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Diaschismic/Chords: Difference between revisions

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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
|}
|}
Retrieved from "https://en.xen.wiki/w/Diaschismic/Chords"