Hemififths/Chords: Difference between revisions

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A striking feature of these hemififths chords is that essentially just chords tend to be of higher complexity than essentially tempered chords. Hemififths has MOS of size 7, 10, 17 and 24, and even seven notes are well-supplied with chords, mostly but by no means entirely essentially tempered chords. Extending consideration to the 13-limit adds even more such chords.
A striking feature of these hemififths chords is that essentially just chords tend to be of higher complexity than essentially tempered chords. Hemififths has MOS of size 7, 10, 17 and 24, and even seven notes are well-supplied with chords, mostly but by no means entirely essentially tempered chords. Extending consideration to the 13-limit adds even more such chords.
Chords are named with ups and downs. The tilde ~ means mid, half-way between major and minor. The comma (the actual punctuation mark) is pronounced "add", thus C~,7 is "C mid add7".
{| class="wikitable"
|+Hemififth's genchain
!Genspan
!0
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
|-
!Ratio
|1/1
|11/9
|3/2
|11/6
|9/8
|11/8
|27/16
|33/32
|14/11
|14/9
|40/21
|7/6
|10/7
|7/4
|15/14
|21/16
|-
!Interval
|P1
|~3
|P5
|~7
|M2
|~4
|M6
|^1
|M3
|^5
|M7
|^2
|A4
|^6
|A1
|^3
|}


== Triads ==
== Triads ==
Line 10: Line 68:
! Transversal
! Transversal
! Type
! Type
!Name
|-
|-
| 1
| 1
Line 15: Line 74:
| 1-11/9-3/2
| 1-11/9-3/2
| rastmic
| rastmic
|~
|-
|-
| 2
| 2
Line 20: Line 80:
| 1-11/9-11/6
| 1-11/9-11/6
| utonal
| utonal
|~7no5
|-
|-
| 3
| 3
Line 25: Line 86:
| 1-3/2-11/6
| 1-3/2-11/6
| otonal
| otonal
|~7no3
|-
|-
| 4
| 4
Line 30: Line 92:
| 1-11/9-9/8
| 1-11/9-9/8
| rastmic
| rastmic
|
|-
|-
| 5
| 5
Line 35: Line 98:
| 1-3/2-9/8
| 1-3/2-9/8
| ambitonal
| ambitonal
|2 <u>or</u> 4
|-
|-
| 6
| 6
Line 40: Line 104:
| 1-11/6-9/8
| 1-11/6-9/8
| rastmic
| rastmic
|
|-
|-
| 7
| 7
Line 45: Line 110:
| 1-11/9-11/8
| 1-11/9-11/8
| utonal
| utonal
|~6sus2
|-
|-
| 8
| 8
Line 50: Line 116:
| 1-3/2-11/8
| 1-3/2-11/8
| otonal
| otonal
|~7sus4
|-
|-
| 9
| 9
Line 55: Line 122:
| 1-11/6-11/8
| 1-11/6-11/8
| utonal
| utonal
|~2
|-
|-
| 10
| 10
Line 60: Line 128:
| 1-9/8-11/8
| 1-9/8-11/8
| otonal
| otonal
|~,7no5
|-
|-
| 11
|11
|0-2-8
|1-3/2-14/11
|
|(major)
|-
| 12
| 0-3-8
| 0-3-8
| 1-11/6-14/11
| 1-11/6-14/11
| hemimin
| hemimin
|,~7no5
|-
|-
| 12
| 13
| 0-4-8
| 0-4-8
| 1-9/8-14/11
| 1-9/8-14/11
| pentacircle
| pentacircle
|,9no5
|-
|-
| 13
| 14
| 0-5-8
| 0-5-8
| 1-11/8-14/11
| 1-11/8-14/11
| hemimin
| hemimin
|
|-
|-
| 14
| 15
| 0-1-9
| 0-1-9
| 1-11/9-14/9
| 1-11/9-14/9
| otonal
| otonal
|
|-
|-
| 15
| 16
| 0-4-9
| 0-4-9
| 1-9/8-14/9
| 1-9/8-14/9
| pentacircle
| pentacircle
|7~4no5
|-
|-
| 16
| 17
| 0-5-9
| 0-5-9
| 1-11/8-14/9
| 1-11/8-14/9
| pentacircle
| pentacircle
|
|-
|-
| 17
| 18
| 0-8-9
| 0-8-9
| 1-14/11-14/9
| 1-14/11-14/9
| utonal
| utonal
|(^5)
|-
|-
| 18
| 19
| 0-2-11
| 0-2-11
| 1-3/2-7/6
| 1-3/2-7/6
| otonal
| otonal
|
|-
|-
| 19
| 20
| 0-3-11
| 0-3-11
| 1-11/6-7/6
| 1-11/6-7/6
| otonal
| otonal
|
|-
|-
| 20
| 21
| 0-8-11
| 0-8-11
| 1-14/11-7/6
| 1-14/11-7/6
| utonal
| utonal
|
|-
|-
| 21
| 22
| 0-9-11
| 0-9-11
| 1-14/9-7/6
| 1-14/9-7/6
| utonal
| utonal
|
|-
|-
| 22
| 23
| 0-1-12
| 0-1-12
| 1-11/9-10/7
| 1-11/9-10/7
| swetismic
| swetismic
|
|-
|-
| 23
| 24
| 0-3-12
| 0-3-12
| 1-11/6-10/7
| 1-11/6-10/7
| swetismic
| swetismic
|v4(b5)
|-
|-
| 24
| 25
| 0-4-12
| 0-4-12
| 1-9/8-10/7
| 1-9/8-10/7
| werckismic
| werckismic
|
|-
|-
| 25
| 26
| 0-8-12
| 0-8-12
| 1-14/11-10/7
| 1-14/11-10/7
| werckismic
| werckismic
|7(b5)no3
|-
|-
| 26
| 27
| 0-9-12
| 0-9-12
| 1-14/9-10/7
| 1-14/9-10/7
| swetismic
| swetismic
|~2(b5)
|-
|-
| 27
| 28
| 0-11-12
| 0-11-12
| 1-7/6-10/7
| 1-7/6-10/7
| swetismic
| swetismic
|~6(b5)no3
|-
|-
| 28
| 29
| 0-1-13
| 0-1-13
| 1-11/9-7/4
| 1-11/9-7/4
| werckismic
| werckismic
|
|-
|-
| 29
| 30
| 0-2-13
| 0-2-13
| 1-3/2-7/4
| 1-3/2-7/4
| otonal
| otonal
|
|-
|-
| 30
| 31
| 0-4-13
| 0-4-13
| 1-9/8-7/4
| 1-9/8-7/4
| otonal
| otonal
|
|-
|-
| 31
| 32
| 0-5-13
| 0-5-13
| 1-11/8-7/4
| 1-11/8-7/4
| otonal
| otonal
|
|-
|-
| 32
| 33
| 0-8-13
| 0-8-13
| 1-14/11-7/4
| 1-14/11-7/4
| utonal
| utonal
|
|-
|-
| 33
| 34
| 0-9-13
| 0-9-13
| 1-14/9-7/4
| 1-14/9-7/4
| utonal
| utonal
|
|-
|-
| 34
| 35
| 0-11-13
| 0-11-13
| 1-7/6-7/4
| 1-7/6-7/4
| utonal
| utonal
|
|-
|-
| 35
| 36
| 0-12-13
| 0-12-13
| 1-10/7-7/4
| 1-10/7-7/4
| werckismic
| werckismic
|
|-
|-
| 36
| 37
| 0-8-20
| 0-8-20
| 1-14/11-20/11
| 1-14/11-20/11
| otonal
| otonal
|
|-
|-
| 37
| 38
| 0-9-20
| 0-9-20
| 1-14/9-20/11
| 1-14/9-20/11
| swetismic
| swetismic
|
|-
|-
| 38
| 39
| 0-11-20
| 0-11-20
| 1-7/6-20/11
| 1-7/6-20/11
| swetismic
| swetismic
|
|-
|-
| 39
| 40
| 0-12-20
| 0-12-20
| 1-10/7-20/11
| 1-10/7-20/11
| utonal
| utonal
|(b5)
|-
|-
| 40
| 41
| 0-1-21
| 0-1-21
| 1-11/9-10/9
| 1-11/9-10/9
| otonal
| otonal
|
|-
|-
| 41
| 42
| 0-8-21
| 0-8-21
| 1-14/11-10/9
| 1-14/11-10/9
| werckismic
| werckismic
|
|-
|-
| 42
| 43
| 0-9-21
| 0-9-21
| 1-14/9-10/9
| 1-14/9-10/9
| otonal
| otonal
|
|-
|-
| 43
| 44
| 0-12-21
| 0-12-21
| 1-10/7-10/9
| 1-10/7-10/9
| utonal
| utonal
|
|-
|-
| 44
| 45
| 0-13-21
| 0-13-21
| 1-7/4-10/9
| 1-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 45
| 46
| 0-20-21
| 0-20-21
| 1-20/11-10/9
| 1-20/11-10/9
| utonal
| utonal
|
|-
|-
| 46
| 47
| 0-2-23
| 0-2-23
| 1-3/2-5/3
| 1-3/2-5/3
| otonal
| otonal
|
|-
|-
| 47
| 48
| 0-3-23
| 0-3-23
| 1-11/6-5/3
| 1-11/6-5/3
| otonal
| otonal
|
|-
|-
| 48
| 49
| 0-11-23
| 0-11-23
| 1-7/6-5/3
| 1-7/6-5/3
| otonal
| otonal
|
|-
|-
| 49
| 50
| 0-12-23
| 0-12-23
| 1-10/7-5/3
| 1-10/7-5/3
| utonal
| utonal
|
|-
|-
| 50
| 51
| 0-20-23
| 0-20-23
| 1-20/11-5/3
| 1-20/11-5/3
| utonal
| utonal
|
|-
|-
| 51
| 52
| 0-21-23
| 0-21-23
| 1-10/9-5/3
| 1-10/9-5/3
| utonal
| utonal
|
|-
|-
| 52
| 53
| 0-2-25
| 0-2-25
| 1-3/2-5/4
| 1-3/2-5/4
| otonal
| otonal
|
|-
|-
| 53
| 54
| 0-4-25
| 0-4-25
| 1-9/8-5/4
| 1-9/8-5/4
| otonal
| otonal
|
|-
|-
| 54
| 55
| 0-5-25
| 0-5-25
| 1-11/8-5/4
| 1-11/8-5/4
| otonal
| otonal
|
|-
|-
| 55
| 56
| 0-12-25
| 0-12-25
| 1-10/7-5/4
| 1-10/7-5/4
| utonal
| utonal
|
|-
|-
| 56
| 57
| 0-13-25
| 0-13-25
| 1-7/4-5/4
| 1-7/4-5/4
| otonal
| otonal
|
|-
|-
| 57
| 58
| 0-20-25
| 0-20-25
| 1-20/11-5/4
| 1-20/11-5/4
| utonal
| utonal
|
|-
|-
| 58
| 59
| 0-21-25
| 0-21-25
| 1-10/9-5/4
| 1-10/9-5/4
| utonal
| utonal
|
|-
|-
| 59
| 60
| 0-23-25
| 0-23-25
| 1-5/3-5/4
| 1-5/3-5/4
| utonal
| utonal
|
|}
|}


