View source for Unidec/Chords

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

The normal mapping for unidec is uni = [{{val| 2 5 8 5 6 }}, {{val| 0 -6 -11 2 3 }}]. From this we may derive a val v = uni[1] + 100 uni[2] = {{val| 2 -595 -1092 205 306 }} which we may use to sort and normalize the chords of unidec. 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.

Unidec has MOS of size 6, 20, 26, 46, and 72. Even the six-note MOS has some werckismic triads, and there are many more chords in the twenty note MOS, including many of the werckismic tetrad of complexity six and the keenanismic tetrad of complexity ten, which are likely to figure large in any composition in unidec. The essentially tempered chords of unidec either temper out 441/440 or 385/384; putting these together produces portent temperament, but there are no essentially portent chords. Adding the small ragisma, 4375/4374, to the commas of portent gives unidec, with very little additional tuning damage. Unidec is, in fact, quite an accurate temperament even compared to such things as miracle, but still has enough give in it to allow for some interesting essential tempering.

== Triads ==

{| class="wikitable"
|-
! Number
! Chord
! Transversal
! Type
! Complexity
|-
| 1
| 0-100-201
| 1-10/9-7/4
| werckismic
| 4
|-
| 2
| 0-101-201
| 1-11/7-7/4
| werckismic
| 4
|-
| 3
| 0-101-300
| 1-11/7-11/8
| utonal
| 6
|-
| 4
| 0-201-300
| 1-7/4-11/8
| otonal
| 6
|-
| 5
| 0-201-499
| 1-7/4-6/5
| keenanismic
| 10
|-
| 6
| 0-300-499
| 1-11/8-6/5
| keenanismic
| 10
|-
| 7
| 0-100-599
| 1-10/9-4/3
| otonal
| 12
|-
| 8
| 0-499-599
| 1-6/5-4/3
| utonal
| 12
|-
| 9
| 0-201-798
| 1-7/4-7/6
| utonal
| 16
|-
| 10
| 0-599-798
| 1-4/3-7/6
| otonal
| 16
|-
| 11
| 0-101-899
| 1-11/7-11/6
| utonal
| 18
|-
| 12
| 0-300-899
| 1-11/8-11/6
| utonal
| 18
|-
| 13
| 0-599-899
| 1-4/3-11/6
| otonal
| 18
|-
| 14
| 0-798-899
| 1-7/6-11/6
| otonal
| 18
|-
| 15
| 0-201-1098
| 1-7/4-8/5
| keenanismic
| 22
|-
| 16
| 0-300-1098
| 1-11/8-8/5
| keenanismic
| 22
|-
| 17
| 0-499-1098
| 1-6/5-8/5
| otonal
| 22
|-
| 18
| 0-599-1098
| 1-4/3-8/5
| utonal
| 22
|-
| 19
| 0-798-1098
| 1-7/6-8/5
| keenanismic
| 22
|-
| 20
| 0-899-1098
| 1-11/6-8/5
| keenanismic
| 22
|-
| 21
| 0-100-1198
| 1-10/9-16/9
| otonal
| 24
|-
| 22
| 0-599-1198
| 1-4/3-16/9
| ambitonal
| 24
|-
| 23
| 0-1098-1198
| 1-8/5-16/9
| utonal
| 24
|-
| 24
| 0-101-1297
| 1-11/7-7/5
| werckismic
| 26
|-
| 25
| 0-201-1297
| 1-7/4-7/5
| utonal
| 26
|-
| 26
| 0-499-1297
| 1-6/5-7/5
| otonal
| 26
|-
| 27
| 0-798-1297
| 1-7/6-7/5
| utonal
| 26
|-
| 28
| 0-1098-1297
| 1-8/5-7/5
| otonal
| 26
|-
| 29
| 0-1198-1297
| 1-16/9-7/5
| werckismic
| 26
|-
| 30
| 0-101-1396
| 1-11/7-11/10
| utonal
| 28
|-
| 31
| 0-300-1396
| 1-11/8-11/10
| utonal
| 28
|-
| 32
| 0-499-1396
| 1-6/5-11/10
| otonal
| 28
|-
| 33
| 0-899-1396
| 1-11/6-11/10
| utonal
| 28
|-
| 34
| 0-1098-1396
| 1-8/5-11/10
| otonal
| 28
|-
| 35
| 0-1297-1396
| 1-7/5-11/10
| otonal
| 28
|-
| 36
| 0-100-1397
| 1-10/9-14/9
| otonal
| 28
|-
| 37
| 0-201-1397
| 1-7/4-14/9
| utonal
| 28
|-
| 38
| 0-599-1397
| 1-4/3-14/9
| otonal
| 28
|-
| 39
| 0-798-1397
| 1-7/6-14/9
| utonal
| 28
|-
| 40
| 0-1198-1397
| 1-16/9-14/9
| otonal
| 28
|-
| 41
| 0-1297-1397
| 1-7/5-14/9
| utonal
| 28
|-
| 42
| 0-100-1496
| 1-10/9-11/9
| otonal
| 30
|-
| 43
| 0-101-1496
| 1-11/7-11/9
| utonal
| 30
|-
| 44
| 0-201-1496
| 1-7/4-11/9
| werckismic
| 30
|-
| 45
| 0-300-1496
| 1-11/8-11/9
| utonal
| 30
|-
| 46
| 0-599-1496
| 1-4/3-11/9
| otonal
| 30
|-
| 47
| 0-899-1496
| 1-11/6-11/9
| utonal
| 30
|-
| 48
| 0-1198-1496
| 1-16/9-11/9
| otonal
| 30
|-
| 49
| 0-1297-1496
| 1-7/5-11/9
| werckismic
| 30
|-
| 50
| 0-1396-1496
| 1-11/10-11/9
| utonal
| 30
|-
| 51
| 0-1397-1496
| 1-14/9-11/9
| otonal
| 30
|}

