Valentine/Chords: Difference between revisions

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Jdfreivald (talk | contribs)
autopatrolled, emailconfirmed
62 edits
Jdfreivald (talk | contribs)
autopatrolled, emailconfirmed
62 edits
→Tetrads: Added inversions
Line 484: Line 484:
! Transversal
! Transversal
! Type
! Type
! As generated
! 1st inversion
! 2nd inversion
! 3rd inversion
|-
|-
| 1
| 1
Line 489: Line 493:
| 1-11/10-6/5-11/8
| 1-11/10-6/5-11/8
| zeus
| zeus
| 1/1-11/10-6/5-11/8
| 1/1-11/10-5/4-11/6
| 1/1-8/7-5/3-11/6
| 1/1-16/11-8/5-7/4
|-
|-
| 2
| 2
Line 494: Line 502:
| 1-11/10-5/4-11/8
| 1-11/10-5/4-11/8
| valinorsmic
| valinorsmic
| 1/1-11/10-5/4-11/8
| 1/1-8/7-5/4-11/6
| 1/1-11/10-8/5-7/4
| 1/1-16/11-8/5-11/6
|-
|-
| 3
| 3
Line 499: Line 511:
| 1-8/7-5/4-11/8
| 1-8/7-5/4-11/8
| zeus
| zeus
| 1/1-8/7-5/4-11/8
| 1/1-11/10-6/5-7/4
| 1/1-11/10-8/5-11/6
| 1/1-16/11-5/3-11/6
|-
|-
| 4
| 4
Line 504: Line 520:
| 1-8/7-5/4-10/7
| 1-8/7-5/4-10/7
| valinorsmic
| valinorsmic
| 1/1-8/7-5/4-10/7
| 1/1-11/10-5/4-7/4
| 1/1-8/7-8/5-11/6
| 1/1-7/5-8/5-7/4
|-
|-
| 5
| 5
Line 509: Line 529:
| 1-12/11-6/5-3/2
| 1-12/11-6/5-3/2
| utonal
| utonal
| 1/1-12/11-6/5-3/2
| 1/1-11/10-11/8-11/6
| 1/1-5/4-5/3-11/6
| 1/1-4/3-16/11-8/5
|-
|-
| 6
| 6
Line 514: Line 538:
| 1-11/10-5/4-3/2
| 1-11/10-5/4-3/2
| zeus
| zeus
| 1/1-11/10-5/4-3/2
| 1/1-8/7-11/8-11/6
| 1/1-6/5-8/5-7/4
| 1/1-4/3-16/11-5/3
|-
|-
| 7
| 7
Line 519: Line 547:
| 1-11/10-11/8-3/2
| 1-11/10-11/8-3/2
| biyatismic
| biyatismic
| 1/1-11/10-11/8-3/2
| 1/1-5/4-11/8-11/6
| 1/1-11/10-16/11-8/5
| 1/1-4/3-16/11-11/6
|-
|-
| 8
| 8
Line 524: Line 556:
| 1-6/5-11/8-3/2
| 1-6/5-11/8-3/2
| zeus
| zeus
| 1/1-6/5-11/8-3/2
| 1/1-8/7-5/4-5/3
| 1/1-11/10-16/11-7/4
| 1/1-4/3-8/5-11/6
|-
|-
| 9
| 9
Line 529: Line 565:
| 1-5/4-11/8-3/2
| 1-5/4-11/8-3/2
| otonal
| otonal
| 1/1-5/4-11/8-3/2
| 1/1-11/10-6/5-8/5
| 1/1-11/10-16/11-11/6
| 1/1-4/3-5/3-11/6
|-
|-
| 10
| 10
Line 534: Line 574:
| 1-11/10-5/4-11/7
| 1-11/10-5/4-11/7
| valinorsmic
| valinorsmic
| 1/1-11/10-5/4-11/7
| 1/1-8/7-10/7-11/6
| 1/1-5/4-8/5-7/4
| 1/1-14/11-7/5-8/5
|-
|-
| 11
| 11
Line 539: Line 583:
| 1-8/7-5/4-11/7
| 1-8/7-5/4-11/7
| valinorsmic
| valinorsmic
| 1/1-8/7-5/4-11/7
| 1/1-11/10-11/8-7/4
| 1/1-5/4-8/5-11/6
| 1/1-14/11-16/11-8/5
|-
|-
| 12
| 12
Line 544: Line 592:
| 1-11/10-11/8-11/7
| 1-11/10-11/8-11/7
| utonal
| utonal
| 1/1-11/10-11/8-11/7
| 1/1-5/4-10/7-11/6
| 1/1-8/7-16/11-8/5
| 1/1-14/11-7/5-7/4
|-
|-
| 13
| 13
Line 549: Line 601:
| 1-8/7-11/8-11/7
| 1-8/7-11/8-11/7
| keenanismic
| keenanismic
| 1/1-8/7-11/8-11/7
| 1/1-6/5-11/8-7/4
| 1/1-8/7-16/11-5/3
| 1/1-14/11-16/11-7/4
|-
|-
| 14
| 14
Line 554: Line 610:
| 1-5/4-11/8-11/7
| 1-5/4-11/8-11/7
| valinorsmic
| valinorsmic
| 1/1-5/4-11/8-11/7
| 1/1-11/10-5/4-8/5
| 1/1-8/7-16/11-11/6
| 1/1-14/11-8/5-7/4
|-
|-
| 15
| 15
Line 559: Line 619:
| 1-8/7-10/7-11/7
| 1-8/7-10/7-11/7
| otonal
| otonal
| 1/1-8/7-10/7-11/7
| 1/1-5/4-11/8-7/4
| 1/1-11/10-7/5-8/5
| 1/1-14/11-16/11-11/6
|-
|-
| 16
| 16
Line 564: Line 628:
| 1-5/4-10/7-11/7
| 1-5/4-10/7-11/7
| valinorsmic
| valinorsmic
| 1/1-5/4-10/7-11/7
| 1/1-8/7-5/4-8/5
| 1/1-11/10-7/5-7/4
| 1/1-14/11-8/5-11/6
|-
|-
| 17
| 17
Line 569: Line 637:
| 1-11/10-6/5-18/11
| 1-11/10-6/5-18/11
| biyatismic
| biyatismic
| 1/1-11/10-6/5-18/11
| 1/1-11/10-3/2-11/6
| 1/1-11/8-5/3-11/6
| 1/1-11/9-4/3-16/11
|-
|-
| 18
| 18
Line 574: Line 646:
| 1-11/10-11/8-18/11
| 1-11/10-11/8-18/11
| biyatismic
| biyatismic
| 1/1-11/10-11/8-18/11
| 1/1-5/4-3/2-11/6
| 1/1-6/5-16/11-8/5
| 1/1-11/9-4/3-5/3
|-
|-
| 19
| 19
Line 579: Line 655:
| 1-8/7-11/8-18/11
| 1-8/7-11/8-18/11
| valentine
| valentine
| 1/1-8/7-11/8-18/11
| 1/1-6/5-10/7-7/4
| 1/1-6/5-16/11-5/3
| 1/1-11/9-7/5-5/3
|-
|-
| 20
| 20
Line 584: Line 664:
| 1-6/5-11/8-18/11
| 1-6/5-11/8-18/11
| zeus
| zeus
| 1/1-6/5-11/8-18/11
| 1/1-8/7-11/8-5/3
| 1/1-6/5-16/11-7/4
| 1/1-11/9-16/11-5/3
|-
|-
| 21
| 21
Line 589: Line 673:
| 1-8/7-10/7-18/11
| 1-8/7-10/7-18/11
| werckismic
| werckismic
| 1/1-8/7-10/7-18/11
| 1/1-5/4-10/7-7/4
| 1/1-8/7-7/5-8/5
| 1/1-11/9-7/5-7/4
|-
|-
| 22
| 22
Line 594: Line 682:
| 1-6/5-10/7-18/11
| 1-6/5-10/7-18/11
| valentine
| valentine
| 1/1-6/5-10/7-18/11
| 1/1-6/5-11/8-5/3
| 1/1-8/7-7/5-5/3
| 1/1-11/9-16/11-7/4
|-
|-
| 23
| 23
Line 599: Line 691:
| 1-12/11-3/2-18/11
| 1-12/11-3/2-18/11
| ambitonal
| ambitonal
| 1/1-12/11-3/2-18/11
| 1/1-11/8-3/2-11/6
| 1/1-11/10-4/3-16/11
| 1/1-11/9-4/3-11/6
|-
|-
| 24
| 24
Line 604: Line 700:
| 1-6/5-3/2-18/11
| 1-6/5-3/2-18/11
| biyatismic
| biyatismic
| 1/1-6/5-3/2-18/11
| 1/1-5/4-11/8-5/3
| 1/1-11/10-4/3-8/5
| 1/1-11/9-16/11-11/6
|-
|-
| 25
| 25
Line 609: Line 709:
| 1-11/8-3/2-18/11
| 1-11/8-3/2-18/11
| biyatismic
| biyatismic
| 1/1-11/8-3/2-18/11
| 1/1-11/10-6/5-16/11
| 1/1-11/10-4/3-11/6
| 1/1-11/9-5/3-11/6
|-
|-
| 26
| 26
Line 614: Line 718:
| 1-12/11-6/5-12/7
| 1-12/11-6/5-12/7
| utonal
| utonal
| 1/1-12/11-6/5-12/7
| 1/1-11/10-11/7-11/6
| 1/1-10/7-5/3-11/6
| 1/1-7/6-14/11-7/5
|-
|-
| 27
| 27
Line 619: Line 727:
| 1-11/10-5/4-12/7
| 1-11/10-5/4-12/7
| zeus
| zeus
| 1/1-11/10-5/4-12/7
| 1/1-8/7-11/7-11/6
| 1/1-11/8-8/5-7/4
| 1/1-7/6-14/11-16/11
|-
|-
| 28
| 28
Line 624: Line 736:
| 1-8/7-5/4-12/7
| 1-8/7-5/4-12/7
| zeus
| zeus
| 1/1-8/7-5/4-12/7
| 1/1-11/10-3/2-7/4
| 1/1-11/8-8/5-11/6
| 1/1-7/6-4/3-16/11
|-
|-
| 29
| 29
Line 629: Line 745:
| 1-11/10-11/8-12/7
| 1-11/10-11/8-12/7
| zeus
| zeus
| 1/1-11/10-11/8-12/7
| 1/1-5/4-11/7-11/6
| 1/1-5/4-16/11-8/5
| 1/1-7/6-14/11-8/5
|-
|-
| 30
| 30
Line 634: Line 754:
| 1-8/7-11/8-12/7
| 1-8/7-11/8-12/7
| keenanismic
| keenanismic
| 1/1-8/7-11/8-12/7
| 1/1-6/5-3/2-7/4
| 1/1-5/4-16/11-5/3
| 1/1-7/6-4/3-8/5
|-
|-
| 31
| 31
Line 639: Line 763:
| 1-6/5-11/8-12/7
| 1-6/5-11/8-12/7
| keenanismic
| keenanismic
| 1/1-6/5-11/8-12/7