Line 314: Line 438:
! Transversal
! Transversal
! Type
! Type
!Name
|-
|-
| 1
| 1
Line 319: Line 444:
| 1-11/9-3/2-11/6
| 1-11/9-3/2-11/6
| rastmic
| rastmic
|~7
|-
|-
| 2
| 2
Line 324: Line 450:
| 1-11/9-3/2-9/8
| 1-11/9-3/2-9/8
| rastmic
| rastmic
|~,9
|-
|-
| 3
| 3
Line 329: Line 456:
| 1-11/9-11/6-9/8
| 1-11/9-11/6-9/8
| rastmic
| rastmic
|~9no5
|-
|-
| 4
| 4
Line 334: Line 462:
| 1-3/2-11/6-9/8
| 1-3/2-11/6-9/8
| rastmic
| rastmic
|~9no3
|-
|-
| 5
| 5
Line 339: Line 468:
| 1-11/9-3/2-11/8
| 1-11/9-3/2-11/8
| rastmic
| rastmic
|~6,9
|-
|-
| 6
| 6
Line 344: Line 474:
| 1-11/9-11/6-11/8
| 1-11/9-11/6-11/8
| utonal
| utonal
|
|-
|-
| 7
| 7
Line 349: Line 480:
| 1-3/2-11/6-11/8
| 1-3/2-11/6-11/8
| ambitonal
| ambitonal
|
|-
|-
| 8
| 8
Line 354: Line 486:
| 1-11/9-9/8-11/8
| 1-11/9-9/8-11/8
| rastmic
| rastmic
|
|-
|-
| 9
| 9
Line 359: Line 492:
| 1-3/2-9/8-11/8
| 1-3/2-9/8-11/8
| otonal
| otonal
|
|-
|-
| 10
| 10
Line 364: Line 498:
| 1-11/6-9/8-11/8
| 1-11/6-9/8-11/8
| rastmic
| rastmic
|~11no35
|-
|11
|0-4-5-6
|1-11/9-3/2-16/9
|
|~,7
|-
|-
| 11
| 12
| 0-3-4-8
| 0-3-4-8
| 1-11/6-9/8-14/11
| 1-11/6-9/8-14/11
| parahemif
| parahemif
|9(~7)no5
|-
|-
| 12
| 13
| 0-3-5-8
| 0-3-5-8
| 1-11/6-11/8-14/11
| 1-11/6-11/8-14/11
| hemimin
| hemimin
|,~7~11no5
|-
|-
| 13
| 14
| 0-4-5-8
| 0-4-5-8
| 1-9/8-11/8-14/11
| 1-9/8-11/8-14/11
| parahemif
| parahemif
|
|-
|-
| 14
| 15
| 0-1-4-9
| 0-1-4-9
| 1-11/9-9/8-14/9
| 1-11/9-9/8-14/9
| parahemif
| parahemif
|
|-
|-
| 15
| 16
| 0-1-5-9
| 0-1-5-9
| 1-11/9-11/8-14/9
| 1-11/9-11/8-14/9
| pentacircle
| pentacircle
|,~6,9no5
|-
|-
| 16
| 17
| 0-4-5-9
| 0-4-5-9
| 1-9/8-11/8-14/9
| 1-9/8-11/8-14/9
| pentacircle
| pentacircle
|
|-
|-
| 17
| 18
| 0-4-8-9
| 0-4-8-9
| 1-9/8-14/11-14/9
| 1-9/8-14/11-14/9
| pentacircle
| pentacircle
|
|-
|-
| 18
| 19
| 0-5-8-9
| 0-5-8-9
| 1-11/8-14/11-14/9
| 1-11/8-14/11-14/9
| parahemif
| parahemif
|
|-
|-
| 19
| 20
| 0-2-3-11
| 0-2-3-11
| 1-3/2-11/6-7/6
| 1-3/2-11/6-7/6
| otonal
| otonal
|
|-
|-
| 20
| 21
| 0-3-8-11
| 0-3-8-11
| 1-11/6-14/11-7/6
| 1-11/6-14/11-7/6
| hemimin
| hemimin
|
|-
|-
| 21
| 22
| 0-8-9-11
| 0-8-9-11
| 1-14/11-14/9-7/6
| 1-14/11-14/9-7/6
| utonal
| utonal
|
|-
|-
| 22
| 23
| 0-1-3-12
| 0-1-3-12
| 1-11/9-11/6-10/7
| 1-11/9-11/6-10/7
| swetismic
| swetismic
|
|-
|-
| 23
| 24
| 0-1-4-12
| 0-1-4-12
| 1-11/9-9/8-10/7
| 1-11/9-9/8-10/7
| jove
| jove
|
|-
|-
| 24
| 25
| 0-3-4-12
| 0-3-4-12
| 1-11/6-9/8-10/7
| 1-11/6-9/8-10/7
| jove
| jove
|
|-
|-
| 25
| 26
| 0-3-8-12
| 0-3-8-12
| 1-11/6-14/11-10/7
| 1-11/6-14/11-10/7
| hemififths
| hemififths
|
|-
|-
| 26
| 27
| 0-4-8-12
| 0-4-8-12
| 1-9/8-14/11-10/7
| 1-9/8-14/11-10/7
| pele
| pele
|
|-
|-
| 27
| 28
| 0-1-9-12
| 0-1-9-12
| 1-11/9-14/9-10/7
| 1-11/9-14/9-10/7
| swetismic
| swetismic
|
|-
|-
| 28
| 29
| 0-4-9-12
| 0-4-9-12
| 1-9/8-14/9-10/7
| 1-9/8-14/9-10/7
| hemififths
| hemififths
|
|-
|-
| 29
| 30
| 0-8-9-12
| 0-8-9-12
| 1-14/11-14/9-10/7
| 1-14/11-14/9-10/7
| jove
| jove
|
|-
|-
| 30
| 31
| 0-3-11-12
| 0-3-11-12
| 1-11/6-7/6-10/7
| 1-11/6-7/6-10/7
| swetismic
| swetismic
|
|-
|-
| 31
| 32
| 0-8-11-12
| 0-8-11-12
| 1-14/11-7/6-10/7
| 1-14/11-7/6-10/7
| jove
| jove
|
|-
|-
| 32
| 33
| 0-9-11-12
| 0-9-11-12
| 1-14/9-7/6-10/7
| 1-14/9-7/6-10/7
| swetismic
| swetismic
|
|-
|-
| 33
| 34
| 0-1-2-13
| 0-1-2-13
| 1-11/9-3/2-7/4
| 1-11/9-3/2-7/4
| jove
| jove
|
|-
|-
| 34
| 35
| 0-1-4-13
| 0-1-4-13
| 1-11/9-9/8-7/4
| 1-11/9-9/8-7/4
| jove
| jove
|
|-
|-
| 35
| 36
| 0-2-4-13
| 0-2-4-13
| 1-3/2-9/8-7/4
| 1-3/2-9/8-7/4
| otonal
| otonal
|
|-
|-
| 36
| 37
| 0-1-5-13
| 0-1-5-13
| 1-11/9-11/8-7/4
| 1-11/9-11/8-7/4
| werckismic
| werckismic
|
|-
|-
| 37
| 38
| 0-2-5-13
| 0-2-5-13
| 1-3/2-11/8-7/4
| 1-3/2-11/8-7/4
| otonal
| otonal
|
|-
|-
| 38
| 39
| 0-4-5-13
| 0-4-5-13
| 1-9/8-11/8-7/4
| 1-9/8-11/8-7/4
| otonal
| otonal
|
|-
|-
| 39
| 40
| 0-4-8-13
| 0-4-8-13
| 1-9/8-14/11-7/4
| 1-9/8-14/11-7/4
| pentacircle
| pentacircle
|
|-
|-
| 40
| 41
| 0-5-8-13
| 0-5-8-13
| 1-11/8-14/11-7/4
| 1-11/8-14/11-7/4
| hemimin
| hemimin
|
|-
|-
| 41
| 42
| 0-1-9-13
| 0-1-9-13
| 1-11/9-14/9-7/4
| 1-11/9-14/9-7/4
| werckismic
| werckismic
|
|-
|-
| 42
| 43
| 0-4-9-13
| 0-4-9-13
| 1-9/8-14/9-7/4
| 1-9/8-14/9-7/4
| pentacircle
| pentacircle
|
|-
|-
| 43
| 44
| 0-5-9-13
| 0-5-9-13
| 1-11/8-14/9-7/4
| 1-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|-
|-
| 44
| 45
| 0-8-9-13
| 0-8-9-13
| 1-14/11-14/9-7/4
| 1-14/11-14/9-7/4
| utonal
| utonal
|
|-
|-
| 45
| 46
| 0-2-11-13
| 0-2-11-13
| 1-3/2-7/6-7/4
| 1-3/2-7/6-7/4
| ambitonal
| ambitonal
|
|-
|-
| 46
| 47
| 0-8-11-13
| 0-8-11-13
| 1-14/11-7/6-7/4
| 1-14/11-7/6-7/4
| utonal
| utonal
|
|-
|-
| 47
| 48
| 0-9-11-13
| 0-9-11-13
| 1-14/9-7/6-7/4
| 1-14/9-7/6-7/4
| utonal
| utonal
|
|-
|-
| 48
| 49
| 0-1-12-13
| 0-1-12-13
| 1-11/9-10/7-7/4
| 1-11/9-10/7-7/4