== Tetrads ==

{| class="wikitable"
|-
! Number
! Chord
! Transversal
! Type
! Complexity
|-
| 1
| 0-101-201-300
| 1-11/7-7/4-11/8
| werckismic
| 6
|-
| 2
| 0-201-300-499
| 1-7/4-11/8-6/5
| keenanismic
| 10
|-
| 3
| 0-101-300-899
| 1-11/7-11/8-11/6
| utonal
| 18
|-
| 4
| 0-599-798-899
| 1-4/3-7/6-11/6
| otonal
| 18
|-
| 5
| 0-201-300-1098
| 1-7/4-11/8-8/5
| keenanismic
| 22
|-
| 6
| 0-201-499-1098
| 1-7/4-6/5-8/5
| keenanismic
| 22
|-
| 7
| 0-300-499-1098
| 1-11/8-6/5-8/5
| keenanismic
| 22
|-
| 8
| 0-499-599-1098
| 1-6/5-4/3-8/5
| ambitonal
| 22
|-
| 9
| 0-201-798-1098
| 1-7/4-7/6-8/5
| keenanismic
| 22
|-
| 10
| 0-599-798-1098
| 1-4/3-7/6-8/5
| keenanismic
| 22
|-
| 11
| 0-300-899-1098
| 1-11/8-11/6-8/5
| keenanismic
| 22
|-
| 12
| 0-599-899-1098
| 1-4/3-11/6-8/5
| keenanismic
| 22
|-
| 13
| 0-798-899-1098
| 1-7/6-11/6-8/5
| keenanismic
| 22
|-
| 14
| 0-100-599-1198
| 1-10/9-4/3-16/9
| otonal
| 24
|-
| 15
| 0-599-1098-1198
| 1-4/3-8/5-16/9
| utonal
| 24
|-
| 16
| 0-101-201-1297
| 1-11/7-7/4-7/5
| werckismic
| 26
|-
| 17
| 0-201-499-1297
| 1-7/4-6/5-7/5
| keenanismic
| 26
|-
| 18
| 0-201-798-1297
| 1-7/4-7/6-7/5
| utonal
| 26
|-
| 19
| 0-201-1098-1297
| 1-7/4-8/5-7/5
| keenanismic
| 26
|-
| 20
| 0-499-1098-1297
| 1-6/5-8/5-7/5
| otonal
| 26
|-
| 21
| 0-798-1098-1297
| 1-7/6-8/5-7/5
| keenanismic
| 26
|-
| 22
| 0-1098-1198-1297
| 1-8/5-16/9-7/5
| werckismic
| 26
|-
| 23
| 0-101-300-1396
| 1-11/7-11/8-11/10
| utonal
| 28
|-
| 24
| 0-300-499-1396
| 1-11/8-6/5-11/10
| keenanismic
| 28
|-
| 25
| 0-101-899-1396
| 1-11/7-11/6-11/10
| utonal
| 28
|-
| 26
| 0-300-899-1396
| 1-11/8-11/6-11/10
| utonal
| 28
|-
| 27
| 0-300-1098-1396
| 1-11/8-8/5-11/10
| keenanismic
| 28
|-
| 28
| 0-499-1098-1396
| 1-6/5-8/5-11/10
| otonal
| 28
|-
| 29
| 0-899-1098-1396
| 1-11/6-8/5-11/10
| keenanismic
| 28
|-
| 30
| 0-101-1297-1396
| 1-11/7-7/5-11/10
| werckismic
| 28
|-
| 31
| 0-499-1297-1396
| 1-6/5-7/5-11/10
