Partially delta-rational tetrads in small edos: Difference between revisions

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Shown below are approximate [[Delta-rational chord|partially delta-rational]] tetrads (with signature +a+?+b) spanning an interval < octave, in edos < 24, with least-squares error < 0.001. All delta signatures are in the 3-integer limit ignoring the +? term.
Shown below are approximate [[Delta-rational chord|partially delta-rational]] tetrads with signature +a+?+b spanning an interval < octave, in edos < 24, with least-squares error < 0.001. All delta signatures are in the 3-integer limit ignoring the +? term.
{| class="wikitable sortable"
!|edo
!|chord
!|delta signature
!|least-squares error
|-
|6
|0,1,3,5
| +1+?+3
|0.00006
|-
|6
|0,2,3,4
| +3+?+2
|0.00006
|-
|7
|0,1,4,5
| +2+?+3
|0.00071
|-
|10
|0,1,6,7
| +2+?+3
|0.00055
|-
|10
|0,3,7,8
| +2+?+1
|0.00068
|-
|11
|0,1,6,8
| +1+?+3
|0.00027
|-
|11
|0,2,4,7
| +1+?+2
|0.00036
|-
|11
|0,2,5,6
| +3+?+2
|0.00026
|-
|11
|0,3,6,10
| +1+?+2
|0.00090
|-
|11
|0,3,7,9
| +1+?+1
|0.00040
|-
|11
|0,4,5,8
| +1+?+1
|0.00087
|-
|11
|0,4,6,7
| +3+?+1
|0.00043
|-
|12
|0,1,7,8
| +2+?+3
|0.00005
|-
|12
|0,2,6,10
| +1+?+3
|0.00006
|-
|12
|0,2,7,9
| +2+?+3
|0.00010
|-
|12
|0,3,7,10
| +2+?+3
|0.00016
|-
|12
|0,3,8,9
| +2+?+1
|0.00014
|-
|12
|0,4,6,8
| +3+?+2
|0.00006
|-
|12
|0,4,7,11
| +2+?+3
|0.00021
|-
|12
|0,6,9,11
| +2+?+1
|0.00077
|-
|13
|0,1,7,9
| +1+?+3
|0.00026
|-
|13
|0,1,8,9
| +2+?+3
|0.00085
|-
|13
|0,2,5,8
| +1+?+2
|0.00057
|-
|13
|0,2,6,7
| +3+?+2
|0.00025
|-
|13
|0,3,6,12
| +1+?+3
|0.00037
|-
|13
|0,3,7,11
| +1+?+2
|0.00067
|-
|13
|0,3,8,10
| +1+?+1
|0.00062
|-
|13
|0,4,6,9
| +1+?+1
|0.00065
|-
|13
|0,4,7,8
| +3+?+1
|0.00021
|-
|13
|0,6,7,10
| +3+?+2
|0.00038
|-
|14
|0,1,8,9
| +2+?+3
|0.00034
|-
|14
|0,1,8,10
| +1+?+3
|0.00073
|-
|14
|0,2,6,7
| +3+?+2
|0.00069
|-
|14
|0,2,7,11
| +1+?+3
|0.00076
|-
|14
|0,2,8,10
| +2+?+3
|0.00071
|-
|14
|0,3,9,10
| +2+?+1
|0.00054
|-
|14
|0,4,7,8
| +3+?+1
|0.00084
|-
|14
|0,4,7,9
| +3+?+2
|0.00076
|-
|14
|0,5,6,8
| +2+?+1
|0.00023
|-
|14
|0,8,9,11
| +3+?+1
|0.00036
|-
|15
|0,1,8,10
| +1+?+3
|0.00053
|-
|15
|0,1,9,10
