Xenharmonic Wiki

Diaschismic/Chords: Difference between revisions

← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,295 edits
m Categorised this uncategorised page
Cleanup; linking; categories; start bracketed indices with 0
Line 1: Line 1:
Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Diaschismic_family#Diaschismic|diaschismic temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 441/440 are labeled werckismic, by 176/175 valinorsmic, by 896/891 pentacircle, and by 126/125 starling. Those requiring tempering by any two of 126/125, 176/175 or 441/440 are labeled thrush, and by both 896/891 and 441/440 pele.
Below are listed the [[dyadic chord]]s of 11-limit [[diaschismic]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[441/440]] are labeled [[Werckismic chords|werckismic]], by [[176/175]] [[Valinorsmic chords|valinorsmic]], by [[896/891]] [[Pentacircle chords|pentacircle]], and by [[126/125]] [[Starling chords|starling]]. Those requiring tempering by any two of 126/125, 176/175 or 441/440 are labeled thrush, and by both 896/891 and 441/440 pele.


The normal mapping for diaschismic is dia = [<2 0 11 31 45|, <0 1 -2 -8 -12|]. From this we may derive a val v = dia[1] - 100 dia[2] = <2 -100 211 831 1245| which we may use to sort and normalize the chords of diaschismic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by v. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the Graham complexity of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.
The normal mapping for diaschismic is V<sub>dia</sub> = {{mapping| 2 0 11 31 45 | 0 1 -2 -8 -12 }}. From this we may derive a val V = V<sub>dia</sub>[0] - 100 V<sub>dia</sub>[1] = {{val| 2 -100 211 831 1245 }} which we may use to sort and normalize the chords of diaschismic. Under "Chord" is listed the chord, normalized to start from zero, in the mapping by V. If we look at the highest, rightmost, element of the chord, divide that by 100, round, and multiply by 2, we get the [[Graham complexity]] of the chord. Redundantly for the sake of convenience, the Graham complexity is listed in the last column.


Diaschsmic has MOS of size 10, 12, 22, 34, 46 and 58. It may be seen that even ten notes are not without resources, mostly essentially just. By the time we get to 22 notes, we are well-supplied.
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.


=Triads=
== Triads ==


{| class="wikitable"
{| class="wikitable center-1"
|-
|-
| | Number
! #
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