| 1/1-8/7-10/7-5/3
| 1/1-5/4-16/11-7/4
| 1/1-7/6-7/5-8/5
|-
|-
| 32
| 32
Line 644: Line 772:
| 1-5/4-11/8-12/7
| 1-5/4-11/8-12/7
| keenanismic
| keenanismic
| 1/1-5/4-11/8-12/7
| 1/1-11/10-11/8-8/5
| 1/1-5/4-16/11-11/6
| 1/1-7/6-16/11-8/5
|-
|-
| 33
| 33
Line 649: Line 781:
| 1-8/7-10/7-12/7
| 1-8/7-10/7-12/7
| otonal
| otonal
| 1/1-8/7-10/7-12/7
| 1/1-5/4-3/2-7/4
| 1/1-6/5-7/5-8/5
| 1/1-7/6-4/3-5/3
|-
|-
| 34
| 34
Line 654: Line 790:
| 1-6/5-10/7-12/7
| 1-6/5-10/7-12/7
| starling
| starling
| 1/1-6/5-10/7-12/7
| 1/1-6/5-10/7-5/3
| 1/1-6/5-7/5-5/3
| 1/1-7/6-7/5-5/3
|-
|-
| 35
| 35
Line 659: Line 799:
| 1-5/4-10/7-12/7
| 1-5/4-10/7-12/7
| keenanismic
| keenanismic
| 1/1-5/4-10/7-12/7
| 1/1-8/7-11/8-8/5
| 1/1-6/5-7/5-7/4
| 1/1-7/6-16/11-5/3
|-
|-
| 36
| 36
Line 664: Line 808:
| 1-12/11-3/2-12/7
| 1-12/11-3/2-12/7
| utonal
| utonal
| 1/1-12/11-3/2-12/7
| 1/1-11/8-11/7-11/6
| 1/1-8/7-4/3-16/11
| 1/1-7/6-14/11-7/4
|-
|-
| 37
| 37
Line 669: Line 817:
| 1-6/5-3/2-12/7
| 1-6/5-3/2-12/7
| utonal
| utonal
| 1/1-6/5-3/2-12/7
| 1/1-5/4-10/7-5/3
| 1/1-8/7-4/3-8/5
| 1/1-7/6-7/5-7/4
|-
|-
| 38
| 38
Line 674: Line 826:
| 1-5/4-3/2-12/7
| 1-5/4-3/2-12/7
| keenanismic
| keenanismic
| 1/1-5/4-3/2-12/7
| 1/1-6/5-11/8-8/5
| 1/1-8/7-4/3-5/3
| 1/1-7/6-16/11-7/4
|-
|-
| 39
| 39
Line 679: Line 835:
| 1-11/8-3/2-12/7
| 1-11/8-3/2-12/7
| zeus
| zeus
| 1/1-11/8-3/2-12/7
| 1/1-11/10-5/4-16/11
| 1/1-8/7-4/3-11/6
| 1/1-7/6-8/5-7/4
|-
|-
| 40
| 40
Line 684: Line 844:
| 1-11/10-11/7-12/7
| 1-11/10-11/7-12/7
| biyatismic
| biyatismic
| 1/1-11/10-11/7-12/7
| 1/1-10/7-11/7-11/6
| 1/1-11/10-14/11-7/5
| 1/1-7/6-14/11-11/6
|-
|-
| 41
| 41
Line 689: Line 853:
| 1-8/7-11/7-12/7
| 1-8/7-11/7-12/7
| otonal
| otonal
| 1/1-8/7-11/7-12/7
| 1/1-11/8-3/2-7/4
| 1/1-11/10-14/11-16/11
| 1/1-7/6-4/3-11/6
|-
|-
| 42
| 42
Line 694: Line 862:
| 1-5/4-11/7-12/7
| 1-5/4-11/7-12/7
| zeus
| zeus
| 1/1-5/4-11/7-12/7
| 1/1-5/4-11/8-8/5
| 1/1-11/10-14/11-8/5
| 1/1-7/6-16/11-11/6
|-
|-
| 43
| 43
Line 699: Line 871:
| 1-11/8-11/7-12/7
| 1-11/8-11/7-12/7
| zeus
| zeus
| 1/1-11/8-11/7-12/7
| 1/1-8/7-5/4-16/11
| 1/1-11/10-14/11-7/4
| 1/1-7/6-8/5-11/6
|-
|-
| 44
| 44
Line 704: Line 880:
| 1-10/7-11/7-12/7
| 1-10/7-11/7-12/7
| otonal
| otonal
| 1/1-10/7-11/7-12/7
| 1/1-11/10-6/5-7/5
| 1/1-11/10-14/11-11/6
| 1/1-7/6-5/3-11/6
|-
|-
| 45
| 45
Line 709: Line 889:
| 1-11/10-6/5-9/5
| 1-11/10-6/5-9/5
| otonal
| otonal
| 1/1-11/10-6/5-9/5
| 1/1-11/10-18/11-11/6
| 1/1-3/2-5/3-11/6
| 1/1-10/9-11/9-4/3
|-
|-
| 46
| 46
Line 714: Line 898:
| 1-11/10-5/4-9/5
| 1-11/10-5/4-9/5
| thrush
| thrush
| 1/1-11/10-5/4-9/5
| 1/1-8/7-18/11-11/6
| 1/1-10/7-8/5-7/4
| 1/1-10/9-11/9-7/5
|-
|-
| 47
| 47
Line 719: Line 907:
| 1-8/7-5/4-9/5
| 1-8/7-5/4-9/5
| thrush
| thrush
| 1/1-8/7-5/4-9/5
| 1/1-11/10-11/7-7/4
| 1/1-10/7-8/5-11/6
| 1/1-10/9-14/11-7/5
|-
|-
| 48
| 48
Line 724: Line 916:
| 1-8/7-10/7-9/5
| 1-8/7-10/7-9/5
| thrush
| thrush
| 1/1-8/7-10/7-9/5
| 1/1-5/4-11/7-7/4
| 1/1-5/4-7/5-8/5
| 1/1-10/9-14/11-8/5
|-
|-
| 49
| 49
Line 729: Line 925:
| 1-6/5-10/7-9/5
| 1-6/5-10/7-9/5
| starling
| starling
| 1/1-6/5-10/7-9/5
| 1/1-6/5-3/2-5/3
| 1/1-5/4-7/5-5/3
| 1/1-10/9-4/3-8/5
|-
|-
| 50
| 50
Line 734: Line 934:
| 1-5/4-10/7-9/5
| 1-5/4-10/7-9/5
| starling
| starling
| 1/1-5/4-10/7-9/5
| 1/1-8/7-10/7-8/5
| 1/1-5/4-7/5-7/4
| 1/1-10/9-7/5-8/5
|-
|-
| 51
| 51
Line 739: Line 943:
| 1-11/10-3/2-9/5
| 1-11/10-3/2-9/5
| biyatismic
| biyatismic
| 1/1-11/10-3/2-9/5
| 1/1-11/8-18/11-11/6
| 1/1-6/5-4/3-16/11
| 1/1-10/9-11/9-5/3
|-
|-
| 52
| 52
Line 744: Line 952:
| 1-6/5-3/2-9/5
| 1-6/5-3/2-9/5
| ambitonal
| ambitonal
| 1/1-6/5-3/2-9/5
| 1/1-5/4-3/2-5/3
| 1/1-6/5-4/3-8/5
| 1/1-10/9-4/3-5/3
|-
|-
| 53
| 53
Line 749: Line 961:
| 1-5/4-3/2-9/5
| 1-5/4-3/2-9/5
| starling
| starling
| 1/1-5/4-3/2-9/5
| 1/1-6/5-10/7-8/5
| 1/1-6/5-4/3-5/3
| 1/1-10/9-7/5-5/3
|-
|-
| 54
| 54
Line 754: Line 970:
| 1-11/10-11/7-9/5
| 1-11/10-11/7-9/5
| werckismic
| werckismic
| 1/1-11/10-11/7-9/5
| 1/1-10/7-18/11-11/6
| 1/1-8/7-14/11-7/5
| 1/1-10/9-11/9-7/4
|-
|-
| 55
| 55
Line 759: Line 979:
| 1-8/7-11/7-9/5
| 1-8/7-11/7-9/5
| werckismic
| werckismic
| 1/1-8/7-11/7-9/5
| 1/1-11/8-11/7-7/4
| 1/1-8/7-14/11-16/11
| 1/1-10/9-14/11-7/4
|-
|-
| 56
| 56
Line 764: Line 988:
| 1-5/4-11/7-9/5
| 1-5/4-11/7-9/5
| thrush
| thrush
| 1/1-5/4-11/7-9/5
| 1/1-5/4-10/7-8/5
| 1/1-8/7-14/11-8/5
| 1/1-10/9-7/5-7/4
|-
|-
| 57
| 57
Line 769: Line 997:
| 1-10/7-11/7-9/5
| 1-10/7-11/7-9/5
| thrush
| thrush
| 1/1-10/7-11/7-9/5
| 1/1-11/10-5/4-7/5
| 1/1-8/7-14/11-11/6
| 1/1-10/9-8/5-7/4
|-
|-
| 58
| 58
Line 774: Line 1,006:
| 1-11/10-18/11-9/5
| 1-11/10-18/11-9/5
| biyatismic
| biyatismic
| 1/1-11/10-18/11-9/5
| 1/1-3/2-18/11-11/6
| 1/1-11/10-11/9-4/3
| 1/1-10/9-11/9-11/6
|-
|-
| 59
| 59
Line 779: Line 1,015:
| 1-8/7-18/11-9/5
| 1-8/7-18/11-9/5
| werckismic
| werckismic
| 1/1-8/7-18/11-9/5
| 1/1-10/7-11/7-7/4
| 1/1-11/10-11/9-7/5
| 1/1-10/9-14/11-11/6
|-
|-
| 60
| 60
Line 784: Line 1,024:
| 1-6/5-18/11-9/5
| 1-6/5-18/11-9/5
| biyatismic
| biyatismic
| 1/1-6/5-18/11-9/5
| 1/1-11/8-3/2-5/3
| 1/1-11/10-11/9-16/11
| 1/1-10/9-4/3-11/6
|-
|-
| 61
| 61
Line 789: Line 1,033:
| 1-10/7-18/11-9/5
| 1-10/7-18/11-9/5
| thrush
| thrush
| 1/1-10/7-18/11-9/5
| 1/1-8/7-5/4-7/5
| 1/1-11/10-11/9-7/4
| 1/1-10/9-8/5-11/6
|-
|-
| 62
| 62
Line 794: Line 1,042:
| 1-3/2-18/11-9/5
| 1-3/2-18/11-9/5
| utonal
| utonal
| 1/1-3/2-18/11-9/5
| 1/1-11/10-6/5-4/3
| 1/1-11/10-11/9-11/6
| 1/1-10/9-5/3-11/6
|-
|-
| 63
| 63
Line 799: Line 1,051:
| 1-5/4-11/8-9/8
| 1-5/4-11/8-9/8
| otonal
| otonal
| 1/1-9/8-5/4-11/8
| 1/1-10/9-11/9-16/9
| 1/1-11/10-8/5-9/5
| 1/1-16/11-18/11-11/6
|-
|-
| 64
| 64
Line 804: Line 1,060:
| 1-5/4-10/7-9/8
| 1-5/4-10/7-9/8
| werckismic
| werckismic
| 1/1-9/8-5/4-10/7
| 1/1-10/9-14/11-16/9
| 1/1-8/7-8/5-9/5