| otonal
| 28
|-
| 32
| 0-1098-1297-1396
| 1-8/5-7/5-11/10
| otonal
| 28
|-
| 33
| 0-100-201-1397
| 1-10/9-7/4-14/9
| werckismic
| 28
|-
| 34
| 0-100-599-1397
| 1-10/9-4/3-14/9
| otonal
| 28
|-
| 35
| 0-201-798-1397
| 1-7/4-7/6-14/9
| utonal
| 28
|-
| 36
| 0-599-798-1397
| 1-4/3-7/6-14/9
| ambitonal
| 28
|-
| 37
| 0-100-1198-1397
| 1-10/9-16/9-14/9
| otonal
| 28
|-
| 38
| 0-599-1198-1397
| 1-4/3-16/9-14/9
| otonal
| 28
|-
| 39
| 0-201-1297-1397
| 1-7/4-7/5-14/9
| utonal
| 28
|-
| 40
| 0-798-1297-1397
| 1-7/6-7/5-14/9
| utonal
| 28
|-
| 41
| 0-1198-1297-1397
| 1-16/9-7/5-14/9
| werckismic
| 28
|-
| 42
| 0-100-201-1496
| 1-10/9-7/4-11/9
| werckismic
| 30
|-
| 43
| 0-101-201-1496
| 1-11/7-7/4-11/9
| werckismic
| 30
|-
| 44
| 0-101-300-1496
| 1-11/7-11/8-11/9
| utonal
| 30
|-
| 45
| 0-201-300-1496
| 1-7/4-11/8-11/9
| werckismic
| 30
|-
| 46
| 0-100-599-1496
| 1-10/9-4/3-11/9
| otonal
| 30
|-
| 47
| 0-101-899-1496
| 1-11/7-11/6-11/9
| utonal
| 30
|-
| 48
| 0-300-899-1496
| 1-11/8-11/6-11/9
| utonal
| 30
|-
| 49
| 0-599-899-1496
| 1-4/3-11/6-11/9
| ambitonal
| 30
|-
| 50
| 0-100-1198-1496
| 1-10/9-16/9-11/9
| otonal
| 30
|-
| 51
| 0-599-1198-1496
| 1-4/3-16/9-11/9
| otonal
| 30
|-
| 52
| 0-101-1297-1496
| 1-11/7-7/5-11/9
| werckismic
| 30
|-
| 53
| 0-201-1297-1496
| 1-7/4-7/5-11/9
| werckismic
| 30
|-
| 54
| 0-1198-1297-1496
| 1-16/9-7/5-11/9
| werckismic
| 30
|-
| 55
| 0-101-1396-1496
| 1-11/7-11/10-11/9
| utonal
| 30
|-
| 56
| 0-300-1396-1496
| 1-11/8-11/10-11/9
| utonal
| 30
|-
| 57
| 0-899-1396-1496
| 1-11/6-11/10-11/9
| utonal
| 30
|-
| 58
| 0-1297-1396-1496
| 1-7/5-11/10-11/9
| werckismic
| 30
|-
| 59
| 0-100-1397-1496
| 1-10/9-14/9-11/9
| otonal
| 30
|-
| 60
| 0-201-1397-1496
| 1-7/4-14/9-11/9
| werckismic
| 30
|-
| 61
| 0-599-1397-1496
| 1-4/3-14/9-11/9
| otonal
| 30
|-
| 62
| 0-1198-1397-1496
| 1-16/9-14/9-11/9
| otonal
| 30
|-
| 63
| 0-1297-1397-1496
| 1-7/5-14/9-11/9
| werckismic
| 30
|}

