View source for Chords of hemiwur

Below are listed the [[Dyadic_chord|dyadic chords]] of 11-limit [[Würschmidt_family#Hemiwürschmidt|hemiwur temperament]]. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 121/120 are biyatismic, by 176/175 valinorsmic, and by 385/384 keenanismic. Chords requiring any two of the above are labeled zeus.

Hemiwur has MOS of size 6, 7, 13, 19, 25, 31, 37 and 68. The largest chords on these lists have complexity 32, and so would require the 37 note MOS, but there are many chords of much lower complexity, so that the 13-note MOS, for instance, has a couple of hexads, plus many more pentads, tetrads and triads.

=Triads=

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

=Tetrads=

{| class="wikitable"
|-
| | Number
| | Chord
| | Transversal
| | Type
|-
| | 1
| | 0-2-4-7
| | 1-5/4-11/7-11/10
| | valinorsmic
|-
| | 2
| | 0-2-5-7
| | 1-5/4-7/4-11/10
| | valinorsmic
|-
| | 3
| | 0-3-5-7
| | 1-7/5-7/4-11/10
| | valinorsmic
|-
| | 4
| | 0-2-4-9
| | 1-5/4-11/7-11/8
| | valinorsmic
|-
| | 5
| | 0-2-5-9
| | 1-5/4-7/4-11/8
| | otonal
|-
| | 6
| | 0-2-7-9
| | 1-5/4-11/10-11/8
| | valinorsmic
|-
| | 7
| | 0-4-7-9
| | 1-11/7-11/10-11/8
| | utonal
|-
| | 8
| | 0-5-7-9
| | 1-7/4-11/10-11/8
| | valinorsmic
|-
| | 9
| | 0-2-4-11
| | 1-5/4-11/7-12/7
| | zeus
|-
| | 10
| | 0-2-7-11
| | 1-5/4-11/10-12/7
| | zeus
|-
| | 11
| | 0-4-7-11
| | 1-11/7-11/10-12/7
| | biyatismic
|-
| | 12
| | 0-2-9-11
| | 1-5/4-11/8-12/7
| | keenanismic
|-
| | 13
| | 0-4-9-11
| | 1-11/7-11/8-12/7
| | zeus
|-
| | 14
| | 0-7-9-11
| | 1-11/10-11/8-12/7
| | zeus
|-
| | 15
| | 0-3-5-14
| | 1-7/5-7/4-6/5
| | keenanismic
|-
| | 16
| | 0-3-7-14
| | 1-7/5-11/10-6/5
| | otonal
|-
| | 17
| | 0-5-7-14
| | 1-7/4-11/10-6/5
| | zeus
|-
| | 18
| | 0-5-9-14
| | 1-7/4-11/8-6/5
| | keenanismic
|-
| | 19
| | 0-7-9-14
| | 1-11/10-11/8-6/5
| | zeus
|-
| | 20
| | 0-7-11-14
| | 1-12/11-12/7-6/5
| | utonal
|-
| | 21
| | 0-9-11-14
| | 1-11/8-12/7-6/5
| | keenanismic
|-
| | 22
| | 0-2-5-16
| | 1-5/4-7/4-3/2
| | otonal
|-
| | 23
| | 0-2-7-16
| | 1-5/4-11/10-3/2
| | zeus
|-
| | 24
| | 0-5-7-16
| | 1-7/4-11/10-3/2
| | zeus
|-
| | 25
| | 0-2-9-16
| | 1-5/4-11/8-3/2
| | otonal
|-
| | 26
| | 0-5-9-16
| | 1-7/4-11/8-3/2
| | otonal
|-
| | 27