| | Complexity
! Complexity
|-
|-
| | 1
| 1
| | 0-104-208
| 0-104-208
| | 1-4/3-16/9
| 1-4/3-16/9
| | ambitonal
| ambitonal
| | 4
| 4
|-
|-
| | 2
| 2
| | 0-104-311
| 0-104-311
| | 1-4/3-5/3
| 1-4/3-5/3
| | otonal
| otonal
| | 6
| 6
|-
|-
| | 3
| 3
| | 0-207-311
| 0-207-311
| | 1-5/4-5/3
| 1-5/4-5/3
| | utonal
| utonal
| | 6
| 6
|-
|-
| | 4
| 4
| | 0-104-413
| 0-104-413
| | 1-4/3-10/9
| 1-4/3-10/9
| | otonal
| otonal
| | 8
| 8
|-
|-
| | 5
| 5
| | 0-207-413
| 0-207-413
| | 1-5/4-10/9
| 1-5/4-10/9
| | utonal
| utonal
| | 8
| 8
|-
|-
| | 6
| 6
| | 0-208-413
| 0-208-413
| | 1-16/9-10/9
| 1-16/9-10/9
| | otonal
| otonal
| | 8
| 8
|-
|-
| | 7
| 7
| | 0-311-413
| 0-311-413
| | 1-5/3-10/9
| 1-5/3-10/9
| | utonal
| utonal
| | 8
| 8
|-
|-
| | 8
| 8
| | 0-207-414
| 0-207-414
| | 1-5/4-11/7
| 1-5/4-11/7
| | valinorsmic
| valinorsmic
| | 8
| 8
|-
|-
| | 9
| 9
| | 0-208-414
| 0-208-414
| | 1-16/9-11/7
| 1-16/9-11/7
| | pentacircle
| pentacircle
| | 8
| 8
|-
|-
| | 10
| 10
| | 0-207-620
| 0-207-620
| | 1-5/4-7/5
| 1-5/4-7/5
| | starling
| starling
| | 12
| 12
|-
|-
| | 11
| 11
| | 0-208-620
| 0-208-620
| | 1-16/9-7/5
| 1-16/9-7/5
| | werckismic
| werckismic
| | 12
| 12
|-
|-
| | 12
| 12
| | 0-311-620
| 0-311-620
| | 1-5/3-7/5
| 1-5/3-7/5
| | starling
| starling
| | 12
| 12
|-
|-
| | 13
| 13
| | 0-413-620
| 0-413-620
| | 1-10/9-7/5
| 1-10/9-7/5
| | starling
| starling
| | 12
| 12
|-
|-
| | 14
| 14
| | 0-414-620
| 0-414-620
| | 1-11/7-7/5
| 1-11/7-7/5
| | werckismic
| werckismic
| | 12
| 12
|-
|-
| | 15
| 15
| | 0-207-827
| 0-207-827
| | 1-5/4-7/4
| 1-5/4-7/4
| | otonal
| otonal
| | 16
| 16
|-
|-
| | 16
| 16
| | 0-413-827
| 0-413-827
| | 1-10/9-7/4
| 1-10/9-7/4
| | werckismic
| werckismic
| | 16
| 16
|-
|-
| | 17
| 17
| | 0-414-827
| 0-414-827
| | 1-11/7-7/4
| 1-11/7-7/4
| | werckismic
| werckismic
| | 16
| 16
|-
|-
| | 18
| 18
| | 0-620-827
| 0-620-827
| | 1-7/5-7/4
| 1-7/5-7/4
| | utonal
| utonal
| | 16
| 16
|-
|-
| | 19
| 19
| | 0-104-929
| 0-104-929
| | 1-4/3-7/6
| 1-4/3-7/6
| | otonal
| otonal
| | 18
| 18
|-
|-
| | 20
| 20
| | 0-311-929
| 0-311-929
| | 1-5/3-7/6
| 1-5/3-7/6
| | otonal
| otonal
| | 18
| 18
|-
|-
| | 21
| 21
| | 0-620-929
| 0-620-929
| | 1-7/5-7/6
| 1-7/5-7/6
| | utonal
| utonal
| | 18
| 18
|-
|-
| | 22
| 22
| | 0-827-929
| 0-827-929
| | 1-7/4-7/6
| 1-7/4-7/6
| | utonal
| utonal
| | 18
| 18
|-
|-
| | 23
| 23
| | 0-207-1032
| 0-207-1032
| | 1-5/4-11/10
| 1-5/4-11/10
| | valinorsmic
| valinorsmic
| | 20
| 20
|-
|-
| | 24
| 24
| | 0-414-1032
| 0-414-1032
| | 1-11/7-11/10