== Pentads ==

{| class="wikitable"
|-
! Number
! Chord
! Transversal
! Type
! Complexity
|-
| 1
| 0-201-300-499-1098
| 1-7/4-11/8-6/5-8/5
| keenanismic
| 22
|-
| 2
| 0-599-798-899-1098
| 1-4/3-7/6-11/6-8/5
| keenanismic
| 22
|-
| 3
| 0-201-499-1098-1297
| 1-7/4-6/5-8/5-7/5
| keenanismic
| 26
|-
| 4
| 0-201-798-1098-1297
| 1-7/4-7/6-8/5-7/5
| keenanismic
| 26
|-
| 5
| 0-101-300-899-1396
| 1-11/7-11/8-11/6-11/10
| utonal
| 28
|-
| 6
| 0-300-499-1098-1396
| 1-11/8-6/5-8/5-11/10
| keenanismic
| 28
|-
| 7
| 0-300-899-1098-1396
| 1-11/8-11/6-8/5-11/10
| keenanismic
| 28
|-
| 8
| 0-499-1098-1297-1396
| 1-6/5-8/5-7/5-11/10
| otonal
| 28
|-
| 9
| 0-100-599-1198-1397
| 1-10/9-4/3-16/9-14/9
| otonal
| 28
|-
| 10
| 0-201-798-1297-1397
| 1-7/4-7/6-7/5-14/9
| utonal
| 28
|-
| 11
| 0-101-201-300-1496
| 1-11/7-7/4-11/8-11/9
| werckismic
| 30
|-
| 12
| 0-101-300-899-1496
| 1-11/7-11/8-11/6-11/9
| utonal
| 30
|-
| 13
| 0-100-599-1198-1496
| 1-10/9-4/3-16/9-11/9
| otonal
| 30
|-
| 14
| 0-101-201-1297-1496
| 1-11/7-7/4-7/5-11/9
| werckismic
| 30
|-
| 15
| 0-101-300-1396-1496
| 1-11/7-11/8-11/10-11/9
| utonal
| 30
|-
| 16
| 0-101-899-1396-1496
| 1-11/7-11/6-11/10-11/9
| utonal
| 30
|-
| 17
| 0-300-899-1396-1496
| 1-11/8-11/6-11/10-11/9
| utonal
| 30
|-
| 18
| 0-101-1297-1396-1496
| 1-11/7-7/5-11/10-11/9
| werckismic
| 30
|-
| 19
| 0-100-201-1397-1496
| 1-10/9-7/4-14/9-11/9
| werckismic
| 30
|-
| 20
| 0-100-599-1397-1496
| 1-10/9-4/3-14/9-11/9
| otonal
| 30
|-
| 21
| 0-100-1198-1397-1496
| 1-10/9-16/9-14/9-11/9
| otonal
| 30
|-
| 22
| 0-599-1198-1397-1496
| 1-4/3-16/9-14/9-11/9
| otonal
| 30
|-
| 23
| 0-201-1297-1397-1496
| 1-7/4-7/5-14/9-11/9
| werckismic
| 30
|-
| 24
| 0-1198-1297-1397-1496
| 1-16/9-7/5-14/9-11/9
| werckismic
| 30
|}

== Hexads ==

{| class="wikitable"
|-
! Number
! Chord
! Transversal
! Type
! Complexity
|-
| 1
| 0-101-300-899-1396-1496
| 1-11/7-11/8-11/6-11/10-11/9
| utonal
| 30
|-
| 2
| 0-100-599-1198-1397-1496
| 1-10/9-4/3-16/9-14/9-11/9
| otonal
| 30
|}

[[Category:Lists of chords]]
[[Category:Unidec]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Pentads]]
[[Category:Hexads]]