| | 0-7-9-16
| | 1-11/10-11/8-3/2
| | biyatismic
|-
| | 28
| | 0-2-11-16
| | 1-5/4-12/7-3/2
| | keenanismic
|-
| | 29
| | 0-7-11-16
| | 1-12/11-12/7-3/2
| | utonal
|-
| | 30
| | 0-9-11-16
| | 1-11/8-12/7-3/2
| | zeus
|-
| | 31
| | 0-5-14-16
| | 1-7/4-6/5-3/2
| | keenanismic
|-
| | 32
| | 0-7-14-16
| | 1-12/11-6/5-3/2
| | utonal
|-
| | 33
| | 0-9-14-16
| | 1-11/8-6/5-3/2
| | zeus
|-
| | 34
| | 0-11-14-16
| | 1-12/7-6/5-3/2
| | utonal
|-
| | 35
| | 0-7-9-23
| | 1-11/10-11/8-18/11
| | biyatismic
|-
| | 36
| | 0-7-14-23
| | 1-11/10-6/5-18/11
| | biyatismic
|-
| | 37
| | 0-9-14-23
| | 1-11/8-6/5-18/11
| | zeus
|-
| | 38
| | 0-7-16-23
| | 1-12/11-3/2-18/11
| | ambitonal
|-
| | 39
| | 0-9-16-23
| | 1-11/8-3/2-18/11
| | biyatismic
|-
| | 40
| | 0-14-16-23
| | 1-6/5-3/2-18/11
| | biyatismic
|-
| | 41
| | 0-4-11-27
| | 1-11/7-12/7-9/7
| | otonal
|-
| | 42
| | 0-11-16-27
| | 1-12/7-3/2-9/7
| | ambitonal
|-
| | 43
| | 0-16-23-27
| | 1-3/2-18/11-9/7
| | utonal
|-
| | 44
| | 0-3-7-30
| | 1-7/5-11/10-9/5
| | otonal
|-
| | 45
| | 0-3-14-30
| | 1-7/5-6/5-9/5
| | otonal
|-
| | 46
| | 0-7-14-30
| | 1-11/10-6/5-9/5
| | otonal
|-
| | 47
| | 0-7-16-30
| | 1-11/10-3/2-9/5
| | biyatismic
|-
| | 48
| | 0-14-16-30
| | 1-6/5-3/2-9/5
| | ambitonal
|-
| | 49
| | 0-7-23-30
| | 1-11/10-18/11-9/5
| | biyatismic
|-
| | 50
| | 0-14-23-30
| | 1-6/5-18/11-9/5
| | biyatismic
|-
| | 51
| | 0-16-23-30
| | 1-3/2-18/11-9/5
| | utonal
|-
| | 52
| | 0-16-27-30
| | 1-3/2-9/7-9/5
| | utonal
|-
| | 53
| | 0-23-27-30
| | 1-18/11-9/7-9/5
| | utonal
|-
| | 54
| | 0-2-5-32
| | 1-5/4-7/4-9/8
| | otonal
|-
| | 55
| | 0-2-9-32
| | 1-5/4-11/8-9/8
| | otonal
|-
| | 56
| | 0-5-9-32
| | 1-7/4-11/8-9/8
| | otonal
|-
| | 57
| | 0-2-16-32
| | 1-5/4-3/2-9/8
| | otonal
|-
| | 58
| | 0-5-16-32
| | 1-7/4-3/2-9/8
| | otonal
|-
| | 59
| | 0-9-16-32
| | 1-11/8-3/2-9/8
| | otonal
|-
| | 60
| | 0-9-23-32
| | 1-11/8-18/11-9/8
| | biyatismic
|-
| | 61
| | 0-16-23-32
| | 1-3/2-18/11-9/8
| | utonal
|-
| | 62
| | 0-16-27-32
| | 1-3/2-9/7-9/8
| | utonal
|-
| | 63
| | 0-23-27-32
| | 1-18/11-9/7-9/8
| | utonal
|-
| | 64
| | 0-16-30-32
| | 1-3/2-9/5-9/8
| | utonal
|-
| | 65
| | 0-23-30-32
| | 1-18/11-9/5-9/8
| | utonal
|-
| | 66
| | 0-27-30-32
| | 1-9/7-9/5-9/8
| | utonal
|}