| 1-11/7-11/10
| | utonal
| utonal
| | 20
| 20
|-
|-
| | 25
| 25
| | 0-620-1032
| 0-620-1032
| | 1-7/5-11/10
| 1-7/5-11/10
| | otonal
| otonal
| | 20
| 20
|-
|-
| | 26
| 26
| | 0-827-1032
| 0-827-1032
| | 1-7/4-11/10
| 1-7/4-11/10
| | valinorsmic
| valinorsmic
| | 20
| 20
|-
|-
| | 27
| 27
| | 0-104-1033
| 0-104-1033
| | 1-4/3-14/9
| 1-4/3-14/9
| | otonal
| otonal
| | 20
| 20
|-
|-
| | 28
| 28
| | 0-208-1033
| 0-208-1033
| | 1-16/9-14/9
| 1-16/9-14/9
| | otonal
| otonal
| | 20
| 20
|-
|-
| | 29
| 29
| | 0-413-1033
| 0-413-1033
| | 1-10/9-14/9
| 1-10/9-14/9
| | otonal
| otonal
| | 20
| 20
|-
|-
| | 30
| 30
| | 0-620-1033
| 0-620-1033
| | 1-7/5-14/9
| 1-7/5-14/9
| | utonal
| utonal
| | 20
| 20
|-
|-
| | 31
| 31
| | 0-827-1033
| 0-827-1033
| | 1-7/4-14/9
| 1-7/4-14/9
| | utonal
| utonal
| | 20
| 20
|-
|-
| | 32
| 32
| | 0-929-1033
| 0-929-1033
| | 1-7/6-14/9
| 1-7/6-14/9
| | utonal
| utonal
| | 20
| 20
|-
|-
| | 33
| 33
| | 0-207-1239
| 0-207-1239
| | 1-5/4-11/8
| 1-5/4-11/8
| | otonal
| otonal
| | 24
| 24
|-
|-
| | 34
| 34
| | 0-208-1239
| 0-208-1239
| | 1-16/9-11/8
| 1-16/9-11/8
| | pentacircle
| pentacircle
| | 24
| 24
|-
|-
| | 35
| 35
| | 0-414-1239
| 0-414-1239
| | 1-11/7-11/8
| 1-11/7-11/8
| | utonal
| utonal
| | 24
| 24
|-
|-
| | 36
| 36
| | 0-827-1239
| 0-827-1239
| | 1-7/4-11/8
| 1-7/4-11/8
| | otonal
| otonal
| | 24
| 24
|-
|-
| | 37
| 37
| | 0-1032-1239
| 0-1032-1239
| | 1-11/10-11/8
| 1-11/10-11/8
| | utonal
| utonal
| | 24
| 24
|-
|-
| | 38
| 38
| | 0-1033-1239
| 0-1033-1239
| | 1-14/9-11/8
| 1-14/9-11/8
| | pentacircle
| pentacircle
| | 24
| 24
|-
|-
| | 39
| 39
| | 0-104-1343
| 0-104-1343
| | 1-4/3-11/6
| 1-4/3-11/6
| | otonal
| otonal
| | 26
| 26
|-
|-
| | 40
| 40
| | 0-311-1343
| 0-311-1343
| | 1-5/3-11/6
| 1-5/3-11/6
| | otonal
| otonal
| | 26
| 26
|-
|-
| | 41
| 41
| | 0-414-1343
| 0-414-1343
| | 1-11/7-11/6
| 1-11/7-11/6
| | utonal
| utonal
| | 26
| 26
|-
|-
| | 42
| 42
| | 0-929-1343
| 0-929-1343
| | 1-7/6-11/6
| 1-7/6-11/6
| | otonal
| otonal
| | 26
| 26
|-
|-
| | 43
| 43
| | 0-1032-1343
| 0-1032-1343
| | 1-11/10-11/6
| 1-11/10-11/6
| | utonal
| utonal
| | 26
| 26
|-
|-
| | 44
| 44
| | 0-1239-1343
| 0-1239-1343
| | 1-11/8-11/6
| 1-11/8-11/6
| | utonal
| utonal
| | 26
| 26
|-
|-
| | 45
| 45
| | 0-104-1445
| 0-104-1445
| | 1-4/3-11/9
| 1-4/3-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 46
| 46
| | 0-208-1445
| 0-208-1445
| | 1-16/9-11/9
| 1-16/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 47
| 47
| | 0-413-1445
| 0-413-1445