| 1/1-7/5-11/7-7/4
|-
|-
| 65
| 65
Line 809: Line 1,069:
| 1-5/4-3/2-9/8
| 1-5/4-3/2-9/8
| otonal
| otonal
| 1/1-9/8-5/4-3/2
| 1/1-10/9-4/3-16/9
| 1/1-6/5-8/5-9/5
| 1/1-4/3-3/2-5/3
|-
|-
| 66
| 66
Line 814: Line 1,078:
| 1-11/8-3/2-9/8
| 1-11/8-3/2-9/8
| otonal
| otonal
| 1/1-9/8-11/8-3/2
| 1/1-11/9-4/3-16/9
| 1/1-11/10-16/11-18/11
| 1/1-4/3-3/2-11/6
|-
|-
| 67
| 67
Line 819: Line 1,087:
| 1-5/4-11/7-9/8
| 1-5/4-11/7-9/8
| thrush
| thrush
| 1/1-9/8-5/4-11/7
| 1/1-10/9-7/5-16/9
| 1/1-5/4-8/5-9/5
| 1/1-14/11-10/7-8/5
|-
|-
| 68
| 68
Line 824: Line 1,096:
| 1-11/8-11/7-9/8
| 1-11/8-11/7-9/8
| werckismic
| werckismic
| 1/1-9/8-11/8-11/7
| 1/1-11/9-7/5-16/9
| 1/1-8/7-16/11-18/11
| 1/1-14/11-10/7-7/4
|-
|-
| 69
| 69
Line 829: Line 1,105:
| 1-10/7-11/7-9/8
| 1-10/7-11/7-9/8
| werckismic
| werckismic
| 1/1-9/8-10/7-11/7
| 1/1-14/11-7/5-16/9
| 1/1-11/10-7/5-11/7
| 1/1-14/11-10/7-11/6
|-
|-
| 70
| 70
Line 834: Line 1,114:
| 1-11/8-18/11-9/8
| 1-11/8-18/11-9/8
| biyatismic
| biyatismic
| 1/1-9/8-11/8-18/11
| 1/1-11/9-16/11-16/9
| 1/1-6/5-16/11-18/11
| 1/1-11/9-11/8-5/3
|-
|-
| 71
| 71
Line 839: Line 1,123:
| 1-10/7-18/11-9/8
| 1-10/7-18/11-9/8
| werckismic
| werckismic
| 1/1-9/8-10/7-18/11
| 1/1-14/11-16/11-16/9
| 1/1-8/7-7/5-11/7
| 1/1-11/9-11/8-7/4
|-
|-
| 72
| 72
Line 844: Line 1,132:
| 1-3/2-18/11-9/8
| 1-3/2-18/11-9/8
| utonal
| utonal
| 1/1-9/8-3/2-18/11
| 1/1-4/3-16/11-16/9
| 1/1-11/10-4/3-3/2
| 1/1-11/9-11/8-11/6
|-
|-
| 73
| 73
Line 849: Line 1,141:
| 1-5/4-9/5-9/8
| 1-5/4-9/5-9/8
| starling
| starling
| 1/1-9/8-5/4-9/5
| 1/1-10/9-8/5-16/9
| 1/1-10/7-8/5-9/5
| 1/1-10/9-5/4-25/18
|-
|-
| 74
| 74
Line 854: Line 1,150:
| 1-10/7-9/5-9/8
| 1-10/7-9/5-9/8
| thrush
| thrush
| 1/1-9/8-10/7-9/5
| 1/1-14/11-8/5-16/9
| 1/1-5/4-7/5-11/7
| 1/1-10/9-5/4-8/5
|-
|-
| 75
| 75
Line 859: Line 1,159:
| 1-3/2-9/5-9/8
| 1-3/2-9/5-9/8
| utonal
| utonal
| 1/1-9/8-3/2-9/5
| 1/1-4/3-8/5-16/9
| 1/1-6/5-4/3-3/2
| 1/1-10/9-5/4-5/3
|-
|-
| 76
| 76
Line 864: Line 1,168:
| 1-11/7-9/5-9/8
| 1-11/7-9/5-9/8
| werckismic
| werckismic
| 1/1-9/8-11/7-9/5
| 1/1-7/5-8/5-16/9
| 1/1-8/7-14/11-10/7
| 1/1-10/9-5/4-7/4
|-
|-
| 77
| 77
Line 869: Line 1,177:
| 1-18/11-9/5-9/8
| 1-18/11-9/5-9/8
| utonal
| utonal
| 1/1-9/8-18/11-9/5
| 1/1-16/11-8/5-16/9
| 1/1-11/10-11/9-11/8
| 1/1-10/9-5/4-11/6
|-
|-
| 78
| 78
Line 874: Line 1,186:
| 1-8/7-10/7-9/7
| 1-8/7-10/7-9/7
| otonal
| otonal
| 1/1-8/7-9/7-10/7
| 1/1-9/8-5/4-7/4
| 1/1-10/9-14/9-16/9
| 1/1-7/5-8/5-9/5
|-
|-
| 79
| 79
Line 879: Line 1,195:
| 1-8/7-11/7-9/7
| 1-8/7-11/7-9/7
| otonal
| otonal
| 1/1-8/7-9/7-11/7
| 1/1-9/8-11/8-7/4
| 1/1-11/9-14/9-16/9
| 1/1-14/11-16/11-18/11
|-
|-
| 80
| 80
Line 884: Line 1,204:
| 1-10/7-11/7-9/7
| 1-10/7-11/7-9/7
| otonal
| otonal
| 1/1-9/7-10/7-11/7
| 1/1-10/9-11/9-14/9
| 1/1-11/10-7/5-9/5
| 1/1-14/11-18/11-11/6
|-
|-
| 81
| 81
Line 889: Line 1,213:
| 1-8/7-18/11-9/7
| 1-8/7-18/11-9/7
| werckismic
| werckismic
| 1/1-8/7-9/7-18/11
| 1/1-9/8-10/7-7/4
| 1/1-14/11-14/9-16/9
| 1/1-11/9-7/5-11/7
|-
|-
| 82
| 82
Line 894: Line 1,222:
| 1-10/7-18/11-9/7
| 1-10/7-18/11-9/7
| werckismic
| werckismic
| 1/1-9/7-10/7-18/11
| 1/1-10/9-14/11-14/9
| 1/1-8/7-7/5-9/5
| 1/1-11/9-11/7-7/4
|-
|-
| 83
| 83
Line 899: Line 1,231:
| 1-3/2-18/11-9/7
| 1-3/2-18/11-9/7
| utonal
| utonal
| 1/1-9/7-3/2-18/11
| 1/1-7/6-14/11-14/9
| 1/1-11/10-4/3-12/7
| 1/1-11/9-11/7-11/6
|-
|-
| 84
| 84
Line 904: Line 1,240:
| 1-8/7-12/7-9/7
| 1-8/7-12/7-9/7
| otonal
| otonal
| 1/1-8/7-9/7-12/7
| 1/1-9/8-3/2-7/4
| 1/1-4/3-14/9-16/9
| 1/1-7/6-4/3-3/2
|-
|-
| 85
| 85
Line 909: Line 1,249:
| 1-10/7-12/7-9/7
| 1-10/7-12/7-9/7
| otonal
| otonal
| 1/1-9/7-10/7-12/7
| 1/1-10/9-4/3-14/9
| 1/1-6/5-7/5-9/5
| 1/1-7/6-3/2-5/3
|-
|-
| 86
| 86
Line 914: Line 1,258:
| 1-3/2-12/7-9/7
| 1-3/2-12/7-9/7
| ambitonal
| ambitonal
| 1/1-9/7-3/2-12/7
| 1/1-7/6-4/3-14/9
| 1/1-8/7-4/3-12/7
| 1/1-7/6-3/2-7/4
|-
|-
| 87
| 87
Line 919: Line 1,267:
| 1-11/7-12/7-9/7
| 1-11/7-12/7-9/7
| otonal
| otonal
| 1/1-9/7-11/7-12/7
| 1/1-11/9-4/3-14/9
| 1/1-11/10-14/11-18/11
| 1/1-7/6-3/2-11/6
|-
|-
| 88
| 88
Line 924: Line 1,276:
| 1-8/7-9/5-9/7
| 1-8/7-9/5-9/7
| werckismic
| werckismic
| 1/1-8/7-9/7-9/5
| 1/1-9/8-11/7-7/4
| 1/1-7/5-14/9-16/9
| 1/1-10/9-14/11-10/7
|-
|-
| 89
| 89
Line 929: Line 1,285:
| 1-10/7-9/5-9/7
| 1-10/7-9/5-9/7
| starling
| starling
| 1/1-9/7-10/7-9/5
| 1/1-10/9-7/5-14/9
| 1/1-5/4-7/5-9/5
| 1/1-10/9-10/7-8/5
|-
|-
| 90
| 90
Line 934: Line 1,294:
| 1-3/2-9/5-9/7
| 1-3/2-9/5-9/7
| utonal
| utonal
| 1/1-9/7-3/2-9/5
| 1/1-7/6-7/5-14/9
| 1/1-6/5-4/3-12/7
| 1/1-10/9-10/7-5/3
|-
|-
| 91
| 91
Line 939: Line 1,303:
| 1-11/7-9/5-9/7
| 1-11/7-9/5-9/7
| werckismic
| werckismic
| 1/1-9/7-11/7-9/5
| 1/1-11/9-7/5-14/9
| 1/1-8/7-14/11-18/11
| 1/1-10/9-10/7-7/4
|-
|-
| 92
| 92
Line 944: Line 1,312:
| 1-18/11-9/5-9/7
| 1-18/11-9/5-9/7
| utonal
| utonal
| 1/1-9/7-18/11-9/5
| 1/1-14/11-7/5-14/9
| 1/1-11/10-11/9-11/7
| 1/1-10/9-10/7-11/6
|-
|-
| 93
| 93
Line 949: Line 1,321:
| 1-10/7-9/8-9/7
| 1-10/7-9/8-9/7
| werckismic
| werckismic
| 1/1-9/8-9/7-10/7
| 1/1-8/7-14/11-16/9
| 1/1-10/9-14/9-7/4
| 1/1-7/5-11/7-9/5
|-
|-
| 94
| 94
Line 954: Line 1,330:
| 1-3/2-9/8-9/7
| 1-3/2-9/8-9/7
| utonal
| utonal
| 1/1-9/8-9/7-3/2
| 1/1-8/7-4/3-16/9
| 1/1-7/6-14/9-7/4
| 1/1-4/3-3/2-12/7
|-
|-
| 95
| 95
Line 959: Line 1,339:
| 1-11/7-9/8-9/7
| 1-11/7-9/8-9/7
| werckismic
| werckismic
| 1/1-9/8-9/7-11/7
| 1/1-8/7-7/5-16/9
| 1/1-11/9-14/9-7/4
| 1/1-14/11-10/7-18/11
|-
|-
| 96
| 96
Line 964: Line 1,348:
| 1-18/11-9/8-9/7
| 1-18/11-9/8-9/7
| utonal
| utonal
| 1/1-9/8-9/7-18/11
| 1/1-8/7-16/11-16/9
| 1/1-14/11-14/9-7/4
| 1/1-11/9-11/8-11/7
|-
|-
| 97
| 97
Line 969: Line 1,357:
| 1-9/5-9/8-9/7
| 1-9/5-9/8-9/7
| utonal
| utonal
| 1/1-9/8-9/7-9/5
| 1/1-8/7-8/5-16/9
| 1/1-7/5-14/9-7/4
| 1/1-10/9-5/4-10/7
|}
|}