=Pentads=

{| class="wikitable"
|-
| | Number
| | Chord
| | Transversal
| | Type
|-
| | 1
| | 0-2-4-7-9
| | 1-5/4-11/7-11/10-11/8
| | valinorsmic
|-
| | 2
| | 0-2-5-7-9
| | 1-5/4-7/4-11/10-11/8
| | valinorsmic
|-
| | 3
| | 0-2-4-7-11
| | 1-5/4-11/7-11/10-12/7
| | zeus
|-
| | 4
| | 0-2-4-9-11
| | 1-5/4-11/7-11/8-12/7
| | zeus
|-
| | 5
| | 0-2-7-9-11
| | 1-5/4-11/10-11/8-12/7
| | zeus
|-
| | 6
| | 0-4-7-9-11
| | 1-11/7-11/10-11/8-12/7
| | zeus
|-
| | 7
| | 0-3-5-7-14
| | 1-7/5-7/4-11/10-6/5
| | zeus
|-
| | 8
| | 0-5-7-9-14
| | 1-7/4-11/10-11/8-6/5
| | zeus
|-
| | 9
| | 0-7-9-11-14
| | 1-11/10-11/8-12/7-6/5
| | zeus
|-
| | 10
| | 0-2-5-7-16
| | 1-5/4-7/4-11/10-3/2
| | zeus
|-
| | 11
| | 0-2-5-9-16
| | 1-5/4-7/4-11/8-3/2
| | otonal
|-
| | 12
| | 0-2-7-9-16
| | 1-5/4-11/10-11/8-3/2
| | zeus
|-
| | 13
| | 0-5-7-9-16
| | 1-7/4-11/10-11/8-3/2
| | zeus
|-
| | 14
| | 0-2-7-11-16
| | 1-5/4-11/10-12/7-3/2
| | zeus
|-
| | 15
| | 0-2-9-11-16
| | 1-5/4-11/8-12/7-3/2
| | zeus
|-
| | 16
| | 0-7-9-11-16
| | 1-11/10-11/8-12/7-3/2
| | zeus
|-
| | 17
| | 0-5-7-14-16
| | 1-7/4-11/10-6/5-3/2
| | zeus
|-
| | 18
| | 0-5-9-14-16
| | 1-7/4-11/8-6/5-3/2
| | zeus
|-
| | 19
| | 0-7-9-14-16
| | 1-11/10-11/8-6/5-3/2
| | zeus
|-
| | 20
| | 0-7-11-14-16
| | 1-12/11-12/7-6/5-3/2
| | utonal
|-
| | 21
| | 0-9-11-14-16
| | 1-11/8-12/7-6/5-3/2
| | zeus
|-
| | 22
| | 0-7-9-14-23
| | 1-11/10-11/8-6/5-18/11
| | zeus
|-
| | 23
| | 0-7-9-16-23
| | 1-11/10-11/8-3/2-18/11
| | biyatismic
|-
| | 24
| | 0-7-14-16-23
| | 1-11/10-6/5-3/2-18/11
| | biyatismic
|-
| | 25
| | 0-9-14-16-23
| | 1-11/8-6/5-3/2-18/11
| | zeus
|-
| | 26
| | 0-3-7-14-30
| | 1-7/5-11/10-6/5-9/5
| | otonal
|-
| | 27
| | 0-7-14-16-30
| | 1-11/10-6/5-3/2-9/5
| | biyatismic
|-
| | 28
| | 0-7-14-23-30
| | 1-11/10-6/5-18/11-9/5
| | biyatismic
|-
| | 29
| | 0-7-16-23-30
| | 1-11/10-3/2-18/11-9/5
| | biyatismic
|-
| | 30
| | 0-14-16-23-30
| | 1-6/5-3/2-18/11-9/5
| | biyatismic
|-
| | 31
| | 0-16-23-27-30
| | 1-3/2-18/11-9/7-9/5
| | utonal
|-
| | 32
| | 0-2-5-9-32
| | 1-5/4-7/4-11/8-9/8
| | otonal
|-
| | 33
| | 0-2-5-16-32
| | 1-5/4-7/4-3/2-9/8
| | otonal
|-
| | 34
| | 0-2-9-16-32
| | 1-5/4-11/8-3/2-9/8
| | otonal
|-
| | 35
| | 0-5-9-16-32
| | 1-7/4-11/8-3/2-9/8
| | otonal
|-
| | 36
| | 0-9-16-23-32
| | 1-11/8-3/2-18/11-9/8
| | biyatismic
|-
| | 37
| | 0-16-23-27-32
| | 1-3/2-18/11-9/7-9/8
| | utonal
|-
| | 38
| | 0-16-23-30-32
| | 1-3/2-18/11-9/5-9/8
| | utonal
|-
| | 39
| | 0-16-27-30-32
| | 1-3/2-9/7-9/5-9/8
| | utonal
|-
| | 40
| | 0-23-27-30-32
| | 1-18/11-9/7-9/5-9/8
| | utonal
|}

=Hexads=

{| class="wikitable"
|-
| | Number
| | Chord
| | Transversal
| | Type
|-
| | 1
| | 0-2-4-7-9-11
| | 1-5/4-11/7-11/10-11/8-12/7
| | zeus
|-
| | 2
| | 0-2-5-7-9-16
| | 1-5/4-7/4-11/10-11/8-3/2
| | zeus
|-
| | 3
| | 0-2-7-9-11-16
| | 1-5/4-11/10-11/8-12/7-3/2
| | zeus
|-
| | 4
| | 0-5-7-9-14-16
| | 1-7/4-11/10-11/8-6/5-3/2
| | zeus
|-
| | 5
| | 0-7-9-11-14-16
| | 1-11/10-11/8-12/7-6/5-3/2
| | zeus
|-
| | 6
| | 0-7-9-14-16-23
| | 1-11/10-11/8-6/5-3/2-18/11
| | zeus
|-
| | 7
| | 0-7-14-16-23-30
| | 1-11/10-6/5-3/2-18/11-9/5
| | biyatismic
|-
| | 8
| | 0-2-5-9-16-32
| | 1-5/4-7/4-11/8-3/2-9/8
| | otonal
|-
| | 9
| | 0-16-23-27-30-32
| | 1-3/2-18/11-9/7-9/5-9/8
| | utonal
|}
[[Category:Lists of chords]]
[[Category:Dyadic chords]]
[[Category:11-limit]]
[[Category:Hemiwur]]