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