Revision as of 13:54, 16 February 2022

Below are listed the dyadic chords of 11-limit valentine temperament. Typing the chords requires consideration of the fact that valentine conflates 12/11 and 11/10 and so also 11/6 and 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 11/10 and 20/11.

If only 126/125 needs to be tempered out, the chord is labeled starling, if 121/120, biyatismic, if 176/175, valinorsmic, if 385/384, keenanismic, and if 441/440, werckismic. Chords which require any two of 121/120, 176/175 or 385/384 are labeled zeus, if they require any two of 126/125, 176/175 or 441/440, they are labeled thrush. Finally, if they require any three independent commas among those discussed above, it is labeled valentine.

Valentine has MOS of size 15, 16, 31 and 46. It is readily observed from the list below that even the smallest of these is well-supplied with chords. Because Carlos Alpha is the generator chain of valentine in the tuning with pure 3/2's, the list below is also a list of chords of Carlos Alpha, so long as the transversals are adjusted so that the notes are in the correct octave. This means that a number in a chord listed under "chord" less than 16 corresponds to a note in the transversal which should be left unaltered, whereas the notes from 16 to 21 correspond to transversal notes which should be adjusted up an octave. Hence, tetrad 8, the 0-2-5-9 chord with transversal 1-6/5-11/8-3/2, is an essentially zeus chord of Carlos Alpha as well as valentine. On the other hand, tetrad 76, 0-10-13-18 with transversal 1-11/7-9/5-9/8, corresponds to the werckismic 1-11/7-9/5-9/4 chord of Carlos Alpha.

In other words, each chord here has an unlimited number of "voicings" in valentine temperament, but exactly one voicing in Carlos Alpha, because there are no octaves.

Triads

The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of valentine.

Example 1: Chord #13 is generators 0-5-9 and is a traditional five-limit major chord, 1/1-5/4-3/2. It occurs for the first time on the ninth generation, and will therefore occur six times (15-9=6) in valentine[15].

Example 2: Chord #38 is generators 0-8-13, which is 1/1-5/4-7/5, occurs for the first time on the thirteenth generation, and therefore appears only twice (15-13=2) in valentine[15].

Each of the triads generated has three "inversions", i.e., can be written starting on any one of the three tones in the triad. The first chord is based on the number of generator steps for each tone. This ordering makes it easy to see how often it will occur in a given MOS, as noted in the examples above, but it may seem surprising if you're new to it: For example, chord #8 is 1/1-8/7-10/7, but it might seem more "natural" to use 1/1-5/4-7/4, which is listed as the second inversion. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.