| | 1-10/9-11/9
| 1-10/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 48
| 48
| | 0-414-1445
| 0-414-1445
| | 1-11/7-11/9
| 1-11/7-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 49
| 49
| | 0-620-1445
| 0-620-1445
| | 1-7/5-11/9
| 1-7/5-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 50
| 50
| | 0-827-1445
| 0-827-1445
| | 1-7/4-11/9
| 1-7/4-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 51
| 51
| | 0-1032-1445
| 0-1032-1445
| | 1-11/10-11/9
| 1-11/10-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 52
| 52
| | 0-1033-1445
| 0-1033-1445
| | 1-14/9-11/9
| 1-14/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 53
| 53
| | 0-1239-1445
| 0-1239-1445
| | 1-11/8-11/9
| 1-11/8-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 54
| 54
| | 0-1343-1445
| 0-1343-1445
| | 1-11/6-11/9
| 1-11/6-11/9
| | utonal
| utonal
| | 28
| 28
|}
|}


=Tetrads=
== Tetrads ==


{| class="wikitable"
{| class="wikitable center-1"
|-
|-
| | Number
! #
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
| | Complexity
! Complexity
|-
|-
| | 1
| 1
| | 0-104-208-413
| 0-104-208-413
| | 1-4/3-16/9-10/9
| 1-4/3-16/9-10/9
| | otonal
| otonal
| | 8
| 8
|-
|-
| | 2
| 2
| | 0-104-311-413
| 0-104-311-413
| | 1-4/3-5/3-10/9
| 1-4/3-5/3-10/9
| | ambitonal
| ambitonal
| | 8
| 8
|-
|-
| | 3
| 3
| | 0-207-311-413
| 0-207-311-413
| | 1-5/4-5/3-10/9
| 1-5/4-5/3-10/9
| | utonal
| utonal
| | 8
| 8
|-
|-
| | 4
| 4
| | 0-207-311-620
| 0-207-311-620
| | 1-5/4-5/3-7/5
| 1-5/4-5/3-7/5
| | starling
| starling
| | 12
| 12
|-
|-
| | 5
| 5
| | 0-207-413-620
| 0-207-413-620
| | 1-5/4-10/9-7/5
| 1-5/4-10/9-7/5
| | starling
| starling
| | 12
| 12
|-
|-
| | 6
| 6
| | 0-208-413-620
| 0-208-413-620
| | 1-16/9-10/9-7/5
| 1-16/9-10/9-7/5
| | thrush
| thrush
| | 12
| 12
|-
|-
| | 7
| 7
| | 0-311-413-620
| 0-311-413-620
| | 1-5/3-10/9-7/5
| 1-5/3-10/9-7/5
| | starling
| starling
| | 12
| 12
|-
|-
| | 8
| 8
| | 0-207-414-620
| 0-207-414-620
| | 1-5/4-11/7-7/5
| 1-5/4-11/7-7/5
| | thrush
| thrush
| | 12
| 12
|-
|-
| | 9
| 9
| | 0-208-414-620
| 0-208-414-620
| | 1-16/9-11/7-7/5
| 1-16/9-11/7-7/5
| | pele
| pele
| | 12
| 12
|-
|-
| | 10
| 10
| | 0-207-413-827
| 0-207-413-827
| | 1-5/4-10/9-7/4
| 1-5/4-10/9-7/4
| | werckismic
| werckismic
| | 16
| 16
|-
|-
| | 11
| 11
| | 0-207-414-827
| 0-207-414-827
| | 1-5/4-11/7-7/4
| 1-5/4-11/7-7/4
| | thrush
| thrush
| | 16
| 16
|-
|-
| | 12
| 12
| | 0-207-620-827
| 0-207-620-827
| | 1-5/4-7/5-7/4
| 1-5/4-7/5-7/4
| | starling
| starling
| | 16
| 16
|-
|-
