Luna and hemithirds/Chords: Difference between revisions

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Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Gamelismic_clan#Hemithirds|hemithirds temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.
Below are listed the [[dyadic chord]]s of [[11-limit]] [[hemithirds]] temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.


Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS.
Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS.


=Triads=
== Triads ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | Number
! Number
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
|-
|-
| | 1
| 1
| | 0-2-5
| 0-2-5
| | 1-5/4-7/4
| 1-5/4-7/4
| | otonal
| otonal
|-
|-
| | 2
| 2
| | 0-3-5
| 0-3-5
| | 1-7/5-7/4
| 1-7/5-7/4
| | utonal
| utonal
|-
|-
| | 3
| 3
| | 0-2-7
| 0-2-7
| | 1-5/4-12/11
| 1-5/4-12/11
| | keenanismic
| keenanismic
|-
|-
| | 4
| 4
| | 0-5-7
| 0-5-7
| | 1-7/4-12/11
| 1-7/4-12/11
| | keenanismic
| keenanismic
|-
|-
| | 5
| 5
| | 0-3-8
| 0-3-8
| | 1-7/5-11/9
| 1-7/5-11/9
| | werckismic
| werckismic
|-
|-
| | 6
| 6
| | 0-5-8
| 0-5-8
| | 1-7/4-11/9
| 1-7/4-11/9
| | werckismic
| werckismic
|-
|-
| | 7
| 7
| | 0-7-15
| 0-7-15
| | 1-12/11-4/3
| 1-12/11-4/3
| | utonal
| utonal
|-
|-
| | 8
| 8
| | 0-8-15
| 0-8-15
| | 1-11/9-4/3
| 1-11/9-4/3
| | otonal
| otonal
|-
|-
| | 9
| 9
| | 0-2-17
| 0-2-17
| | 1-5/4-5/3
| 1-5/4-5/3
| | utonal
| utonal
|-
|-
| | 10
| 10
| | 0-15-17
| 0-15-17
| | 1-4/3-5/3
| 1-4/3-5/3
| | otonal
| otonal
|-
|-
| | 11
| 11
| | 0-3-20
| 0-3-20
| | 1-7/5-7/6
| 1-7/5-7/6
| | utonal
| utonal
|-
|-
| | 12
| 12
| | 0-5-20
| 0-5-20
| | 1-7/4-7/6
| 1-7/4-7/6
| | utonal
| utonal
|-
|-
| | 13
| 13
| | 0-15-20
| 0-15-20
| | 1-4/3-7/6
| 1-4/3-7/6
| | otonal
| otonal
|-
|-
| | 14
| 14
| | 0-17-20
| 0-17-20
| | 1-5/3-7/6
| 1-5/3-7/6
| | otonal
| otonal
|-
|-
| | 15
| 15
| | 0-2-22
| 0-2-22
| | 1-5/4-16/11
| 1-5/4-16/11
| | keenanismic
| keenanismic
|-
|-
| | 16
| 16
| | 0-5-22
| 0-5-22
| | 1-7/4-16/11
| 1-7/4-16/11
| | keenanismic
| keenanismic
|-
|-
| | 17
| 17
| | 0-7-22
| 0-7-22
| | 1-12/11-16/11
| 1-12/11-16/11
| | otonal
| otonal
|-
|-
| | 18
| 18
| | 0-15-22
| 0-15-22
| | 1-4/3-16/11
| 1-4/3-16/11
| | utonal
| utonal
|-
|-
| | 19
| 19
| | 0-17-22
| 0-17-22
| | 1-5/3-16/11
| 1-5/3-16/11
| | keenanismic
| keenanismic
|-
|-
| | 20
| 20
| | 0-20-22
| 0-20-22
| | 1-7/6-16/11
| 1-7/6-16/11
| | keenanismic
| keenanismic
|-
|-
| | 21
| 21
| | 0-2-24
| 0-2-24
| | 1-5/4-20/11
| 1-5/4-20/11
| | utonal
| utonal
|-
|-
| | 22
| 22
| | 0-7-24
| 0-7-24
| | 1-12/11-20/11
| 1-12/11-20/11
| | otonal
| otonal
|-
|-
| | 23