Number Chord Transversal Type As generated 1st inversion 2nd inversion
1 0-2-4 1-11/10-6/5 otonal 1/1-11/10-6/5 1/1-11/10-11/6 1/1-5/3-11/6
2 0-2-5 1-11/10-5/4 valinorsmic 1/1-11/10-5/4 1/1-8/7-20/11 1/1-8/5-7/4
3 0-3-5 1-8/7-5/4 valinorsmic 1/1-8/7-5/4 1/1-11/10-7/4 1/1-8/5-20/11
4 0-2-7 1-11/10-11/8 utonal 1/1-11/10-11/8 1/1-5/4-20/11 1/1-16/11-8/5
5 0-3-7 1-8/7-11/8 keenanismic 1/1-8/7-11/8 1/1-6/5-7/4 1/1-16/11-5/3
6 0-4-7 1-6/5-11/8 keenanismic 1/1-6/5-11/8 1/1-8/7-5/3 1/1-16/11-7/4
7 0-5-7 1-5/4-11/8 otonal 1/1-5/4-11/8 1/1-11/10-8/5 1/1-16/11-11/6
8 0-3-8 1-8/7-10/7 otonal 1/1-8/7-10/7 1/1-5/4-7/4 1/1-7/5-8/5
9 0-4-8 1-6/5-10/7 starling 1/1-6/5-10/7 1/1-6/5-5/3 1/1-7/5-5/3
10 0-5-8 1-5/4-10/7 utonal 1/1-5/4-10/7 1/1-8/7-8/5 1/1-7/5-7/4
11 0-2-9 1-12/11-3/2 utonal 1/1-12/11-3/2 1/1-11/8-11/6 1/1-4/3-16/11
12 0-4-9 1-6/5-3/2 utonal 1/1-6/5-3/2 1/1-5/4-5/3 1/1-4/3-8/5
13 0-5-9 1-5/4-3/2 otonal 1/1-5/4-3/2 1/1-6/5-8/5 1/1-4/3-5/3
14 0-7-9 1-11/8-3/2 otonal 1/1-11/8-3/2 1/1-11/10-16/11 1/1-41/31-11/6
15 0-2-10 1-11/10-11/7 utonal 1/1-11/10-11/7 1/1-10/7-11/6 1/1-68/53-7/5
16 0-3-10 1-8/7-11/7 otonal 1/1-8/7-11/7 1/1-11/8-7/4 1/1-14/11-16/11
17 0-5-10 1-5/4-11/7 valinorsmic 1/1-5/4-11/7 1/1-5/4-8/5 1/1-14/11-8/5
18 0-7-10 1-11/8-11/7 utonal 1/1-11/8-11/7 1/1-8/7-16/11 1/1-14/11-7/4
19 0-8-10 1-10/7-11/7 otonal 1/1-10/7-11/7 1/1-11/10-7/5 1/1-14/11-11/6
20 0-2-11 1-12/11-18/11 otonal 1/1-12/11-18/11 1/1-3/2-11/6 1/1-11/9-4/3
21 0-3-11 1-8/7-18/11 werckismic 1/1-8/7-18/11 1/1-10/7-7/4 1/1-11/9-7/5
22 0-4-11 1-6/5-18/11 biyatismic 1/1-6/5-18/11 1/1-11/8-5/3 1/1-11/9-16/11
23 0-7-11 1-11/8-18/11 biyatismic 1/1-11/8-18/11 1/1-6/5-16/11 1/1-11/9-5/3
24 0-8-11 1-10/7-18/11 werckismic 1/1-10/7-18/11 1/1-8/7-7/5 1/1-11/9-7/4
25 0-9-11 1-3/2-18/11 utonal 1/1-3/2-18/11 1/1-11/10-4/3 1/1-97/80-11/6
26 0-2-12 1-12/11-12/7 utonal 1/1-12/11-12/7 1/1-11/7-11/6 1/1-7/6-14/11
27 0-3-12 1-8/7-12/7 otonal 1/1-8/7-12/7 1/1-3/2-7/4 1/1-7/6-4/3
28 0-4-12 1-6/5-12/7 utonal 1/1-6/5-12/7 1/1-10/7-5/3 1/1-7/6-7/5
29 0-5-12 1-5/4-12/7 keenanismic 1/1-5/4-12/7 1/1-11/8-8/5 1/1-7/6-16/11
30 0-7-12 1-11/8-12/7 keenanismic 1/1-11/8-12/7 1/1-5/4-16/11 1/1-7/6-8/5
31 0-8-12 1-10/7-12/7 otonal 1/1-10/7-12/7 1/1-6/5-7/5 1/1-7/6-5/3
32 0-9-12 1-3/2-12/7 utonal 1/1-3/2-12/7 1/1-8/7-4/3 1/1-7/6-7/4
33 0-10-12 1-11/7-12/7 otonal 1/1-11/7-12/7 1/1-12/11-14/11 1/1-7/6-146/79
34 0-2-13 1-11/10-9/5 otonal 1/1-11/10-9/5 1/1-18/11-20/11 1/1-10/9-11/9
35 0-3-13 1-8/7-9/5 werckismic 1/1-8/7-9/5 1/1-11/7-7/4 1/1-10/9-14/11
36 0-4-13 1-6/5-9/5 otonal 1/1-6/5-9/5 1/1-3/2-5/3 1/1-10/9-4/3
37 0-5-13 1-5/4-9/5 starling 1/1-5/4-9/5 1/1-10/7-8/5 1/1-10/9-7/5
38 0-8-13 1-10/7-9/5 starling 1/1-10/7-9/5 1/1-5/4-7/5 1/1-10/9-8/5
39 0-9-13 1-3/2-9/5 utonal 1/1-3/2-9/5 1/1-6/5-4/3 1/1-10/9-5/3
40 0-10-13 1-11/7-9/5 werckismic 1/1-11/7-9/5 1/1-8/7-14/11 1/1-10/9-7/4
41 0-11-13 1-18/11-9/5 utonal 1/1-18/11-9/5 1/1-11/10-11/9 1/1-10/9-11/6
42 0-5-18 1-5/4-9/8 otonal 1/1-9/8-5/4 1/1-10/9-16/9 1/1-8/5-9/5
43 0-7-18 1-11/8-9/8 otonal 1/1-9/8-11/8 1/1-11/9-16/9 1/1-16/11-18/11
44 0-8-18 1-10/7-9/8 werckismic 1/1-9/8-10/7 1/1-14/11-16/9 1/1-7/5-11/7
45 0-9-18 1-3/2-9/8 ambitonal 1/1-9/8-3/2 1/1-4/3-16/9 1/1-4/3-3/2
46 0-10-18 1-11/7-9/8 werckismic 1/1-9/8-11/7 1/1-7/5-16/9 1/1-14/11-10/7
47 0-11-18 1-18/11-9/8 utonal 1/1-9/8-18/11 1/1-16/11-16/9 1/1-11/9-11/8
48 0-13-18 1-9/5-9/8 utonal 1/1-9/8-9/5 1/1-8/5-16/9 1/1-10/9-5/4
49 0-3-21 1-8/7-9/7 otonal 1/1-8/7-9/7 1/1-9/8-7/4 1/1-14/9-16/9
50 0-8-21 1-10/7-9/7 otonal 1/1-9/7-10/7 1/1-10/9-14/9 1/1-7/5-9/5
51 0-9-21 1-3/2-9/7 utonal 1/1-9/7-3/2 1/1-7/6-14/9 1/1-4/3-12/7
52 0-10-21 1-11/7-9/7 otonal 1/1-9/7-11/7 1/1-11/9-14/9 1/1-14/11-18/11
53 0-11-21 1-18/11-9/7 utonal 1/1-9/7-18/11 1/1-14/11-14/9 1/1-11/9-11/7
54 0-12-21 1-12/7-9/7 otonal 1/1-9/7-12/7 1/1-4/3-14/9 1/1-7/6-3/2
55 0-13-21 1-9/5-9/7 utonal 1/1-9/7-9/5 1/1-7/5-14/9 1/1-10/9-10/7
56 0-18-21 1-9/8-9/7 utonal 1/1-9/8-9/7 1/1-8/7-16/9 1/1-14/9-7/4