| jove
| jove
|
|-
|-
| 49
| 50
| 0-4-12-13
| 0-4-12-13
| 1-9/8-10/7-7/4
| 1-9/8-10/7-7/4
| werckismic
| werckismic
|
|-
|-
| 50
| 51
| 0-8-12-13
| 0-8-12-13
| 1-14/11-10/7-7/4
| 1-14/11-10/7-7/4
| werckismic
| werckismic
|
|-
|-
| 51
| 52
| 0-9-12-13
| 0-9-12-13
| 1-14/9-10/7-7/4
| 1-14/9-10/7-7/4
| jove
| jove
|
|-
|-
| 52
| 53
| 0-11-12-13
| 0-11-12-13
| 1-7/6-10/7-7/4
| 1-7/6-10/7-7/4
| jove
| jove
|
|-
|-
| 53
| 54
| 0-8-9-20
| 0-8-9-20
| 1-14/11-14/9-20/11
| 1-14/11-14/9-20/11
| swetismic
| swetismic
|
|-
|-
| 54
| 55
| 0-8-11-20
| 0-8-11-20
| 1-14/11-7/6-20/11
| 1-14/11-7/6-20/11
| swetismic
| swetismic
|
|-
|-
| 55
| 56
| 0-9-11-20
| 0-9-11-20
| 1-14/9-7/6-20/11
| 1-14/9-7/6-20/11
| swetismic
| swetismic
|
|-
|-
| 56
| 57
| 0-8-12-20
| 0-8-12-20
| 1-14/11-10/7-20/11
| 1-14/11-10/7-20/11
| werckismic
| werckismic
|
|-
|-
| 57
| 58
| 0-9-12-20
| 0-9-12-20
| 1-14/9-10/7-20/11
| 1-14/9-10/7-20/11
| swetismic
| swetismic
|
|-
|-
| 58
| 59
| 0-11-12-20
| 0-11-12-20
| 1-7/6-10/7-20/11
| 1-7/6-10/7-20/11
| swetismic
| swetismic
|
|-
|-
| 59
| 60
| 0-1-9-21
| 0-1-9-21
| 1-11/9-14/9-10/9
| 1-11/9-14/9-10/9
| otonal
| otonal
|
|-
|-
| 60
| 61
| 0-8-9-21
| 0-8-9-21
| 1-14/11-14/9-10/9
| 1-14/11-14/9-10/9
| werckismic
| werckismic
|
|-
|-
| 61
| 62
| 0-1-12-21
| 0-1-12-21
| 1-11/9-10/7-10/9
| 1-11/9-10/7-10/9
| swetismic
| swetismic
|
|-
|-
| 62
| 63
| 0-8-12-21
| 0-8-12-21
| 1-14/11-10/7-10/9
| 1-14/11-10/7-10/9
| werckismic
| werckismic
|
|-
|-
| 63
| 64
| 0-9-12-21
| 0-9-12-21
| 1-14/9-10/7-10/9
| 1-14/9-10/7-10/9
| swetismic
| swetismic
|
|-
|-
| 64
| 65
| 0-1-13-21
| 0-1-13-21
| 1-11/9-7/4-10/9
| 1-11/9-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 65
| 66
| 0-8-13-21
| 0-8-13-21
| 1-14/11-7/4-10/9
| 1-14/11-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 66
| 67
| 0-9-13-21
| 0-9-13-21
| 1-14/9-7/4-10/9
| 1-14/9-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 67
| 68
| 0-12-13-21
| 0-12-13-21
| 1-10/7-7/4-10/9
| 1-10/7-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 68
| 69
| 0-8-20-21
| 0-8-20-21
| 1-14/11-20/11-10/9
| 1-14/11-20/11-10/9
| werckismic
| werckismic
|
|-
|-
| 69
| 70
| 0-9-20-21
| 0-9-20-21
| 1-14/9-20/11-10/9
| 1-14/9-20/11-10/9
| swetismic
| swetismic
|
|-
|-
| 70
| 71
| 0-12-20-21
| 0-12-20-21
| 1-10/7-20/11-10/9
| 1-10/7-20/11-10/9
| utonal
| utonal
|
|-
|-
| 71
| 72
| 0-2-3-23
| 0-2-3-23
| 1-3/2-11/6-5/3
| 1-3/2-11/6-5/3
| otonal
| otonal
|
|-
|-
| 72
| 73
| 0-2-11-23
| 0-2-11-23
| 1-3/2-7/6-5/3
| 1-3/2-7/6-5/3
| otonal
| otonal
|
|-
|-
| 73
| 74
| 0-3-11-23
| 0-3-11-23
| 1-11/6-7/6-5/3
| 1-11/6-7/6-5/3
| otonal
| otonal
|
|-
|-
| 74
| 75
| 0-3-12-23
| 0-3-12-23
| 1-11/6-10/7-5/3
| 1-11/6-10/7-5/3
| swetismic
| swetismic
|
|-
|-
| 75
| 76
| 0-11-12-23
| 0-11-12-23
| 1-7/6-10/7-5/3
| 1-7/6-10/7-5/3
| swetismic
| swetismic
|
|-
|-
| 76
| 77
| 0-11-20-23
| 0-11-20-23
| 1-7/6-20/11-5/3
| 1-7/6-20/11-5/3
| swetismic
| swetismic
|
|-
|-
| 77
| 78
| 0-12-20-23
| 0-12-20-23
| 1-10/7-20/11-5/3
| 1-10/7-20/11-5/3
| utonal
| utonal
|
|-
|-
| 78
| 79
| 0-12-21-23
| 0-12-21-23
| 1-10/7-10/9-5/3
| 1-10/7-10/9-5/3
| utonal
| utonal
|
|-
|-
| 79
| 80
| 0-20-21-23
| 0-20-21-23
| 1-20/11-10/9-5/3
| 1-20/11-10/9-5/3
| utonal
| utonal
|
|-
|-
| 80
| 81
| 0-2-4-25
| 0-2-4-25
| 1-3/2-9/8-5/4
| 1-3/2-9/8-5/4
| otonal
| otonal
|
|-
|-
| 81
| 82
| 0-2-5-25
| 0-2-5-25
| 1-3/2-11/8-5/4
| 1-3/2-11/8-5/4
| otonal
| otonal
|
|-
|-
| 82
| 83
| 0-4-5-25
| 0-4-5-25
| 1-9/8-11/8-5/4
| 1-9/8-11/8-5/4
| otonal
| otonal
|
|-
|-
| 83
| 84
| 0-4-12-25
| 0-4-12-25
| 1-9/8-10/7-5/4
| 1-9/8-10/7-5/4
| werckismic
| werckismic
|
|-
|-
| 84
| 85
| 0-2-13-25
| 0-2-13-25
| 1-3/2-7/4-5/4
| 1-3/2-7/4-5/4
| otonal
| otonal
|
|-
|-
| 85
| 86
| 0-4-13-25
| 0-4-13-25
| 1-9/8-7/4-5/4
| 1-9/8-7/4-5/4
| otonal
| otonal
|
|-
|-
| 86
| 87
| 0-5-13-25
| 0-5-13-25
| 1-11/8-7/4-5/4
| 1-11/8-7/4-5/4
| otonal
| otonal
|
|-
|-
| 87
| 88
| 0-12-13-25
| 0-12-13-25
| 1-10/7-7/4-5/4
| 1-10/7-7/4-5/4
| werckismic
| werckismic
|
|-
|-
| 88
| 89
| 0-12-20-25
| 0-12-20-25
| 1-10/7-20/11-5/4
| 1-10/7-20/11-5/4
| utonal
| utonal
|
|-
|-
| 89
| 90
| 0-12-21-25
| 0-12-21-25
| 1-10/7-10/9-5/4
| 1-10/7-10/9-5/4
| utonal
| utonal
|
|-
|-
| 90
| 91
| 0-13-21-25
| 0-13-21-25
| 1-7/4-10/9-5/4
| 1-7/4-10/9-5/4
| werckismic
| werckismic
|
|-
|-
| 91
| 92
| 0-20-21-25
| 0-20-21-25
| 1-20/11-10/9-5/4
| 1-20/11-10/9-5/4
| utonal
| utonal
|
|-
|-
| 92
| 93
| 0-2-23-25
| 0-2-23-25
| 1-3/2-5/3-5/4
| 1-3/2-5/3-5/4
| ambitonal
| ambitonal
|
|-
|-
| 93
| 94
| 0-12-23-25
| 0-12-23-25
| 1-10/7-5/3-5/4
| 1-10/7-5/3-5/4
| utonal
| utonal
|
|-
|-
| 94
| 95
| 0-20-23-25
| 0-20-23-25
| 1-20/11-5/3-5/4
| 1-20/11-5/3-5/4
| utonal
| utonal
|
|-
|-
| 95
| 96
| 0-21-23-25
| 0-21-23-25
| 1-10/9-5/3-5/4
| 1-10/9-5/3-5/4
| utonal
| utonal
|
|}
|}