| 23
| | 0-17-24
| 0-17-24
| | 1-5/3-20/11
| 1-5/3-20/11
| | utonal
| utonal
|-
|-
| | 24
| 24
| | 0-22-24
| 0-22-24
| | 1-16/11-20/11
| 1-16/11-20/11
| | otonal
| otonal
|-
|-
| | 25
| 25
| | 0-3-27
| 0-3-27
| | 1-7/5-14/11
| 1-7/5-14/11
| | utonal
| utonal
|-
|-
| | 26
| 26
| | 0-5-27
| 0-5-27
| | 1-7/4-14/11
| 1-7/4-14/11
| | utonal
| utonal
|-
|-
| | 27
| 27
| | 0-7-27
| 0-7-27
| | 1-12/11-14/11
| 1-12/11-14/11
| | otonal
| otonal
|-
|-
| | 28
| 28
| | 0-20-27
| 0-20-27
| | 1-7/6-14/11
| 1-7/6-14/11
| | utonal
| utonal
|-
|-
| | 29
| 29
| | 0-22-27
| 0-22-27
| | 1-16/11-14/11
| 1-16/11-14/11
| | otonal
| otonal
|-
|-
| | 30
| 30
| | 0-24-27
| 0-24-27
| | 1-20/11-14/11
| 1-20/11-14/11
| | otonal
| otonal
|-
|-
| | 31
| 31
| | 0-3-30
| 0-3-30
| | 1-7/5-16/9
| 1-7/5-16/9
| | werckismic
| werckismic
|-
|-
| | 32
| 32
| | 0-8-30
| 0-8-30
| | 1-11/9-16/9
| 1-11/9-16/9
| | otonal
| otonal
|-
|-
| | 33
| 33
| | 0-15-30
| 0-15-30
| | 1-4/3-16/9
| 1-4/3-16/9
| | ambitonal
| ambitonal
|-
|-
| | 34
| 34
| | 0-22-30
| 0-22-30
| | 1-16/11-16/9
| 1-16/11-16/9
| | utonal
| utonal
|-
|-
| | 35
| 35
| | 0-27-30
| 0-27-30
| | 1-14/11-16/9
| 1-14/11-16/9
| | werckismic
| werckismic
|-
|-
| | 36
| 36
| | 0-2-32
| 0-2-32
| | 1-5/4-10/9
| 1-5/4-10/9
| | utonal
| utonal
|-
|-
| | 37
| 37
| | 0-5-32
| 0-5-32
| | 1-7/4-10/9
| 1-7/4-10/9
| | werckismic
| werckismic
|-
|-
| | 38
| 38
| | 0-8-32
| 0-8-32
| | 1-11/9-10/9
| 1-11/9-10/9
| | otonal
| otonal
|-
|-
| | 39
| 39
| | 0-15-32
| 0-15-32
| | 1-4/3-10/9
| 1-4/3-10/9
| | otonal
| otonal
|-
|-
| | 40
| 40
| | 0-17-32
| 0-17-32
| | 1-5/3-10/9
| 1-5/3-10/9
| | utonal
| utonal
|-
|-
| | 41
| 41
| | 0-24-32
| 0-24-32
| | 1-20/11-10/9
| 1-20/11-10/9
| | utonal
| utonal
|-
|-
| | 42
| 42
| | 0-27-32
| 0-27-32
| | 1-14/11-10/9
| 1-14/11-10/9
| | werckismic
| werckismic
|-
|-
| | 43
| 43
| | 0-30-32
| 0-30-32
| | 1-16/9-10/9
| 1-16/9-10/9
| | otonal
| otonal
|-
|-
| | 44
| 44
| | 0-3-35
| 0-3-35
| | 1-7/5-14/9
| 1-7/5-14/9
| | utonal
| utonal
|-
|-
| | 45
| 45
| | 0-5-35
| 0-5-35
| | 1-7/4-14/9
| 1-7/4-14/9
| | utonal
| utonal
|-
|-
| | 46
| 46
| | 0-8-35
| 0-8-35
| | 1-11/9-14/9
| 1-11/9-14/9
| | otonal
| otonal
|-
|-
| | 47
| 47
| | 0-15-35
| 0-15-35
| | 1-4/3-14/9
| 1-4/3-14/9
| | otonal
| otonal
|-
|-
| | 48
| 48
| | 0-20-35
| 0-20-35
| | 1-7/6-14/9
| 1-7/6-14/9
| | utonal
| utonal
|-
|-
| | 49
| 49
| | 0-27-35
| 0-27-35
| | 1-14/11-14/9
| 1-14/11-14/9
| | utonal
| utonal
|-
|-
| | 50
| 50
| | 0-30-35
| 0-30-35
| | 1-16/9-14/9
| 1-16/9-14/9
| | otonal
| otonal
|-
|-
| | 51
| 51
| | 0-32-35
| 0-32-35
| | 1-10/9-14/9
| 1-10/9-14/9
| | otonal
| otonal
|}
|}