| | 13
| 13
| | 0-413-620-827
| 0-413-620-827
| | 1-10/9-7/5-7/4
| 1-10/9-7/5-7/4
| | thrush
| thrush
| | 16
| 16
|-
|-
| | 14
| 14
| | 0-414-620-827
| 0-414-620-827
| | 1-11/7-7/5-7/4
| 1-11/7-7/5-7/4
| | werckismic
| werckismic
| | 16
| 16
|-
|-
| | 15
| 15
| | 0-104-311-929
| 0-104-311-929
| | 1-4/3-5/3-7/6
| 1-4/3-5/3-7/6
| | otonal
| otonal
| | 18
| 18
|-
|-
| | 16
| 16
| | 0-311-620-929
| 0-311-620-929
| | 1-5/3-7/5-7/6
| 1-5/3-7/5-7/6
| | starling
| starling
| | 18
| 18
|-
|-
| | 17
| 17
| | 0-620-827-929
| 0-620-827-929
| | 1-7/5-7/4-7/6
| 1-7/5-7/4-7/6
| | utonal
| utonal
| | 18
| 18
|-
|-
| | 18
| 18
| | 0-207-414-1032
| 0-207-414-1032
| | 1-5/4-11/7-11/10
| 1-5/4-11/7-11/10
| | valinorsmic
| valinorsmic
| | 20
| 20
|-
|-
| | 19
| 19
| | 0-207-620-1032
| 0-207-620-1032
| | 1-5/4-7/5-11/10
| 1-5/4-7/5-11/10
| | thrush
| thrush
| | 20
| 20
|-
|-
| | 20
| 20
| | 0-414-620-1032
| 0-414-620-1032
| | 1-11/7-7/5-11/10
| 1-11/7-7/5-11/10
| | werckismic
| werckismic
| | 20
| 20
|-
|-
| | 21
| 21
| | 0-207-827-1032
| 0-207-827-1032
| | 1-5/4-7/4-11/10
| 1-5/4-7/4-11/10
| | valinorsmic
| valinorsmic
| | 20
| 20
|-
|-
| | 22
| 22
| | 0-414-827-1032
| 0-414-827-1032
| | 1-11/7-7/4-11/10
| 1-11/7-7/4-11/10
| | thrush
| thrush
| | 20
| 20
|-
|-
| | 23
| 23
| | 0-620-827-1032
| 0-620-827-1032
| | 1-7/5-7/4-11/10
| 1-7/5-7/4-11/10
| | valinorsmic
| valinorsmic
| | 20
| 20
|-
|-
| | 24
| 24
| | 0-104-208-1033
| 0-104-208-1033
| | 1-4/3-16/9-14/9
| 1-4/3-16/9-14/9
| | otonal
| otonal
| | 20
| 20
|-
|-
| | 25
| 25
| | 0-104-413-1033
| 0-104-413-1033
| | 1-4/3-10/9-14/9
| 1-4/3-10/9-14/9
| | otonal
| otonal
| | 20
| 20
|-
|-
| | 26
| 26
| | 0-208-413-1033
| 0-208-413-1033
| | 1-16/9-10/9-14/9
| 1-16/9-10/9-14/9
| | otonal
| otonal
| | 20
| 20
|-
|-
| | 27
| 27
| | 0-208-620-1033
| 0-208-620-1033
| | 1-16/9-7/5-14/9
| 1-16/9-7/5-14/9
| | werckismic
| werckismic
| | 20
| 20
|-
|-
| | 28
| 28
| | 0-413-620-1033
| 0-413-620-1033
| | 1-10/9-7/5-14/9
| 1-10/9-7/5-14/9
| | starling
| starling
| | 20
| 20
|-
|-
| | 29
| 29
| | 0-413-827-1033
| 0-413-827-1033
| | 1-10/9-7/4-14/9
| 1-10/9-7/4-14/9
| | werckismic
| werckismic
| | 20
| 20
|-
|-
| | 30
| 30
| | 0-620-827-1033
| 0-620-827-1033
| | 1-7/5-7/4-14/9
| 1-7/5-7/4-14/9
| | utonal
| utonal
| | 20
| 20
|-
|-
| | 31
| 31
| | 0-104-929-1033
| 0-104-929-1033
| | 1-4/3-7/6-14/9
| 1-4/3-7/6-14/9
| | ambitonal
| ambitonal
| | 20
| 20
|-
|-
| | 32
| 32
| | 0-620-929-1033
| 0-620-929-1033
| | 1-7/5-7/6-14/9
| 1-7/5-7/6-14/9
| | utonal
| utonal