Line 798: Line 1,024:
! Transversal
! Transversal
! Type
! Type
!Name
|-
|-
| 1
| 1
Line 803: Line 1,030:
| 1-11/9-3/2-11/6-9/8
| 1-11/9-3/2-11/6-9/8
| rastmic
| rastmic
|~9
|-
|-
| 2
| 2
Line 808: Line 1,036:
| 1-11/9-3/2-11/6-11/8
| 1-11/9-3/2-11/6-11/8
| rastmic
| rastmic
|~7,~11
|-
|-
| 3
| 3
Line 813: Line 1,042:
| 1-11/9-3/2-9/8-11/8
| 1-11/9-3/2-9/8-11/8
| rastmic
| rastmic
|~,9~11 <u>or</u> ~11no7
|-
|-
| 4
| 4
Line 818: Line 1,048:
| 1-11/9-11/6-9/8-11/8
| 1-11/9-11/6-9/8-11/8
| rastmic
| rastmic
|~11no5
|-
|-
| 5
| 5
Line 823: Line 1,054:
| 1-3/2-11/6-9/8-11/8
| 1-3/2-11/6-9/8-11/8
| rastmic
| rastmic
|~11no3
|-
|-
| 6
| 6
Line 828: Line 1,060:
| 1-11/6-9/8-11/8-14/11
| 1-11/6-9/8-11/8-14/11
| parahemif
| parahemif
|
|-
|-
| 7
| 7
Line 833: Line 1,066:
| 1-11/9-9/8-11/8-14/9
| 1-11/9-9/8-11/8-14/9
| parahemif
| parahemif
|
|-
|-
| 8
| 8
Line 838: Line 1,072:
| 1-9/8-11/8-14/11-14/9
| 1-9/8-11/8-14/11-14/9
| parahemif
| parahemif
|
|-
|-
| 9
| 9
Line 843: Line 1,078:
| 1-11/9-11/6-9/8-10/7
| 1-11/9-11/6-9/8-10/7
| jove
| jove
|
|-
|-
| 10
| 10
Line 848: Line 1,084:
| 1-11/6-9/8-14/11-10/7
| 1-11/6-9/8-14/11-10/7
| hemififths
| hemififths
|
|-
|-
| 11
| 11
Line 853: Line 1,090:
| 1-11/9-9/8-14/9-10/7
| 1-11/9-9/8-14/9-10/7
| hemififths
| hemififths
|
|-
|-
| 12
| 12
Line 858: Line 1,096:
| 1-9/8-14/11-14/9-10/7
| 1-9/8-14/11-14/9-10/7
| hemififths
| hemififths
|
|-
|-
| 13
| 13
Line 863: Line 1,102:
| 1-11/6-14/11-7/6-10/7
| 1-11/6-14/11-7/6-10/7
| hemififths
| hemififths
|
|-
|-
| 14
| 14
Line 868: Line 1,108:
| 1-14/11-14/9-7/6-10/7
| 1-14/11-14/9-7/6-10/7
| jove
| jove
|
|-
|-
| 15
| 15
Line 873: Line 1,114:
| 1-11/9-3/2-9/8-7/4
| 1-11/9-3/2-9/8-7/4
| jove
| jove
|
|-
|-
| 16
| 16
Line 878: Line 1,120:
| 1-11/9-3/2-11/8-7/4
| 1-11/9-3/2-11/8-7/4
| jove
| jove
|
|-
|-
| 17
| 17
Line 883: Line 1,126:
| 1-11/9-9/8-11/8-7/4
| 1-11/9-9/8-11/8-7/4
| jove
| jove
|
|-
|-
| 18
| 18
Line 888: Line 1,132:
| 1-3/2-9/8-11/8-7/4
| 1-3/2-9/8-11/8-7/4
| otonal
| otonal
|
|-
|-
| 19
| 19
Line 893: Line 1,138:
| 1-9/8-11/8-14/11-7/4
| 1-9/8-11/8-14/11-7/4
| parahemif
| parahemif
|
|-
|-
| 20
| 20
Line 898: Line 1,144:
| 1-11/9-9/8-14/9-7/4
| 1-11/9-9/8-14/9-7/4
| hemififths
| hemififths
|
|-
|-
| 21
| 21
Line 903: Line 1,150:
| 1-11/9-11/8-14/9-7/4
| 1-11/9-11/8-14/9-7/4
| pele
| pele
|
|-
|-
| 22
| 22
Line 908: Line 1,156:
| 1-9/8-11/8-14/9-7/4
| 1-9/8-11/8-14/9-7/4
| pentacircle
| pentacircle
|
|-
|-
| 23
| 23
Line 913: Line 1,162:
| 1-9/8-14/11-14/9-7/4
| 1-9/8-14/11-14/9-7/4
| pentacircle
| pentacircle
|
|-
|-
| 24
| 24
Line 918: Line 1,168:
| 1-11/8-14/11-14/9-7/4
| 1-11/8-14/11-14/9-7/4
| parahemif
| parahemif
|
|-
|-
| 25
| 25
Line 923: Line 1,174:
| 1-14/11-14/9-7/6-7/4
| 1-14/11-14/9-7/6-7/4
| utonal
| utonal
|
|-
|-
| 26
| 26
Line 928: Line 1,180:
| 1-11/9-9/8-10/7-7/4
| 1-11/9-9/8-10/7-7/4
| jove
| jove
|
|-
|-
| 27
| 27
Line 933: Line 1,186:
| 1-9/8-14/11-10/7-7/4
| 1-9/8-14/11-10/7-7/4
| pele
| pele
|
|-
|-
| 28
| 28
Line 938: Line 1,192:
| 1-11/9-14/9-10/7-7/4
| 1-11/9-14/9-10/7-7/4
| jove
| jove
|
|-
|-
| 29
| 29
Line 943: Line 1,198:
| 1-9/8-14/9-10/7-7/4
| 1-9/8-14/9-10/7-7/4
| hemififths
| hemififths
|
|-
|-
| 30
| 30
Line 948: Line 1,204:
| 1-14/11-14/9-10/7-7/4
| 1-14/11-14/9-10/7-7/4
| jove
| jove
|
|-
|-
| 31
| 31
Line 953: Line 1,210:
| 1-14/11-7/6-10/7-7/4
| 1-14/11-7/6-10/7-7/4
| jove
| jove
|
|-
|-
| 32
| 32
Line 958: Line 1,216:
| 1-14/9-7/6-10/7-7/4
| 1-14/9-7/6-10/7-7/4
| jove
| jove
|
|-
|-
| 33
| 33
Line 963: Line 1,222:
| 1-14/11-14/9-7/6-20/11
| 1-14/11-14/9-7/6-20/11
| swetismic
| swetismic
|
|-
|-
| 34
| 34
Line 968: Line 1,228:
| 1-14/11-14/9-10/7-20/11
| 1-14/11-14/9-10/7-20/11
| jove
| jove
|
|-
|-
| 35
| 35
Line 973: Line 1,234:
| 1-14/11-7/6-10/7-20/11
| 1-14/11-7/6-10/7-20/11
| jove
| jove
|
|-
|-
| 36
| 36
Line 978: Line 1,240:
| 1-14/9-7/6-10/7-20/11
| 1-14/9-7/6-10/7-20/11
| swetismic
| swetismic
|
|-
|-
| 37
| 37
Line 983: Line 1,246:
| 1-11/9-14/9-10/7-10/9
| 1-11/9-14/9-10/7-10/9
| swetismic
| swetismic
|
|-
|-
| 38
| 38
Line 988: Line 1,252:
| 1-14/11-14/9-10/7-10/9
| 1-14/11-14/9-10/7-10/9
| jove
| jove
|
|-
|-
| 39
| 39
Line 993: Line 1,258:
| 1-11/9-14/9-7/4-10/9
| 1-11/9-14/9-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 40
| 40
Line 998: Line 1,264:
| 1-14/11-14/9-7/4-10/9
| 1-14/11-14/9-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 41
| 41
Line 1,003: Line 1,270:
| 1-11/9-10/7-7/4-10/9
| 1-11/9-10/7-7/4-10/9
| jove
| jove
|
|-
|-
| 42
| 42
Line 1,008: Line 1,276:
| 1-14/11-10/7-7/4-10/9
| 1-14/11-10/7-7/4-10/9
| werckismic
| werckismic
|
|-
|-
| 43
| 43
Line 1,013: Line 1,282:
| 1-14/9-10/7-7/4-10/9
| 1-14/9-10/7-7/4-10/9
| jove
| jove
|
|-
|-
| 44
| 44
Line 1,018: Line 1,288:
| 1-14/11-14/9-20/11-10/9
| 1-14/11-14/9-20/11-10/9
| jove
| jove
|
|-
|-
| 45
| 45
Line 1,023: Line 1,294:
| 1-14/11-10/7-20/11-10/9
| 1-14/11-10/7-20/11-10/9
| werckismic
| werckismic
|
|-
|-
| 46
| 46
Line 1,028: Line 1,300:
| 1-14/9-10/7-20/11-10/9
| 1-14/9-10/7-20/11-10/9
| swetismic
| swetismic
|
|-
|-
| 47
| 47
Line 1,033: Line 1,306:
| 1-3/2-11/6-7/6-5/3
| 1-3/2-11/6-7/6-5/3
| otonal
| otonal
|
|-
|-
| 48
| 48
Line 1,038: Line 1,312:
| 1-11/6-7/6-10/7-5/3
| 1-11/6-7/6-10/7-5/3
| swetismic
| swetismic
|
|-
|-
| 49
| 49
Line 1,043: Line 1,318:
| 1-7/6-10/7-20/11-5/3
| 1-7/6-10/7-20/11-5/3
| swetismic
| swetismic
|
|-
|-
| 50
| 50
Line 1,048: Line 1,324:
| 1-10/7-20/11-10/9-5/3
| 1-10/7-20/11-10/9-5/3
| utonal
| utonal
|
|-
|-
| 51
| 51
Line 1,053: Line 1,330:
| 1-3/2-9/8-11/8-5/4
| 1-3/2-9/8-11/8-5/4
| otonal
| otonal
|
|-
|-
| 52
| 52
Line 1,058: Line 1,336:
| 1-3/2-9/8-7/4-5/4
| 1-3/2-9/8-7/4-5/4
| otonal
| otonal
|
|-
|-
| 53
| 53
Line 1,063: Line 1,342:
| 1-3/2-11/8-7/4-5/4
| 1-3/2-11/8-7/4-5/4
| otonal
| otonal
|
|-
|-
| 54
| 54
Line 1,068: Line 1,348:
| 1-9/8-11/8-7/4-5/4
| 1-9/8-11/8-7/4-5/4
| otonal
| otonal
|
|-
|-
| 55
| 55
Line 1,073: Line 1,354:
| 1-9/8-10/7-7/4-5/4
| 1-9/8-10/7-7/4-5/4
| werckismic
| werckismic
|
|-
|-
| 56
| 56
Line 1,078: Line 1,360:
| 1-10/7-7/4-10/9-5/4
| 1-10/7-7/4-10/9-5/4
| werckismic
| werckismic
|
|-
|-
| 57
| 57
Line 1,083: Line 1,366:
| 1-10/7-20/11-10/9-5/4
| 1-10/7-20/11-10/9-5/4
| utonal
| utonal
|
|-
|-
| 58
| 58
Line 1,088: Line 1,372:
| 1-10/7-20/11-5/3-5/4
| 1-10/7-20/11-5/3-5/4
| utonal
| utonal
|
|-
|-
| 59
| 59
Line 1,093: Line 1,378:
| 1-10/7-10/9-5/3-5/4
| 1-10/7-10/9-5/3-5/4
| utonal
| utonal
|
|-
|-
| 60
| 60
Line 1,098: Line 1,384:
| 1-20/11-10/9-5/3-5/4
| 1-20/11-10/9-5/3-5/4
| utonal
| utonal
|
|}
|}