=Tetrads=
== Tetrads ==


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


=Pentads=
== Pentads ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | Number
! Number
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
|-
|-
| | 1
| 1
| | 0-2-5-7-22
| 0-2-5-7-22
| | 1-5/4-7/4-12/11-16/11
| 1-5/4-7/4-12/11-16/11
| | keenanismic
| keenanismic
|-
|-
| | 2
| 2
| | 0-15-17-20-22
| 0-15-17-20-22
| | 1-4/3-5/3-7/6-16/11
| 1-4/3-5/3-7/6-16/11
| | keenanismic
| keenanismic
|-
|-
| | 3
| 3
| | 0-2-7-22-24
| 0-2-7-22-24
| | 1-5/4-12/11-16/11-20/11
| 1-5/4-12/11-16/11-20/11
| | keenanismic
| keenanismic
|-
|-
| | 4
| 4
| | 0-2-17-22-24
| 0-2-17-22-24
| | 1-5/4-5/3-16/11-20/11
| 1-5/4-5/3-16/11-20/11
| | keenanismic
| keenanismic
|-
|-
| | 5
| 5
| | 0-3-5-20-27
| 0-3-5-20-27
| | 1-7/5-7/4-7/6-14/11
| 1-7/5-7/4-7/6-14/11
| | utonal
| utonal
|-
|-
| | 6
| 6
| | 0-5-7-22-27
| 0-5-7-22-27
| | 1-7/4-12/11-16/11-14/11
| 1-7/4-12/11-16/11-14/11
| | keenanismic
| keenanismic
|-
|-
| | 7
| 7
| | 0-5-20-22-27
| 0-5-20-22-27
| | 1-7/4-7/6-16/11-14/11
| 1-7/4-7/6-16/11-14/11
| | keenanismic
| keenanismic
|-
|-
| | 8
| 8
| | 0-7-22-24-27
| 0-7-22-24-27
| | 1-12/11-16/11-20/11-14/11
| 1-12/11-16/11-20/11-14/11
| | otonal
| otonal
|-
|-
| | 9
| 9
| | 0-2-17-24-32
| 0-2-17-24-32
| | 1-5/4-5/3-20/11-10/9
| 1-5/4-5/3-20/11-10/9
| | utonal
| utonal
|-
|-
| | 10
| 10
| | 0-8-15-30-32
| 0-8-15-30-32
| | 1-11/9-4/3-16/9-10/9
| 1-11/9-4/3-16/9-10/9
| | otonal
| otonal
|-
|-
| | 11
| 11
| | 0-3-5-8-35
| 0-3-5-8-35
| | 1-7/5-7/4-11/9-14/9
| 1-7/5-7/4-11/9-14/9
| | werckismic
| werckismic
|-
|-
| | 12
| 12
| | 0-3-5-20-35
| 0-3-5-20-35
| | 1-7/5-7/4-7/6-14/9
| 1-7/5-7/4-7/6-14/9
| | utonal
| utonal
|-
|-
| | 13
| 13
| | 0-3-5-27-35
| 0-3-5-27-35
| | 1-7/5-7/4-14/11-14/9
| 1-7/5-7/4-14/11-14/9
| | utonal
| utonal
|-
|-
| | 14
| 14
| | 0-3-20-27-35
| 0-3-20-27-35
| | 1-7/5-7/6-14/11-14/9
| 1-7/5-7/6-14/11-14/9
| | utonal
| utonal
|-
|-
| | 15
| 15
| | 0-5-20-27-35
| 0-5-20-27-35
| | 1-7/4-7/6-14/11-14/9
| 1-7/4-7/6-14/11-14/9
| | utonal
| utonal
|-
|-
| | 16
| 16
| | 0-3-8-30-35
| 0-3-8-30-35
| | 1-7/5-11/9-16/9-14/9
| 1-7/5-11/9-16/9-14/9
| | werckismic
| werckismic
|-
|-
| | 17
| 17
| | 0-8-15-30-35
| 0-8-15-30-35
| | 1-11/9-4/3-16/9-14/9
| 1-11/9-4/3-16/9-14/9
| | otonal
| otonal
|-
|-
| | 18
| 18
| | 0-3-27-30-35
| 0-3-27-30-35
| | 1-7/5-14/11-16/9-14/9
| 1-7/5-14/11-16/9-14/9
| | werckismic
| werckismic
|-
|-
| | 19
| 19
| | 0-5-8-32-35
| 0-5-8-32-35
| | 1-7/4-11/9-10/9-14/9
| 1-7/4-11/9-10/9-14/9
| | werckismic
| werckismic
|-
|-
| | 20
| 20
| | 0-8-15-32-35
| 0-8-15-32-35
| | 1-11/9-4/3-10/9-14/9
| 1-11/9-4/3-10/9-14/9
| | otonal
| otonal
|-
|-
| | 21
| 21
| | 0-5-27-32-35
| 0-5-27-32-35
| | 1-7/4-14/11-10/9-14/9
| 1-7/4-14/11-10/9-14/9
| | werckismic
| werckismic
|-
|-
| | 22
| 22
| | 0-8-30-32-35
| 0-8-30-32-35
| | 1-11/9-16/9-10/9-14/9
| 1-11/9-16/9-10/9-14/9
| | otonal
| otonal
|-
|-
| | 23
| 23
| | 0-15-30-32-35
| 0-15-30-32-35
| | 1-4/3-16/9-10/9-14/9
| 1-4/3-16/9-10/9-14/9
| | otonal
| otonal
|-
|-
| | 24
| 24
| | 0-27-30-32-35
| 0-27-30-32-35
| | 1-14/11-16/9-10/9-14/9
| 1-14/11-16/9-10/9-14/9
| | werckismic
| werckismic
|}
|}