Tetrads

Number Chord Transversal Type As generated 1st inversion 2nd inversion 3rd inversion
1 0-2-4-7 1-11/10-6/5-11/8 zeus 1/1-11/10-6/5-11/8 1/1-11/10-5/4-11/6 1/1-8/7-5/3-11/6 1/1-16/11-8/5-7/4
2 0-2-5-7 1-11/10-5/4-11/8 valinorsmic 1/1-11/10-5/4-11/8 1/1-8/7-5/4-11/6 1/1-11/10-8/5-7/4 1/1-16/11-8/5-11/6
3 0-3-5-7 1-8/7-5/4-11/8 zeus 1/1-8/7-5/4-11/8 1/1-11/10-6/5-7/4 1/1-11/10-8/5-11/6 1/1-16/11-5/3-11/6
4 0-3-5-8 1-8/7-5/4-10/7 valinorsmic 1/1-8/7-5/4-10/7 1/1-11/10-5/4-7/4 1/1-8/7-8/5-11/6 1/1-7/5-8/5-7/4
5 0-2-4-9 1-12/11-6/5-3/2 utonal 1/1-12/11-6/5-3/2 1/1-11/10-11/8-11/6 1/1-5/4-5/3-11/6 1/1-4/3-16/11-8/5
6 0-2-5-9 1-11/10-5/4-3/2 zeus 1/1-11/10-5/4-3/2 1/1-8/7-11/8-11/6 1/1-6/5-8/5-7/4 1/1-4/3-16/11-5/3
7 0-2-7-9 1-11/10-11/8-3/2 biyatismic 1/1-11/10-11/8-3/2 1/1-5/4-11/8-11/6 1/1-11/10-16/11-8/5 1/1-4/3-16/11-11/6
8 0-4-7-9 1-6/5-11/8-3/2 zeus 1/1-6/5-11/8-3/2 1/1-8/7-5/4-5/3 1/1-11/10-16/11-7/4 1/1-4/3-8/5-11/6
9 0-5-7-9 1-5/4-11/8-3/2 otonal 1/1-5/4-11/8-3/2 1/1-11/10-6/5-8/5 1/1-11/10-16/11-11/6 1/1-4/3-5/3-11/6
10 0-2-5-10 1-11/10-5/4-11/7 valinorsmic 1/1-11/10-5/4-11/7 1/1-8/7-10/7-11/6 1/1-5/4-8/5-7/4 1/1-14/11-7/5-8/5
11 0-3-5-10 1-8/7-5/4-11/7 valinorsmic 1/1-8/7-5/4-11/7 1/1-11/10-11/8-7/4 1/1-5/4-8/5-11/6 1/1-14/11-16/11-8/5
12 0-2-7-10 1-11/10-11/8-11/7 utonal 1/1-11/10-11/8-11/7 1/1-5/4-10/7-11/6 1/1-8/7-16/11-8/5 1/1-14/11-7/5-7/4
13 0-3-7-10 1-8/7-11/8-11/7 keenanismic 1/1-8/7-11/8-11/7 1/1-6/5-11/8-7/4 1/1-8/7-16/11-5/3 1/1-14/11-16/11-7/4
14 0-5-7-10 1-5/4-11/8-11/7 valinorsmic 1/1-5/4-11/8-11/7 1/1-11/10-5/4-8/5 1/1-8/7-16/11-11/6 1/1-14/11-8/5-7/4
15 0-3-8-10 1-8/7-10/7-11/7 otonal 1/1-8/7-10/7-11/7 1/1-5/4-11/8-7/4 1/1-11/10-7/5-8/5 1/1-14/11-16/11-11/6
16 0-5-8-10 1-5/4-10/7-11/7 valinorsmic 1/1-5/4-10/7-11/7 1/1-8/7-5/4-8/5 1/1-11/10-7/5-7/4 1/1-14/11-8/5-11/6
17 0-2-4-11 1-11/10-6/5-18/11 biyatismic 1/1-11/10-6/5-18/11 1/1-11/10-3/2-11/6 1/1-11/8-5/3-11/6 1/1-11/9-4/3-16/11
18 0-2-7-11 1-11/10-11/8-18/11 biyatismic 1/1-11/10-11/8-18/11 1/1-5/4-3/2-11/6 1/1-6/5-16/11-8/5 1/1-11/9-4/3-5/3
19 0-3-7-11 1-8/7-11/8-18/11 valentine 1/1-8/7-11/8-18/11 1/1-6/5-10/7-7/4 1/1-6/5-16/11-5/3 1/1-11/9-7/5-5/3
20 0-4-7-11 1-6/5-11/8-18/11 zeus 1/1-6/5-11/8-18/11 1/1-8/7-11/8-5/3 1/1-6/5-16/11-7/4 1/1-11/9-16/11-5/3
21 0-3-8-11 1-8/7-10/7-18/11 werckismic 1/1-8/7-10/7-18/11 1/1-5/4-10/7-7/4 1/1-8/7-7/5-8/5 1/1-11/9-7/5-7/4
22 0-4-8-11 1-6/5-10/7-18/11 valentine 1/1-6/5-10/7-18/11 1/1-6/5-11/8-5/3 1/1-8/7-7/5-5/3 1/1-11/9-16/11-7/4
23 0-2-9-11 1-12/11-3/2-18/11 ambitonal 1/1-12/11-3/2-18/11 1/1-11/8-3/2-11/6 1/1-11/10-4/3-16/11 1/1-11/9-4/3-11/6
24 0-4-9-11 1-6/5-3/2-18/11 biyatismic 1/1-6/5-3/2-18/11 1/1-5/4-11/8-5/3 1/1-11/10-4/3-8/5 1/1-11/9-16/11-11/6
25 0-7-9-11 1-11/8-3/2-18/11 biyatismic 1/1-11/8-3/2-18/11 1/1-11/10-6/5-16/11 1/1-11/10-4/3-11/6 1/1-11/9-5/3-11/6
26 0-2-4-12 1-12/11-6/5-12/7 utonal 1/1-12/11-6/5-12/7 1/1-11/10-11/7-11/6 1/1-10/7-5/3-11/6 1/1-7/6-14/11-7/5
27 0-2-5-12 1-11/10-5/4-12/7 zeus 1/1-11/10-5/4-12/7 1/1-8/7-11/7-11/6 1/1-11/8-8/5-7/4 1/1-7/6-14/11-16/11
28 0-3-5-12 1-8/7-5/4-12/7 zeus 1/1-8/7-5/4-12/7 1/1-11/10-3/2-7/4 1/1-11/8-8/5-11/6 1/1-7/6-4/3-16/11
29 0-2-7-12 1-11/10-11/8-12/7 zeus 1/1-11/10-11/8-12/7 1/1-5/4-11/7-11/6 1/1-5/4-16/11-8/5 1/1-7/6-14/11-8/5
30 0-3-7-12 1-8/7-11/8-12/7 keenanismic 1/1-8/7-11/8-12/7 1/1-6/5-3/2-7/4 1/1-5/4-16/11-5/3 1/1-7/6-4/3-8/5
31 0-4-7-12 1-6/5-11/8-12/7 keenanismic 1/1-6/5-11/8-12/7 1/1-8/7-10/7-5/3 1/1-5/4-16/11-7/4 1/1-7/6-7/5-8/5
32 0-5-7-12 1-5/4-11/8-12/7 keenanismic 1/1-5/4-11/8-12/7 1/1-11/10-11/8-8/5 1/1-5/4-16/11-11/6 1/1-7/6-16/11-8/5
33 0-3-8-12 1-8/7-10/7-12/7 otonal 1/1-8/7-10/7-12/7 1/1-5/4-3/2-7/4 1/1-6/5-7/5-8/5 1/1-7/6-4/3-5/3
34 0-4-8-12 1-6/5-10/7-12/7 starling 1/1-6/5-10/7-12/7 1/1-6/5-10/7-5/3 1/1-6/5-7/5-5/3 1/1-7/6-7/5-5/3
35 0-5-8-12 1-5/4-10/7-12/7 keenanismic 1/1-5/4-10/7-12/7 1/1-8/7-11/8-8/5 1/1-6/5-7/5-7/4 1/1-7/6-16/11-5/3
36 0-2-9-12 1-12/11-3/2-12/7 utonal 1/1-12/11-3/2-12/7 1/1-11/8-11/7-11/6 1/1-8/7-4/3-16/11 1/1-7/6-14/11-7/4
37 0-4-9-12 1-6/5-3/2-12/7 utonal 1/1-6/5-3/2-12/7 1/1-5/4-10/7-5/3 1/1-8/7-4/3-8/5 1/1-7/6-7/5-7/4
38 0-5-9-12 1-5/4-3/2-12/7 keenanismic 1/1-5/4-3/2-12/7 1/1-6/5-11/8-8/5 1/1-8/7-4/3-5/3 1/1-7/6-16/11-7/4
39 0-7-9-12 1-11/8-3/2-12/7 zeus 1/1-11/8-3/2-12/7 1/1-11/10-5/4-16/11 1/1-8/7-4/3-11/6 1/1-7/6-8/5-7/4
40 0-2-10-12 1-11/10-11/7-12/7 biyatismic 1/1-11/10-11/7-12/7 1/1-10/7-11/7-11/6 1/1-11/10-14/11-7/5 1/1-7/6-14/11-11/6
41 0-3-10-12 1-8/7-11/7-12/7 otonal 1/1-8/7-11/7-12/7 1/1-11/8-3/2-7/4 1/1-11/10-14/11-16/11 1/1-7/6-4/3-11/6
42 0-5-10-12 1-5/4-11/7-12/7 zeus 1/1-5/4-11/7-12/7 1/1-5/4-11/8-8/5 1/1-11/10-14/11-8/5 1/1-7/6-16/11-11/6
43 0-7-10-12 1-11/8-11/7-12/7 zeus 1/1-11/8-11/7-12/7 1/1-8/7-5/4-16/11 1/1-11/10-14/11-7/4 1/1-7/6-8/5-11/6
44 0-8-10-12 1-10/7-11/7-12/7 otonal 1/1-10/7-11/7-12/7 1/1-11/10-6/5-7/5 1/1-11/10-14/11-11/6 1/1-7/6-5/3-11/6
45 0-2-4-13 1-11/10-6/5-9/5 otonal 1/1-11/10-6/5-9/5 1/1-11/10-18/11-11/6 1/1-3/2-5/3-11/6 1/1-10/9-11/9-4/3
46 0-2-5-13 1-11/10-5/4-9/5 thrush 1/1-11/10-5/4-9/5 1/1-8/7-18/11-11/6 1/1-10/7-8/5-7/4 1/1-10/9-11/9-7/5
47 0-3-5-13 1-8/7-5/4-9/5 thrush 1/1-8/7-5/4-9/5 1/1-11/10-11/7-7/4 1/1-10/7-8/5-11/6 1/1-10/9-14/11-7/5
48 0-3-8-13 1-8/7-10/7-9/5 thrush 1/1-8/7-10/7-9/5 1/1-5/4-11/7-7/4 1/1-5/4-7/5-8/5 1/1-10/9-14/11-8/5