Line 1,107: Line 1,394:
! Transversal
! Transversal
! Type
! Type
!Name
|-
|-
| 1
| 1
Line 1,112: Line 1,400:
| 1-11/9-3/2-11/6-9/8-11/8
| 1-11/9-3/2-11/6-9/8-11/8
| rastmic
| rastmic
|~11
|-
|-
| 2
| 2
Line 1,117: Line 1,406:
| 1-11/9-3/2-9/8-11/8-7/4
| 1-11/9-3/2-9/8-11/8-7/4
| jove
| jove
|
|-
|-
| 3
| 3
Line 1,122: Line 1,412:
| 1-11/9-9/8-11/8-14/9-7/4
| 1-11/9-9/8-11/8-14/9-7/4
| hemififths
| hemififths
|
|-
|-
| 4
| 4
Line 1,127: Line 1,418:
| 1-9/8-11/8-14/11-14/9-7/4
| 1-9/8-11/8-14/11-14/9-7/4
| nofives
| nofives
|
|-
|-
| 5
| 5
Line 1,132: Line 1,424:
| 1-11/9-9/8-14/9-10/7-7/4
| 1-11/9-9/8-14/9-10/7-7/4
| hemififths
| hemififths
|
|-
|-
| 6
| 6
Line 1,137: Line 1,430:
| 1-9/8-14/11-14/9-10/7-7/4
| 1-9/8-14/11-14/9-10/7-7/4
| hemififths
| hemififths
|
|-
|-
| 7
| 7
Line 1,142: Line 1,436:
| 1-14/11-14/9-7/6-10/7-7/4
| 1-14/11-14/9-7/6-10/7-7/4
| jove
| jove
|
|-
|-
| 8
| 8
Line 1,147: Line 1,442:
| 1-14/11-14/9-7/6-10/7-20/11
| 1-14/11-14/9-7/6-10/7-20/11
| jove
| jove
|
|-
|-
| 9
| 9
Line 1,152: Line 1,448:
| 1-11/9-14/9-10/7-7/4-10/9
| 1-11/9-14/9-10/7-7/4-10/9
| jove
| jove
|
|-
|-
| 10
| 10
Line 1,157: Line 1,454:
| 1-14/11-14/9-10/7-7/4-10/9
| 1-14/11-14/9-10/7-7/4-10/9
| jove
| jove
|
|-
|-
| 11
| 11
Line 1,162: Line 1,460:
| 1-14/11-14/9-10/7-20/11-10/9
| 1-14/11-14/9-10/7-20/11-10/9
| jove
| jove
|
|-
|-
| 12
| 12
Line 1,167: Line 1,466:
| 1-3/2-9/8-11/8-7/4-5/4
| 1-3/2-9/8-11/8-7/4-5/4
| otonal
| otonal
|
|-
|-
| 13
| 13
Line 1,172: Line 1,472:
| 1-10/7-20/11-10/9-5/3-5/4
| 1-10/7-20/11-10/9-5/3-5/4
| utonal
| utonal
|
|}
|}