| | 20
| 20
|-
|-
| | 33
| 33
| | 0-827-929-1033
| 0-827-929-1033
| | 1-7/4-7/6-14/9
| 1-7/4-7/6-14/9
| | utonal
| utonal
| | 20
| 20
|-
|-
| | 34
| 34
| | 0-207-414-1239
| 0-207-414-1239
| | 1-5/4-11/7-11/8
| 1-5/4-11/7-11/8
| | valinorsmic
| valinorsmic
| | 24
| 24
|-
|-
| | 35
| 35
| | 0-208-414-1239
| 0-208-414-1239
| | 1-16/9-11/7-11/8
| 1-16/9-11/7-11/8
| | pentacircle
| pentacircle
| | 24
| 24
|-
|-
| | 36
| 36
| | 0-207-827-1239
| 0-207-827-1239
| | 1-5/4-7/4-11/8
| 1-5/4-7/4-11/8
| | otonal
| otonal
| | 24
| 24
|-
|-
| | 37
| 37
| | 0-414-827-1239
| 0-414-827-1239
| | 1-11/7-7/4-11/8
| 1-11/7-7/4-11/8
| | werckismic
| werckismic
| | 24
| 24
|-
|-
| | 38
| 38
| | 0-207-1032-1239
| 0-207-1032-1239
| | 1-5/4-11/10-11/8
| 1-5/4-11/10-11/8
| | valinorsmic
| valinorsmic
| | 24
| 24
|-
|-
| | 39
| 39
| | 0-414-1032-1239
| 0-414-1032-1239
| | 1-11/7-11/10-11/8
| 1-11/7-11/10-11/8
| | utonal
| utonal
| | 24
| 24
|-
|-
| | 40
| 40
| | 0-827-1032-1239
| 0-827-1032-1239
| | 1-7/4-11/10-11/8
| 1-7/4-11/10-11/8
| | valinorsmic
| valinorsmic
| | 24
| 24
|-
|-
| | 41
| 41
| | 0-208-1033-1239
| 0-208-1033-1239
| | 1-16/9-14/9-11/8
| 1-16/9-14/9-11/8
| | pentacircle
| pentacircle
| | 24
| 24
|-
|-
| | 42
| 42
| | 0-827-1033-1239
| 0-827-1033-1239
| | 1-7/4-14/9-11/8
| 1-7/4-14/9-11/8
| | pentacircle
| pentacircle
| | 24
| 24
|-
|-
| | 43
| 43
| | 0-104-311-1343
| 0-104-311-1343
| | 1-4/3-5/3-11/6
| 1-4/3-5/3-11/6
| | otonal
| otonal
| | 26
| 26
|-
|-
| | 44
| 44
| | 0-104-929-1343
| 0-104-929-1343
| | 1-4/3-7/6-11/6
| 1-4/3-7/6-11/6
| | otonal
| otonal
| | 26
| 26
|-
|-
| | 45
| 45
| | 0-311-929-1343
| 0-311-929-1343
| | 1-5/3-7/6-11/6
| 1-5/3-7/6-11/6
| | otonal
| otonal
| | 26
| 26
|-
|-
| | 46
| 46
| | 0-414-1032-1343
| 0-414-1032-1343
| | 1-11/7-11/10-11/6
| 1-11/7-11/10-11/6
| | utonal
| utonal
| | 26
| 26
|-
|-
| | 47
| 47
| | 0-414-1239-1343
| 0-414-1239-1343
| | 1-11/7-11/8-11/6
| 1-11/7-11/8-11/6
| | utonal
| utonal
| | 26
| 26
|-
|-
| | 48
| 48
| | 0-1032-1239-1343
| 0-1032-1239-1343
| | 1-11/10-11/8-11/6
| 1-11/10-11/8-11/6
| | utonal
| utonal
| | 26
| 26
|-
|-
| | 49
| 49
| | 0-104-208-1445
| 0-104-208-1445
| | 1-4/3-16/9-11/9
| 1-4/3-16/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 50
| 50
| | 0-104-413-1445
| 0-104-413-1445
| | 1-4/3-10/9-11/9
| 1-4/3-10/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 51
| 51
| | 0-208-413-1445
| 0-208-413-1445
| | 1-16/9-10/9-11/9
| 1-16/9-10/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 52
| 52