49 0-4-8-13 1-6/5-10/7-9/5 starling 1/1-6/5-10/7-9/5 1/1-6/5-3/2-5/3 1/1-5/4-7/5-5/3 1/1-10/9-4/3-8/5
50 0-5-8-13 1-5/4-10/7-9/5 starling 1/1-5/4-10/7-9/5 1/1-8/7-10/7-8/5 1/1-5/4-7/5-7/4 1/1-10/9-7/5-8/5
51 0-2-9-13 1-11/10-3/2-9/5 biyatismic 1/1-11/10-3/2-9/5 1/1-11/8-18/11-11/6 1/1-6/5-4/3-16/11 1/1-10/9-11/9-5/3
52 0-4-9-13 1-6/5-3/2-9/5 ambitonal 1/1-6/5-3/2-9/5 1/1-5/4-3/2-5/3 1/1-6/5-4/3-8/5 1/1-10/9-4/3-5/3
53 0-5-9-13 1-5/4-3/2-9/5 starling 1/1-5/4-3/2-9/5 1/1-6/5-10/7-8/5 1/1-6/5-4/3-5/3 1/1-10/9-7/5-5/3
54 0-2-10-13 1-11/10-11/7-9/5 werckismic 1/1-11/10-11/7-9/5 1/1-10/7-18/11-11/6 1/1-8/7-14/11-7/5 1/1-10/9-11/9-7/4
55 0-3-10-13 1-8/7-11/7-9/5 werckismic 1/1-8/7-11/7-9/5 1/1-11/8-11/7-7/4 1/1-8/7-14/11-16/11 1/1-10/9-14/11-7/4
56 0-5-10-13 1-5/4-11/7-9/5 thrush 1/1-5/4-11/7-9/5 1/1-5/4-10/7-8/5 1/1-8/7-14/11-8/5 1/1-10/9-7/5-7/4
57 0-8-10-13 1-10/7-11/7-9/5 thrush 1/1-10/7-11/7-9/5 1/1-11/10-5/4-7/5 1/1-8/7-14/11-11/6 1/1-10/9-8/5-7/4
58 0-2-11-13 1-11/10-18/11-9/5 biyatismic 1/1-11/10-18/11-9/5 1/1-3/2-18/11-11/6 1/1-11/10-11/9-4/3 1/1-10/9-11/9-11/6
59 0-3-11-13 1-8/7-18/11-9/5 werckismic 1/1-8/7-18/11-9/5 1/1-10/7-11/7-7/4 1/1-11/10-11/9-7/5 1/1-10/9-14/11-11/6
60 0-4-11-13 1-6/5-18/11-9/5 biyatismic 1/1-6/5-18/11-9/5 1/1-11/8-3/2-5/3 1/1-11/10-11/9-16/11 1/1-10/9-4/3-11/6
61 0-8-11-13 1-10/7-18/11-9/5 thrush 1/1-10/7-18/11-9/5 1/1-8/7-5/4-7/5 1/1-11/10-11/9-7/4 1/1-10/9-8/5-11/6
62 0-9-11-13 1-3/2-18/11-9/5 utonal 1/1-3/2-18/11-9/5 1/1-11/10-6/5-4/3 1/1-11/10-11/9-11/6 1/1-10/9-5/3-11/6
63 0-5-7-18 1-5/4-11/8-9/8 otonal 1/1-9/8-5/4-11/8 1/1-10/9-11/9-16/9 1/1-11/10-8/5-9/5 1/1-16/11-18/11-11/6
64 0-5-8-18 1-5/4-10/7-9/8 werckismic 1/1-9/8-5/4-10/7 1/1-10/9-14/11-16/9 1/1-8/7-8/5-9/5 1/1-7/5-11/7-7/4
65 0-5-9-18 1-5/4-3/2-9/8 otonal 1/1-9/8-5/4-3/2 1/1-10/9-4/3-16/9 1/1-6/5-8/5-9/5 1/1-4/3-3/2-5/3
66 0-7-9-18 1-11/8-3/2-9/8 otonal 1/1-9/8-11/8-3/2 1/1-11/9-4/3-16/9 1/1-11/10-16/11-18/11 1/1-4/3-3/2-11/6
67 0-5-10-18 1-5/4-11/7-9/8 thrush 1/1-9/8-5/4-11/7 1/1-10/9-7/5-16/9 1/1-5/4-8/5-9/5 1/1-14/11-10/7-8/5
68 0-7-10-18 1-11/8-11/7-9/8 werckismic 1/1-9/8-11/8-11/7 1/1-11/9-7/5-16/9 1/1-8/7-16/11-18/11 1/1-14/11-10/7-7/4
69 0-8-10-18 1-10/7-11/7-9/8 werckismic 1/1-9/8-10/7-11/7 1/1-14/11-7/5-16/9 1/1-11/10-7/5-11/7 1/1-14/11-10/7-11/6
70 0-7-11-18 1-11/8-18/11-9/8 biyatismic 1/1-9/8-11/8-18/11 1/1-11/9-16/11-16/9 1/1-6/5-16/11-18/11 1/1-11/9-11/8-5/3
71 0-8-11-18 1-10/7-18/11-9/8 werckismic 1/1-9/8-10/7-18/11 1/1-14/11-16/11-16/9 1/1-8/7-7/5-11/7 1/1-11/9-11/8-7/4
72 0-9-11-18 1-3/2-18/11-9/8 utonal 1/1-9/8-3/2-18/11 1/1-4/3-16/11-16/9 1/1-11/10-4/3-3/2 1/1-11/9-11/8-11/6
73 0-5-13-18 1-5/4-9/5-9/8 starling 1/1-9/8-5/4-9/5 1/1-10/9-8/5-16/9 1/1-10/7-8/5-9/5 1/1-10/9-5/4-25/18
74 0-8-13-18 1-10/7-9/5-9/8 thrush 1/1-9/8-10/7-9/5 1/1-14/11-8/5-16/9 1/1-5/4-7/5-11/7 1/1-10/9-5/4-8/5
75 0-9-13-18 1-3/2-9/5-9/8 utonal 1/1-9/8-3/2-9/5 1/1-4/3-8/5-16/9 1/1-6/5-4/3-3/2 1/1-10/9-5/4-5/3
76 0-10-13-18 1-11/7-9/5-9/8 werckismic 1/1-9/8-11/7-9/5 1/1-7/5-8/5-16/9 1/1-8/7-14/11-10/7 1/1-10/9-5/4-7/4
77 0-11-13-18 1-18/11-9/5-9/8 utonal 1/1-9/8-18/11-9/5 1/1-16/11-8/5-16/9 1/1-11/10-11/9-11/8 1/1-10/9-5/4-11/6
78 0-3-8-21 1-8/7-10/7-9/7 otonal 1/1-8/7-9/7-10/7 1/1-9/8-5/4-7/4 1/1-10/9-14/9-16/9 1/1-7/5-8/5-9/5
79 0-3-10-21 1-8/7-11/7-9/7 otonal 1/1-8/7-9/7-11/7 1/1-9/8-11/8-7/4 1/1-11/9-14/9-16/9 1/1-14/11-16/11-18/11
80 0-8-10-21 1-10/7-11/7-9/7 otonal 1/1-9/7-10/7-11/7 1/1-10/9-11/9-14/9 1/1-11/10-7/5-9/5 1/1-14/11-18/11-11/6
81 0-3-11-21 1-8/7-18/11-9/7 werckismic 1/1-8/7-9/7-18/11 1/1-9/8-10/7-7/4 1/1-14/11-14/9-16/9 1/1-11/9-7/5-11/7
82 0-8-11-21 1-10/7-18/11-9/7 werckismic 1/1-9/7-10/7-18/11 1/1-10/9-14/11-14/9 1/1-8/7-7/5-9/5 1/1-11/9-11/7-7/4
83 0-9-11-21 1-3/2-18/11-9/7 utonal 1/1-9/7-3/2-18/11 1/1-7/6-14/11-14/9 1/1-11/10-4/3-12/7 1/1-11/9-11/7-11/6
84 0-3-12-21 1-8/7-12/7-9/7 otonal 1/1-8/7-9/7-12/7 1/1-9/8-3/2-7/4 1/1-4/3-14/9-16/9 1/1-7/6-4/3-3/2
85 0-8-12-21 1-10/7-12/7-9/7 otonal 1/1-9/7-10/7-12/7 1/1-10/9-4/3-14/9 1/1-6/5-7/5-9/5 1/1-7/6-3/2-5/3
86 0-9-12-21 1-3/2-12/7-9/7 ambitonal 1/1-9/7-3/2-12/7 1/1-7/6-4/3-14/9 1/1-8/7-4/3-12/7 1/1-7/6-3/2-7/4
87 0-10-12-21 1-11/7-12/7-9/7 otonal 1/1-9/7-11/7-12/7 1/1-11/9-4/3-14/9 1/1-11/10-14/11-18/11 1/1-7/6-3/2-11/6
88 0-3-13-21 1-8/7-9/5-9/7 werckismic 1/1-8/7-9/7-9/5 1/1-9/8-11/7-7/4 1/1-7/5-14/9-16/9 1/1-10/9-14/11-10/7
89 0-8-13-21 1-10/7-9/5-9/7 starling 1/1-9/7-10/7-9/5 1/1-10/9-7/5-14/9 1/1-5/4-7/5-9/5 1/1-10/9-10/7-8/5
90 0-9-13-21 1-3/2-9/5-9/7 utonal 1/1-9/7-3/2-9/5 1/1-7/6-7/5-14/9 1/1-6/5-4/3-12/7 1/1-10/9-10/7-5/3
91 0-10-13-21 1-11/7-9/5-9/7 werckismic 1/1-9/7-11/7-9/5 1/1-11/9-7/5-14/9 1/1-8/7-14/11-18/11 1/1-10/9-10/7-7/4
92 0-11-13-21 1-18/11-9/5-9/7 utonal 1/1-9/7-18/11-9/5 1/1-14/11-7/5-14/9 1/1-11/10-11/9-11/7 1/1-10/9-10/7-11/6
93 0-8-18-21 1-10/7-9/8-9/7 werckismic 1/1-9/8-9/7-10/7 1/1-8/7-14/11-16/9 1/1-10/9-14/9-7/4 1/1-7/5-11/7-9/5
94 0-9-18-21 1-3/2-9/8-9/7 utonal 1/1-9/8-9/7-3/2 1/1-8/7-4/3-16/9 1/1-7/6-14/9-7/4 1/1-4/3-3/2-12/7
95 0-10-18-21 1-11/7-9/8-9/7 werckismic 1/1-9/8-9/7-11/7 1/1-8/7-7/5-16/9 1/1-11/9-14/9-7/4 1/1-14/11-10/7-18/11
96 0-11-18-21 1-18/11-9/8-9/7 utonal 1/1-9/8-9/7-18/11 1/1-8/7-16/11-16/9 1/1-14/11-14/9-7/4 1/1-11/9-11/8-11/7
97 0-13-18-21 1-9/5-9/8-9/7 utonal 1/1-9/8-9/7-9/5 1/1-8/7-8/5-16/9 1/1-7/5-14/9-7/4 1/1-10/9-5/4-10/7