Revision as of 07:34, 15 November 2024

Below are listed the dyadic chords of 11-limit hemififths temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 896/891 pentacircle, by 243/242 rastmic, and by 1344/1331 hemimin. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove. Those requiring both 441/440 and 896/891 are labeled pele. Those requiring any two of 243/242, 896/891 or 1344/1331 are labeled parahemif. If the full hemififths is required because of the tempering out of three independent hemififths commas, the chord is labeled "hemififths".

A striking feature of these hemififths chords is that essentially just chords tend to be of higher complexity than essentially tempered chords. Hemififths has MOS of size 7, 10, 17 and 24, and even seven notes are well-supplied with chords, mostly but by no means entirely essentially tempered chords. Extending consideration to the 13-limit adds even more such chords.

Chords are named with ups and downs. The tilde ~ means mid, half-way between major and minor. The comma (the actual punctuation mark) is pronounced "add", thus C~,7 is "C mid add7".

Hemififth's genchain
Genspan 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ratio 1/1 11/9 3/2 11/6 9/8 11/8 27/16 33/32 14/11 14/9 40/21 7/6 10/7 7/4 15/14 21/16
Interval P1 ~3 P5 ~7 M2 ~4 M6 ^1 M3 ^5 M7 ^2 A4 ^6 A1 ^3