| | 0-208-414-1445
| 0-208-414-1445
| | 1-16/9-11/7-11/9
| 1-16/9-11/7-11/9
| | pentacircle
| pentacircle
| | 28
| 28
|-
|-
| | 53
| 53
| | 0-208-620-1445
| 0-208-620-1445
| | 1-16/9-7/5-11/9
| 1-16/9-7/5-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 54
| 54
| | 0-413-620-1445
| 0-413-620-1445
| | 1-10/9-7/5-11/9
| 1-10/9-7/5-11/9
| | thrush
| thrush
| | 28
| 28
|-
|-
| | 55
| 55
| | 0-414-620-1445
| 0-414-620-1445
| | 1-11/7-7/5-11/9
| 1-11/7-7/5-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 56
| 56
| | 0-413-827-1445
| 0-413-827-1445
| | 1-10/9-7/4-11/9
| 1-10/9-7/4-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 57
| 57
| | 0-414-827-1445
| 0-414-827-1445
| | 1-11/7-7/4-11/9
| 1-11/7-7/4-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 58
| 58
| | 0-620-827-1445
| 0-620-827-1445
| | 1-7/5-7/4-11/9
| 1-7/5-7/4-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 59
| 59
| | 0-414-1032-1445
| 0-414-1032-1445
| | 1-11/7-11/10-11/9
| 1-11/7-11/10-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 60
| 60
| | 0-620-1032-1445
| 0-620-1032-1445
| | 1-7/5-11/10-11/9
| 1-7/5-11/10-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 61
| 61
| | 0-827-1032-1445
| 0-827-1032-1445
| | 1-7/4-11/10-11/9
| 1-7/4-11/10-11/9
| | thrush
| thrush
| | 28
| 28
|-
|-
| | 62
| 62
| | 0-104-1033-1445
| 0-104-1033-1445
| | 1-4/3-14/9-11/9
| 1-4/3-14/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 63
| 63
| | 0-208-1033-1445
| 0-208-1033-1445
| | 1-16/9-14/9-11/9
| 1-16/9-14/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 64
| 64
| | 0-413-1033-1445
| 0-413-1033-1445
| | 1-10/9-14/9-11/9
| 1-10/9-14/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 65
| 65
| | 0-620-1033-1445
| 0-620-1033-1445
| | 1-7/5-14/9-11/9
| 1-7/5-14/9-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 66
| 66
| | 0-827-1033-1445
| 0-827-1033-1445
| | 1-7/4-14/9-11/9
| 1-7/4-14/9-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 67
| 67
| | 0-208-1239-1445
| 0-208-1239-1445
| | 1-16/9-11/8-11/9
| 1-16/9-11/8-11/9
| | pentacircle
| pentacircle
| | 28
| 28
|-
|-
| | 68
| 68
| | 0-414-1239-1445
| 0-414-1239-1445
| | 1-11/7-11/8-11/9
| 1-11/7-11/8-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 69
| 69
| | 0-827-1239-1445
| 0-827-1239-1445
| | 1-7/4-11/8-11/9
| 1-7/4-11/8-11/9
| | werckismic
| werckismic
| | 28
| 28
|-
|-
| | 70
| 70
| | 0-1032-1239-1445
| 0-1032-1239-1445
| | 1-11/10-11/8-11/9
| 1-11/10-11/8-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 71