Pentads

Number Chord Transversal Type
1 0-2-4-7-9 1-11/10-6/5-11/8-3/2 zeus
2 0-2-5-7-9 1-11/10-5/4-11/8-3/2 zeus
3 0-2-5-7-10 1-11/10-5/4-11/8-11/7 valinorsmic
4 0-3-5-7-10 1-8/7-5/4-11/8-11/7 zeus
5 0-3-5-8-10 1-8/7-5/4-10/7-11/7 valinorsmic
6 0-2-4-7-11 1-11/10-6/5-11/8-18/11 zeus
7 0-2-4-9-11 1-11/10-6/5-3/2-18/11 biyatismic
8 0-2-7-9-11 1-11/10-11/8-3/2-18/11 biyatismic
9 0-4-7-9-11 1-6/5-11/8-3/2-18/11 zeus
10 0-2-4-7-12 1-11/10-6/5-11/8-12/7 zeus
11 0-2-5-7-12 1-11/10-5/4-11/8-12/7 zeus
12 0-3-5-7-12 1-8/7-5/4-11/8-12/7 zeus
13 0-3-5-8-12 1-8/7-5/4-10/7-12/7 zeus
14 0-2-4-9-12 1-12/11-6/5-3/2-12/7 utonal
15 0-2-5-9-12 1-11/10-5/4-3/2-12/7 zeus
16 0-2-7-9-12 1-11/10-11/8-3/2-12/7 zeus
17 0-4-7-9-12 1-6/5-11/8-3/2-12/7 zeus
18 0-5-7-9-12 1-5/4-11/8-3/2-12/7 zeus
19 0-2-5-10-12 1-11/10-5/4-11/7-12/7 zeus
20 0-3-5-10-12 1-8/7-5/4-11/7-12/7 zeus
21 0-2-7-10-12 1-11/10-11/8-11/7-12/7 zeus
22 0-3-7-10-12 1-8/7-11/8-11/7-12/7 zeus
23 0-5-7-10-12 1-5/4-11/8-11/7-12/7 zeus
24 0-3-8-10-12 1-8/7-10/7-11/7-12/7 otonal
25 0-5-8-10-12 1-5/4-10/7-11/7-12/7 zeus
26 0-3-5-8-13 1-8/7-5/4-10/7-9/5 thrush
27 0-2-4-9-13 1-11/10-6/5-3/2-9/5 biyatismic
28 0-2-5-9-13 1-11/10-5/4-3/2-9/5 valentine
29 0-2-5-10-13 1-11/10-5/4-11/7-9/5 thrush
30 0-3-5-10-13 1-8/7-5/4-11/7-9/5 thrush
31 0-3-8-10-13 1-8/7-10/7-11/7-9/5 thrush
32 0-5-8-10-13 1-5/4-10/7-11/7-9/5 thrush
33 0-2-4-11-13 1-11/10-6/5-18/11-9/5 biyatismic
34 0-3-8-11-13 1-8/7-10/7-18/11-9/5 thrush
35 0-4-8-11-13 1-6/5-10/7-18/11-9/5 valentine
36 0-2-9-11-13 1-11/10-3/2-18/11-9/5 biyatismic
37 0-4-9-11-13 1-6/5-3/2-18/11-9/5 biyatismic
38 0-5-7-9-18 1-5/4-11/8-3/2-9/8 otonal
39 0-5-7-10-18 1-5/4-11/8-11/7-9/8 thrush
40 0-5-8-10-18 1-5/4-10/7-11/7-9/8 thrush
41 0-7-9-11-18 1-11/8-3/2-18/11-9/8 biyatismic
42 0-5-8-13-18 1-5/4-10/7-9/5-9/8 thrush
43 0-5-9-13-18 1-5/4-3/2-9/5-9/8 starling
44 0-5-10-13-18 1-5/4-11/7-9/5-9/8 thrush
45 0-8-10-13-18 1-10/7-11/7-9/5-9/8 thrush
46 0-8-11-13-18 1-10/7-18/11-9/5-9/8 thrush
47 0-9-11-13-18 1-3/2-18/11-9/5-9/8 utonal
48 0-3-8-10-21 1-8/7-10/7-11/7-9/7 otonal
49 0-3-8-11-21 1-8/7-10/7-18/11-9/7 werckismic
50 0-3-8-12-21 1-8/7-10/7-12/7-9/7 otonal
51 0-3-10-12-21 1-8/7-11/7-12/7-9/7 otonal
52 0-8-10-12-21 1-10/7-11/7-12/7-9/7 otonal
53 0-3-8-13-21 1-8/7-10/7-9/5-9/7 thrush
54 0-3-10-13-21 1-8/7-11/7-9/5-9/7 werckismic
55 0-8-10-13-21 1-10/7-11/7-9/5-9/7 thrush
56 0-3-11-13-21 1-8/7-18/11-9/5-9/7 werckismic
57 0-8-11-13-21 1-10/7-18/11-9/5-9/7 thrush
58 0-9-11-13-21 1-3/2-18/11-9/5-9/7 utonal
59 0-8-10-18-21 1-10/7-11/7-9/8-9/7 werckismic
60 0-8-11-18-21 1-10/7-18/11-9/8-9/7 werckismic
61 0-9-11-18-21 1-3/2-18/11-9/8-9/7 utonal
62 0-8-13-18-21 1-10/7-9/5-9/8-9/7 thrush
63 0-9-13-18-21 1-3/2-9/5-9/8-9/7 utonal
64 0-10-13-18-21 1-11/7-9/5-9/8-9/7 werckismic
65 0-11-13-18-21 1-18/11-9/5-9/8-9/7 utonal

Hexads

Number Chord Transversal Type
1 0-2-4-7-9-11 1-11/10-6/5-11/8-3/2-18/11 zeus
2 0-2-4-7-9-12 1-11/10-6/5-11/8-3/2-12/7 zeus
3 0-2-5-7-9-12 1-11/10-5/4-11/8-3/2-12/7 zeus
4 0-2-5-7-10-12 1-11/10-5/4-11/8-11/7-12/7 zeus
5 0-3-5-7-10-12 1-8/7-5/4-11/8-11/7-12/7 zeus
6 0-3-5-8-10-12 1-8/7-5/4-10/7-11/7-12/7 zeus
7 0-3-5-8-10-13 1-8/7-5/4-10/7-11/7-9/5 thrush
8 0-2-4-9-11-13 1-11/10-6/5-3/2-18/11-9/5 biyatismic
9 0-5-8-10-13-18 1-5/4-10/7-11/7-9/5-9/8 thrush
10 0-3-8-10-12-21 1-8/7-10/7-11/7-12/7-9/7 otonal
11 0-3-8-10-13-21 1-8/7-10/7-11/7-9/5-9/7 thrush
12 0-3-8-11-13-21 1-8/7-10/7-18/11-9/5-9/7 thrush
13 0-8-10-13-18-21 1-10/7-11/7-9/5-9/8-9/7 thrush
14 0-8-11-13-18-21 1-10/7-18/11-9/5-9/8-9/7 thrush
15 0-9-11-13-18-21 1-3/2-18/11-9/5-9/8-9/7 utonal
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