4 -6
|C(b5)
| 20
| 20
|-
|-
Line 163: Line 765:
| 1-7/5-11/10
| 1-7/5-11/10
| otonal
| otonal
|1-11/10-7/5
1-14/11-20/11
|0 -10 -6
0 4 10
|Cvv2(b5)
C,^^7no5
| 20
| 20
|-
|-
Line 169: Line 777:
| 1-7/4-11/10
| 1-7/4-11/10
| valinorsmic
| valinorsmic
|1-7/4-11/5
1-5/4-45/28
|0 -8' -10
0 -2' 8'
|Cv7vv9no35
Cv,v9no5
| 20
| 20
|-
|-
Line 175: Line 789:
| 1-4/3-14/9
| 1-4/3-14/9
| otonal
| otonal
|1-7/6-3/2
|0 -9' 1
|Cvm
| 20
| 20
|-
|-
Line 181: Line 798:
| 1-16/9-14/9
| 1-16/9-14/9
| otonal
| otonal
|1-7/4-9/4
1-9/7-16/7
|0 -8' 2
0 10' 8'
|Cv9no35
C^,^9no5
| 20
| 20
|-
|-
Line 187: Line 810:
| 1-10/9-14/9
| 1-10/9-14/9
| otonal
| otonal
|1-9/7-10/7
|0 10' 6
|C^(^^b5)
| 20
| 20
|-
|-
Line 193: Line 819:
| 1-7/5-14/9
| 1-7/5-14/9
| utonal
| utonal
|1-9/7-9/5
|0 10' 4'
|C^7no5
| 20
| 20
|-
|-
Line 199: Line 828:
| 1-7/4-14/9
| 1-7/4-14/9
| utonal
| utonal
|1-9/7-9/4
1-8/7-16/9
|0 10' 2
0 8' -2
|C^,9no5
C^2,7no5
| 20
| 20
|-
|-
Line 205: Line 840:
| 1-7/6-14/9
| 1-7/6-14/9
| utonal
| utonal
|1-9/7-3/2
|0 10' 1
|C^
| 20
| 20
|-
|-
Line 211: Line 849:
| 1-5/4-11/8
| 1-5/4-11/8
| otonal
| otonal
|1-5/4-11/8
|0 -2' -12'
|Cv(vb5)
| 24
| 24
|-
|-
Line 217: Line 858:
| 1-16/9-11/8
| 1-16/9-11/8
| pentacircle
| pentacircle
|1-9/7-16/11
|0 10' 12'
|C^,^#11no5
| 24
| 24
|-
|-
Line 223: Line 867:
| 1-11/7-11/8
| 1-11/7-11/8
| utonal
| utonal
|1-14/11-7/4
|0 4 -8'
|C,v7no5
| 24
| 24
|-
|-
Line 229: Line 876:
| 1-7/4-11/8
| 1-7/4-11/8
| otonal
| otonal
|1-14/11-16/11
|0 4 12'
|C,^#11no5
| 24
| 24
|-
|-
Line 235: Line 885:
| 1-11/10-11/8
| 1-11/10-11/8
| utonal
| utonal
|1-11/10-11/8
1-5/4-20/11
|0 -10 -12'
0 -2' 10
|Cvv2(vb5)
Cv,^^7no5
| 24
| 24
|-
|-
Line 241: Line 897:
| 1-14/9-11/8
| 1-14/9-11/8
| pentacircle
| pentacircle
|1-9/7-16/9
|0 10' -2
|C^,7no5
| 24
| 24
|-
|-
Line 247: Line 906:
| 1-4/3-11/6
| 1-4/3-11/6
| otonal
| otonal
|1-11/8-3/2
|0 -12' 1
|C,vd5no3
| 26
| 26
|-
|-
Line 253: Line 915:
| 1-5/3-11/6
| 1-5/3-11/6
| otonal
| otonal
|
|
|
| 26
| 26
|-
|-
Line 259: Line 924:
| 1-11/7-11/6
| 1-11/7-11/6
| utonal
| utonal
|
|
|
| 26
| 26
|-
|-
Line 265: Line 933:
| 1-7/6-11/6
| 1-7/6-11/6
| otonal
| otonal
|
|
|
| 26
| 26
|-
|-
Line 271: Line 942:
| 1-11/10-11/6
| 1-11/10-11/6
| utonal
| utonal
|
|
|
| 26
| 26
|-
|-
Line 277: Line 951:
| 1-11/8-11/6
| 1-11/8-11/6
| utonal
| utonal
|
|
|
| 26
| 26
|-
|-
Line 283: Line 960:
| 1-4/3-11/9
| 1-4/3-11/9
| otonal
| otonal
|
|
|
| 28
| 28
|-
|-
Line 289: Line 969:
| 1-16/9-11/9
| 1-16/9-11/9
| otonal
| otonal
|
|
|
| 28
| 28
|-
|-
Line 295: Line 978:
| 1-10/9-11/9
| 1-10/9-11/9
| otonal
| otonal
|
|
|
| 28
| 28
|-
|-
Line 301: Line 987:
| 1-11/7-11/9
| 1-11/7-11/9
| utonal
| utonal
|
|
|
| 28
| 28
|-
|-
Line 307: Line 996:
| 1-7/5-11/9
| 1-7/5-11/9
| werckismic
| werckismic
|
|
|
| 28
| 28
|-
|-
Line 313: Line 1,005:
| 1-7/4-11/9
| 1-7/4-11/9
| werckismic
| werckismic
|
|
|
| 28
| 28
|-
|-
Line 319: Line 1,014:
| 1-11/10-11/9
| 1-11/10-11/9
| utonal
| utonal
|
|
|
| 28
| 28
|-
|-
Line 325: Line 1,023:
| 1-14/9-11/9
| 1-14/9-11/9
| otonal
| otonal
|
|
|
| 28
| 28
|-
|-
Line 331: Line 1,032:
| 1-11/8-11/9
| 1-11/8-11/9
| utonal
| utonal
|
|
|
| 28
| 28
|-
|-
Line 337: Line 1,041:
| 1-11/6-11/9
| 1-11/6-11/9
| utonal
| utonal
|
|
|
| 28
| 28
|}
|}

Revision as of 07:49, 23 November 2024

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⟩.

Diaschismic's two genchains, fifthward halves
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:

Diaschismic's two genchains, fourthward halves
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
Diaschismic's two genchains, with cents in 34edo
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
Retrieved from "https://en.xen.wiki/index.php?title=Diaschismic/Chords&oldid=167276"