| 71
| | 0-1033-1239-1445
| 0-1033-1239-1445
| | 1-14/9-11/8-11/9
| 1-14/9-11/8-11/9
| | pentacircle
| pentacircle
| | 28
| 28
|-
|-
| | 72
| 72
| | 0-104-1343-1445
| 0-104-1343-1445
| | 1-4/3-11/6-11/9
| 1-4/3-11/6-11/9
| | ambitonal
| ambitonal
| | 28
| 28
|-
|-
| | 73
| 73
| | 0-414-1343-1445
| 0-414-1343-1445
| | 1-11/7-11/6-11/9
| 1-11/7-11/6-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 74
| 74
| | 0-1032-1343-1445
| 0-1032-1343-1445
| | 1-11/10-11/6-11/9
| 1-11/10-11/6-11/9
| | utonal
| utonal
| | 28
| 28
|-
|-
| | 75
| 75
| | 0-1239-1343-1445
| 0-1239-1343-1445
| | 1-11/8-11/6-11/9
| 1-11/8-11/6-11/9
| | utonal
| utonal
| | 28
| 28
|}
|}


=Pentads=
== Pentads ==


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


=Hexads=
== Hexads ==


{| class="wikitable"
{| class="wikitable center-1"
|-
|-
| | Number
! #
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
| | Complexity
! Complexity
|-
|-
| | 1
| 1
| | 0-207-414-620-827-1032
| 0-207-414-620-827-1032
| | 1-5/4-11/7-7/5-7/4-11/10
| 1-5/4-11/7-7/5-7/4-11/10
| | thrush
| thrush
| | 20
| 20
|-
|-
| | 2
| 2
| | 0-207-414-827-1032-1239
| 0-207-414-827-1032-1239
| | 1-5/4-11/7-7/4-11/10-11/8
| 1-5/4-11/7-7/4-11/10-11/8
| | thrush
| thrush
| | 24
| 24
|-
|-
| | 3
| 3
| | 0-414-620-827-1032-1445
| 0-414-620-827-1032-1445
| | 1-11/7-7/5-7/4-11/10-11/9
| 1-11/7-7/5-7/4-11/10-11/9
| | thrush
| thrush
| | 28
| 28
|-
|-
| | 4
| 4
| | 0-104-208-413-1033-1445
| 0-104-208-413-1033-1445
| | 1-4/3-16/9-10/9-14/9-11/9
| 1-4/3-16/9-10/9-14/9-11/9
| | otonal
| otonal
| | 28
| 28
|-
|-
| | 5
| 5
| | 0-208-413-620-1033-1445
| 0-208-413-620-1033-1445
| | 1-16/9-10/9-7/5-14/9-11/9
| 1-16/9-10/9-7/5-14/9-11/9
| | thrush
| thrush
| | 28
| 28
|-
|-
| | 6
| 6
| | 0-413-620-827-1033-1445
| 0-413-620-827-1033-1445
| | 1-10/9-7/5-7/4-14/9-11/9
| 1-10/9-7/5-7/4-14/9-11/9
| | thrush
| thrush
| | 28
| 28
|-
|-
| | 7
| 7
| | 0-414-827-1032-1239-1445
| 0-414-827-1032-1239-1445
| | 1-11/7-7/4-11/10-11/8-11/9
| 1-11/7-7/4-11/10-11/8-11/9
| | thrush
| thrush
| | 28
| 28
|-
|-
| | 8
| 8
| | 0-414-1032-1239-1343-1445
| 0-414-1032-1239-1343-1445
| | 1-11/7-11/10-11/8-11/6-11/9
| 1-11/7-11/10-11/8-11/6-11/9
| | utonal
| utonal
| | 28
| 28
|}
|}
[[Category:Lists of chords]]
[[Category:Lists of chords]]
[[Category:Dyadic chords]]
[[Category:Dyadic chords]]
[[Category:11-limit]]
[[Category:Diaschismic]]
[[Category:Diaschismic]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]
Retrieved from "https://en.xen.wiki/w/Diaschismic/Chords"