=Hexads=
== Hexads ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | Number
! Number
| | Chord
! Chord
| | Transversal
! Transversal
| | Type
! Type
|-
|-
| | 1
| 1
| | 0-3-5-20-27-35
| 0-3-5-20-27-35
| | 1-7/5-7/4-7/6-14/11-14/9
| 1-7/5-7/4-7/6-14/11-14/9
| | utonal
| utonal
|-
|-
| | 2
| 2
| | 0-8-15-30-32-35
| 0-8-15-30-32-35
| | 1-11/9-4/3-16/9-10/9-14/9
| 1-11/9-4/3-16/9-10/9-14/9
| | otonal
| otonal
|}
|}
[[Category:Lists of chords]]
[[Category:Hemithirds]]

Latest revision as of 21:48, 22 June 2025

Below are listed the dyadic chords of 11-limit hemithirds temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering by 441/440 are werckismic, and by 385/384 keenanismic.

Hemithirds has MOS of size 6, 7, 13, 19, 25, 31, 56 and 87. It may be seen that adding essentially tempered chords to the mix allows for a notably richer range of harmonies even for the 13 note MOS.

Triads

Number Chord Transversal Type
1 0-2-5 1-5/4-7/4 otonal
2 0-3-5 1-7/5-7/4 utonal
3 0-2-7 1-5/4-12/11 keenanismic
4 0-5-7 1-7/4-12/11 keenanismic
5 0-3-8 1-7/5-11/9 werckismic
6 0-5-8 1-7/4-11/9 werckismic
7 0-7-15 1-12/11-4/3 utonal
8 0-8-15 1-11/9-4/3 otonal
9 0-2-17 1-5/4-5/3 utonal
10 0-15-17 1-4/3-5/3 otonal
11 0-3-20 1-7/5-7/6 utonal
12 0-5-20 1-7/4-7/6 utonal
13 0-15-20 1-4/3-7/6 otonal
14 0-17-20 1-5/3-7/6 otonal
15 0-2-22 1-5/4-16/11 keenanismic
16 0-5-22 1-7/4-16/11 keenanismic
17 0-7-22 1-12/11-16/11 otonal
18 0-15-22 1-4/3-16/11 utonal
19 0-17-22 1-5/3-16/11 keenanismic
20 0-20-22 1-7/6-16/11 keenanismic
21 0-2-24 1-5/4-20/11 utonal
22 0-7-24 1-12/11-20/11 otonal
23 0-17-24 1-5/3-20/11 utonal
24 0-22-24 1-16/11-20/11 otonal
25 0-3-27 1-7/5-14/11 utonal
26 0-5-27 1-7/4-14/11 utonal
27 0-7-27 1-12/11-14/11 otonal
28 0-20-27 1-7/6-14/11 utonal
29 0-22-27 1-16/11-14/11 otonal
30 0-24-27 1-20/11-14/11 otonal
31 0-3-30 1-7/5-16/9 werckismic
32 0-8-30 1-11/9-16/9 otonal
33 0-15-30 1-4/3-16/9 ambitonal