Triads

# Chord Transversal Type Name
1 0-1-2 1-11/9-3/2 rastmic ~
2 0-1-3 1-11/9-11/6 utonal ~7no5
3 0-2-3 1-3/2-11/6 otonal ~7no3
4 0-1-4 1-11/9-9/8 rastmic
5 0-2-4 1-3/2-9/8 ambitonal 2 or 4
6 0-3-4 1-11/6-9/8 rastmic
7 0-1-5 1-11/9-11/8 utonal ~6sus2
8 0-2-5 1-3/2-11/8 otonal ~7sus4
9 0-3-5 1-11/6-11/8 utonal ~2
10 0-4-5 1-9/8-11/8 otonal ~,7no5
11 0-2-8 1-3/2-14/11 (major)
12 0-3-8 1-11/6-14/11 hemimin ,~7no5
13 0-4-8 1-9/8-14/11 pentacircle ,9no5
14 0-5-8 1-11/8-14/11 hemimin
15 0-1-9 1-11/9-14/9 otonal
16 0-4-9 1-9/8-14/9 pentacircle 7~4no5
17 0-5-9 1-11/8-14/9 pentacircle
18 0-8-9 1-14/11-14/9 utonal (^5)
19 0-2-11 1-3/2-7/6 otonal
20 0-3-11 1-11/6-7/6 otonal
21 0-8-11 1-14/11-7/6 utonal
22 0-9-11 1-14/9-7/6 utonal
23 0-1-12 1-11/9-10/7 swetismic
24 0-3-12 1-11/6-10/7 swetismic v4(b5)
25 0-4-12 1-9/8-10/7 werckismic
26 0-8-12 1-14/11-10/7 werckismic 7(b5)no3
27 0-9-12 1-14/9-10/7 swetismic ~2(b5)
28 0-11-12 1-7/6-10/7 swetismic ~6(b5)no3
29 0-1-13 1-11/9-7/4 werckismic
30 0-2-13 1-3/2-7/4 otonal
31 0-4-13 1-9/8-7/4 otonal
32 0-5-13 1-11/8-7/4 otonal
33 0-8-13 1-14/11-7/4 utonal
34 0-9-13 1-14/9-7/4 utonal
35 0-11-13 1-7/6-7/4 utonal
36 0-12-13 1-10/7-7/4 werckismic
37 0-8-20 1-14/11-20/11 otonal
38 0-9-20 1-14/9-20/11 swetismic
39 0-11-20 1-7/6-20/11 swetismic
40 0-12-20 1-10/7-20/11 utonal (b5)
41 0-1-21 1-11/9-10/9 otonal
42 0-8-21 1-14/11-10/9 werckismic
43 0-9-21 1-14/9-10/9 otonal
44 0-12-21 1-10/7-10/9 utonal
45 0-13-21 1-7/4-10/9 werckismic
46 0-20-21 1-20/11-10/9 utonal
47 0-2-23 1-3/2-5/3 otonal
48 0-3-23 1-11/6-5/3 otonal
49 0-11-23 1-7/6-5/3 otonal
50 0-12-23 1-10/7-5/3 utonal
51 0-20-23 1-20/11-5/3 utonal
52 0-21-23 1-10/9-5/3 utonal
53 0-2-25 1-3/2-5/4 otonal
54 0-4-25 1-9/8-5/4 otonal
55 0-5-25 1-11/8-5/4 otonal
56 0-12-25 1-10/7-5/4 utonal
57 0-13-25 1-7/4-5/4 otonal
58 0-20-25 1-20/11-5/4 utonal
59 0-21-25 1-10/9-5/4 utonal
60 0-23-25 1-5/3-5/4 utonal

Tetrads

# Chord Transversal Type Name
1 0-1-2-3 1-11/9-3/2-11/6 rastmic ~7
2 0-1-2-4 1-11/9-3/2-9/8 rastmic ~,9
3 0-1-3-4 1-11/9-11/6-9/8 rastmic ~9no5
4 0-2-3-4 1-3/2-11/6-9/8 rastmic ~9no3
5 0-1-2-5 1-11/9-3/2-11/8 rastmic ~6,9
6 0-1-3-5 1-11/9-11/6-11/8 utonal
7 0-2-3-5 1-3/2-11/6-11/8 ambitonal
8 0-1-4-5 1-11/9-9/8-11/8 rastmic
9 0-2-4-5 1-3/2-9/8-11/8 otonal
10 0-3-4-5 1-11/6-9/8-11/8 rastmic ~11no35
11 0-4-5-6 1-11/9-3/2-16/9 ~,7
12 0-3-4-8 1-11/6-9/8-14/11 parahemif 9(~7)no5
13 0-3-5-8 1-11/6-11/8-14/11 hemimin ,~7~11no5
14 0-4-5-8 1-9/8-11/8-14/11 parahemif
15 0-1-4-9 1-11/9-9/8-14/9 parahemif
16 0-1-5-9 1-11/9-11/8-14/9 pentacircle ,~6,9no5
17 0-4-5-9 1-9/8-11/8-14/9 pentacircle
18 0-4-8-9 1-9/8-14/11-14/9 pentacircle
19 0-5-8-9 1-11/8-14/11-14/9 parahemif
20 0-2-3-11 1-3/2-11/6-7/6 otonal
21 0-3-8-11 1-11/6-14/11-7/6 hemimin
22 0-8-9-11 1-14/11-14/9-7/6 utonal
23 0-1-3-12 1-11/9-11/6-10/7 swetismic
24 0-1-4-12 1-11/9-9/8-10/7 jove
25 0-3-4-12 1-11/6-9/8-10/7 jove
26 0-3-8-12 1-11/6-14/11-10/7 hemififths
27 0-4-8-12 1-9/8-14/11-10/7 pele
28 0-1-9-12 1-11/9-14/9-10/7 swetismic
29 0-4-9-12 1-9/8-14/9-10/7 hemififths
30 0-8-9-12 1-14/11-14/9-10/7 jove
31 0-3-11-12 1-11/6-7/6-10/7 swetismic
32 0-8-11-12 1-14/11-7/6-10/7 jove
33 0-9-11-12 1-14/9-7/6-10/7 swetismic
34 0-1-2-13 1-11/9-3/2-7/4 jove
35 0-1-4-13 1-11/9-9/8-7/4 jove
36 0-2-4-13 1-3/2-9/8-7/4 otonal
37 0-1-5-13 1-11/9-11/8-7/4 werckismic
38 0-2-5-13 1-3/2-11/8-7/4 otonal
39 0-4-5-13 1-9/8-11/8-7/4 otonal
40 0-4-8-13 1-9/8-14/11-7/4 pentacircle
41 0-5-8-13 1-11/8-14/11-7/4 hemimin
42 0-1-9-13 1-11/9-14/9-7/4 werckismic
43 0-4-9-13 1-9/8-14/9-7/4 pentacircle
44 0-5-9-13 1-11/8-14/9-7/4 pentacircle
45 0-8-9-13 1-14/11-14/9-7/4 utonal
46 0-2-11-13 1-3/2-7/6-7/4 ambitonal
47 0-8-11-13 1-14/11-7/6-7/4 utonal
48 0-9-11-13 1-14/9-7/6-7/4 utonal
49 0-1-12-13 1-11/9-10/7-7/4 jove
50 0-4-12-13 1-9/8-10/7-7/4 werckismic
51 0-8-12-13 1-14/11-10/7-7/4 werckismic
52 0-9-12-13 1-14/9-10/7-7/4 jove
53 0-11-12-13 1-7/6-10/7-7/4 jove
54 0-8-9-20 1-14/11-14/9-20/11 swetismic
55 0-8-11-20 1-14/11-7/6-20/11 swetismic
56 0-9-11-20 1-14/9-7/6-20/11 swetismic
57 0-8-12-20 1-14/11-10/7-20/11 werckismic
58 0-9-12-20 1-14/9-10/7-20/11 swetismic
59 0-11-12-20 1-7/6-10/7-20/11 swetismic
60 0-1-9-21 1-11/9-14/9-10/9 otonal
61 0-8-9-21 1-14/11-14/9-10/9 werckismic
62 0-1-12-21 1-11/9-10/7-10/9 swetismic
63 0-8-12-21 1-14/11-10/7-10/9 werckismic
64 0-9-12-21 1-14/9-10/7-10/9 swetismic
65 0-1-13-21 1-11/9-7/4-10/9 werckismic
66 0-8-13-21 1-14/11-7/4-10/9 werckismic
67 0-9-13-21 1-14/9-7/4-10/9 werckismic
68 0-12-13-21 1-10/7-7/4-10/9 werckismic
69 0-8-20-21 1-14/11-20/11-10/9 werckismic
70 0-9-20-21 1-14/9-20/11-10/9 swetismic
71 0-12-20-21 1-10/7-20/11-10/9 utonal
72 0-2-3-23 1-3/2-11/6-5/3 otonal
73 0-2-11-23 1-3/2-7/6-5/3 otonal
74 0-3-11-23 1-11/6-7/6-5/3 otonal
75 0-3-12-23 1-11/6-10/7-5/3 swetismic
76 0-11-12-23 1-7/6-10/7-5/3 swetismic
77 0-11-20-23 1-7/6-20/11-5/3 swetismic
78 0-12-20-23 1-10/7-20/11-5/3 utonal
79 0-12-21-23 1-10/7-10/9-5/3 utonal
80 0-20-21-23 1-20/11-10/9-5/3 utonal
81 0-2-4-25 1-3/2-9/8-5/4 otonal
82 0-2-5-25 1-3/2-11/8-5/4 otonal
83 0-4-5-25 1-9/8-11/8-5/4 otonal
84 0-4-12-25 1-9/8-10/7-5/4 werckismic
85 0-2-13-25 1-3/2-7/4-5/4 otonal
86 0-4-13-25 1-9/8-7/4-5/4 otonal
87 0-5-13-25 1-11/8-7/4-5/4 otonal
88 0-12-13-25 1-10/7-7/4-5/4 werckismic
89 0-12-20-25 1-10/7-20/11-5/4 utonal
90 0-12-21-25 1-10/7-10/9-5/4 utonal
91 0-13-21-25 1-7/4-10/9-5/4 werckismic
92 0-20-21-25 1-20/11-10/9-5/4 utonal
93 0-2-23-25 1-3/2-5/3-5/4 ambitonal
94 0-12-23-25 1-10/7-5/3-5/4 utonal
95 0-20-23-25 1-20/11-5/3-5/4 utonal
96 0-21-23-25 1-10/9-5/3-5/4 utonal