34 0-22-30 1-16/11-16/9 utonal
35 0-27-30 1-14/11-16/9 werckismic
36 0-2-32 1-5/4-10/9 utonal
37 0-5-32 1-7/4-10/9 werckismic
38 0-8-32 1-11/9-10/9 otonal
39 0-15-32 1-4/3-10/9 otonal
40 0-17-32 1-5/3-10/9 utonal
41 0-24-32 1-20/11-10/9 utonal
42 0-27-32 1-14/11-10/9 werckismic
43 0-30-32 1-16/9-10/9 otonal
44 0-3-35 1-7/5-14/9 utonal
45 0-5-35 1-7/4-14/9 utonal
46 0-8-35 1-11/9-14/9 otonal
47 0-15-35 1-4/3-14/9 otonal
48 0-20-35 1-7/6-14/9 utonal
49 0-27-35 1-14/11-14/9 utonal
50 0-30-35 1-16/9-14/9 otonal
51 0-32-35 1-10/9-14/9 otonal

Tetrads

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

Pentads

Number Chord Transversal Type
1 0-2-5-7-22 1-5/4-7/4-12/11-16/11 keenanismic
2 0-15-17-20-22 1-4/3-5/3-7/6-16/11 keenanismic
3 0-2-7-22-24 1-5/4-12/11-16/11-20/11 keenanismic
4 0-2-17-22-24 1-5/4-5/3-16/11-20/11 keenanismic
5 0-3-5-20-27 1-7/5-7/4-7/6-14/11 utonal
6 0-5-7-22-27 1-7/4-12/11-16/11-14/11 keenanismic
7 0-5-20-22-27 1-7/4-7/6-16/11-14/11 keenanismic
8 0-7-22-24-27 1-12/11-16/11-20/11-14/11 otonal
9 0-2-17-24-32 1-5/4-5/3-20/11-10/9 utonal
10 0-8-15-30-32 1-11/9-4/3-16/9-10/9 otonal
11 0-3-5-8-35 1-7/5-7/4-11/9-14/9 werckismic
12 0-3-5-20-35 1-7/5-7/4-7/6-14/9 utonal
13 0-3-5-27-35 1-7/5-7/4-14/11-14/9 utonal
14 0-3-20-27-35 1-7/5-7/6-14/11-14/9 utonal
15 0-5-20-27-35 1-7/4-7/6-14/11-14/9 utonal
16 0-3-8-30-35 1-7/5-11/9-16/9-14/9 werckismic
17 0-8-15-30-35 1-11/9-4/3-16/9-14/9 otonal
18 0-3-27-30-35 1-7/5-14/11-16/9-14/9 werckismic
19 0-5-8-32-35 1-7/4-11/9-10/9-14/9 werckismic
20 0-8-15-32-35 1-11/9-4/3-10/9-14/9 otonal
21 0-5-27-32-35 1-7/4-14/11-10/9-14/9 werckismic
22 0-8-30-32-35 1-11/9-16/9-10/9-14/9 otonal
23 0-15-30-32-35 1-4/3-16/9-10/9-14/9 otonal
24 0-27-30-32-35 1-14/11-16/9-10/9-14/9 werckismic

Hexads

Number Chord Transversal Type
1 0-3-5-20-27-35 1-7/5-7/4-7/6-14/11-14/9 utonal
2 0-8-15-30-32-35 1-11/9-4/3-16/9-10/9-14/9 otonal
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