Pentads

# Chord Transversal Type Name
1 0-1-2-3-4 1-11/9-3/2-11/6-9/8 rastmic ~9
2 0-1-2-3-5 1-11/9-3/2-11/6-11/8 rastmic ~7,~11
3 0-1-2-4-5 1-11/9-3/2-9/8-11/8 rastmic ~,9~11 or ~11no7
4 0-1-3-4-5 1-11/9-11/6-9/8-11/8 rastmic ~11no5
5 0-2-3-4-5 1-3/2-11/6-9/8-11/8 rastmic ~11no3
6 0-3-4-5-8 1-11/6-9/8-11/8-14/11 parahemif
7 0-1-4-5-9 1-11/9-9/8-11/8-14/9 parahemif
8 0-4-5-8-9 1-9/8-11/8-14/11-14/9 parahemif
9 0-1-3-4-12 1-11/9-11/6-9/8-10/7 jove
10 0-3-4-8-12 1-11/6-9/8-14/11-10/7 hemififths
11 0-1-4-9-12 1-11/9-9/8-14/9-10/7 hemififths
12 0-4-8-9-12 1-9/8-14/11-14/9-10/7 hemififths
13 0-3-8-11-12 1-11/6-14/11-7/6-10/7 hemififths
14 0-8-9-11-12 1-14/11-14/9-7/6-10/7 jove
15 0-1-2-4-13 1-11/9-3/2-9/8-7/4 jove
16 0-1-2-5-13 1-11/9-3/2-11/8-7/4 jove
17 0-1-4-5-13 1-11/9-9/8-11/8-7/4 jove
18 0-2-4-5-13 1-3/2-9/8-11/8-7/4 otonal
19 0-4-5-8-13 1-9/8-11/8-14/11-7/4 parahemif
20 0-1-4-9-13 1-11/9-9/8-14/9-7/4 hemififths
21 0-1-5-9-13 1-11/9-11/8-14/9-7/4 pele
22 0-4-5-9-13 1-9/8-11/8-14/9-7/4 pentacircle
23 0-4-8-9-13 1-9/8-14/11-14/9-7/4 pentacircle
24 0-5-8-9-13 1-11/8-14/11-14/9-7/4 parahemif
25 0-8-9-11-13 1-14/11-14/9-7/6-7/4 utonal
26 0-1-4-12-13 1-11/9-9/8-10/7-7/4 jove
27 0-4-8-12-13 1-9/8-14/11-10/7-7/4 pele
28 0-1-9-12-13 1-11/9-14/9-10/7-7/4 jove
29 0-4-9-12-13 1-9/8-14/9-10/7-7/4 hemififths
30 0-8-9-12-13 1-14/11-14/9-10/7-7/4 jove
31 0-8-11-12-13 1-14/11-7/6-10/7-7/4 jove
32 0-9-11-12-13 1-14/9-7/6-10/7-7/4 jove
33 0-8-9-11-20 1-14/11-14/9-7/6-20/11 swetismic
34 0-8-9-12-20 1-14/11-14/9-10/7-20/11 jove
35 0-8-11-12-20 1-14/11-7/6-10/7-20/11 jove
36 0-9-11-12-20 1-14/9-7/6-10/7-20/11 swetismic
37 0-1-9-12-21 1-11/9-14/9-10/7-10/9 swetismic
38 0-8-9-12-21 1-14/11-14/9-10/7-10/9 jove
39 0-1-9-13-21 1-11/9-14/9-7/4-10/9 werckismic
40 0-8-9-13-21 1-14/11-14/9-7/4-10/9 werckismic
41 0-1-12-13-21 1-11/9-10/7-7/4-10/9 jove
42 0-8-12-13-21 1-14/11-10/7-7/4-10/9 werckismic
43 0-9-12-13-21 1-14/9-10/7-7/4-10/9 jove
44 0-8-9-20-21 1-14/11-14/9-20/11-10/9 jove
45 0-8-12-20-21 1-14/11-10/7-20/11-10/9 werckismic
46 0-9-12-20-21 1-14/9-10/7-20/11-10/9 swetismic
47 0-2-3-11-23 1-3/2-11/6-7/6-5/3 otonal
48 0-3-11-12-23 1-11/6-7/6-10/7-5/3 swetismic
49 0-11-12-20-23 1-7/6-10/7-20/11-5/3 swetismic
50 0-12-20-21-23 1-10/7-20/11-10/9-5/3 utonal
51 0-2-4-5-25 1-3/2-9/8-11/8-5/4 otonal
52 0-2-4-13-25 1-3/2-9/8-7/4-5/4 otonal
53 0-2-5-13-25 1-3/2-11/8-7/4-5/4 otonal
54 0-4-5-13-25 1-9/8-11/8-7/4-5/4 otonal
55 0-4-12-13-25 1-9/8-10/7-7/4-5/4 werckismic
56 0-12-13-21-25 1-10/7-7/4-10/9-5/4 werckismic
57 0-12-20-21-25 1-10/7-20/11-10/9-5/4 utonal
58 0-12-20-23-25 1-10/7-20/11-5/3-5/4 utonal
59 0-12-21-23-25 1-10/7-10/9-5/3-5/4 utonal
60 0-20-21-23-25 1-20/11-10/9-5/3-5/4 utonal

Hexads

# Chord Transversal Type Name
1 0-1-2-3-4-5 1-11/9-3/2-11/6-9/8-11/8 rastmic ~11
2 0-1-2-4-5-13 1-11/9-3/2-9/8-11/8-7/4 jove
3 0-1-4-5-9-13 1-11/9-9/8-11/8-14/9-7/4 hemififths
4 0-4-5-8-9-13 1-9/8-11/8-14/11-14/9-7/4 nofives
5 0-1-4-9-12-13 1-11/9-9/8-14/9-10/7-7/4 hemififths
6 0-4-8-9-12-13 1-9/8-14/11-14/9-10/7-7/4 hemififths
7 0-8-9-11-12-13 1-14/11-14/9-7/6-10/7-7/4 jove
8 0-8-9-11-12-20 1-14/11-14/9-7/6-10/7-20/11 jove
9 0-1-9-12-13-21 1-11/9-14/9-10/7-7/4-10/9 jove
10 0-8-9-12-13-21 1-14/11-14/9-10/7-7/4-10/9 jove
11 0-8-9-12-20-21 1-14/11-14/9-10/7-20/11-10/9 jove
12 0-2-4-5-13-25 1-3/2-9/8-11/8-7/4-5/4 otonal
13 0-12-20-21-23-25 1-10/7-20/11-10/9-5/3-5/4 utonal
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