| +2+?+3
|0.00036
|-
|15
|0,2,7,8
| +3+?+2
|0.00052
|-
|15
|0,2,9,11
| +2+?+3
|0.00074
|-
|15
|0,3,10,11
| +2+?+1
|0.00048
|-
|15
|0,4,7,9
| +3+?+2
|0.00099
|-
|15
|0,4,8,9
| +3+?+1
|0.00053
|-
|15
|0,5,13,14
| +3+?+1
|0.00028
|-
|15
|0,6,11,13
| +2+?+1
|0.00081
|-
|16
|0,1,9,10
| +2+?+3
|0.00050
|-
|16
|0,1,9,11
| +1+?+3
|0.00025
|-
|16
|0,1,10,11
| +2+?+3
|0.00091
|-
|16
|0,2,6,9
| +1+?+2
|0.00042
|-
|16
|0,2,7,8
| +3+?+2
|0.00024
|-
|16
|0,3,9,13
| +1+?+2
|0.00075
|-
|16
|0,3,10,11
| +2+?+1
|0.00074
|-
|16
|0,3,10,12
| +1+?+1
|0.00046
|-
|16
|0,4,7,10
| +1+?+1
|0.00072
|-
|16
|0,4,8,9
| +3+?+1
|0.00031
|-
|16
|0,5,14,15
| +3+?+1
|0.00040
|-
|16
|0,9,13,15
| +3+?+1
|0.00001
|-
|17
|0,1,9,11
| +1+?+3
|0.00067
|-
|17
|0,1,10,11
| +2+?+3
|0.00007
|-
|17
|0,1,10,12
| +1+?+3
|0.00087
|-
|17
|0,2,3,8
| +1+?+3
|0.00020
|-
|17
|0,2,7,8
| +3+?+2
|0.00082
|-
|17
|0,2,8,9
| +3+?+2
|0.00065
|-
|17
|0,2,9,13
| +1+?+3
|0.00024
|-
|17
|0,2,10,12
| +2+?+3
|0.00014
|-
|17
|0,3,4,11
| +1+?+3
|0.00046
|-
|17
|0,3,10,13
| +2+?+3
|0.00022
|-
|17
|0,3,11,12
| +2+?+1
|0.00007
|-
|17
|0,4,6,12
| +1+?+2
|0.00013
|-
|17
|0,4,8,9
| +3+?+1
|0.00095
|-
|17
|0,4,8,10
| +3+?+2
|0.00023
|-
|17
|0,4,8,16
| +1+?+3
|0.00090
|-
|17
|0,4,9,10
| +3+?+1
|0.00070
|-
|17
|0,4,10,14
| +2+?+3
|0.00029
|-
|17
|0,4,11,16
| +1+?+2
|0.00007
|-
|17
|0,5,6,10
| +1+?+1
|0.00006
|-
|17
|0,5,7,9
| +2+?+1
|0.00003
|-
|17
|0,5,10,15
| +2+?+3
|0.00037
|-
|17
|0,5,14,16
| +3+?+2
|0.00025
|-
|17
|0,5,15,16
| +3+?+1
|0.00092
|-
|17
|0,6,10,16
| +2+?+3
|0.00046
|-
|17
|0,6,11,15
| +1+?+1
|0.00014
|-
|17
|0,6,12,14
| +2+?+1
|0.00000
|-
|17
|0,7,13,16
| +3+?+2
|0.00055
|-
|17
|0,8,9,13
| +3+?+2
|0.00092
|-
|17
|0,8,10,12
| +3+?+1
|0.00057
|-
|17
|0,9,13,16
| +2+?+1
|0.00040
|-
|18
|0,1,10,11
| +2+?+3
|0.00058
|-
|18
|0,1,10,12
| +1+?+3
|0.00003
|-
|18
|0,1,11,12
| +2+?+3
|0.00052
|-
|18
|0,2,3,8
| +1+?+3
|0.00056
|-
|18
|0,2,7,10
| +1+?+2
|0.00009
|-
|18
|0,2,8,9
| +3+?+2
|0.00003
|-
|18
|0,3,9,15
| +1+?+3
|0.00006
|-
|18
|0,3,10,14
| +1+?+2
|0.00007
|-
|18
|0,3,11,12
| +2+?+1
|0.00084
|-
|18
|0,3,11,13
| +1+?+1
|0.00010
|-
|18
|0,3,12,13
| +2+?+1
|0.00073
|-
|18
|0,4,5,14
| +1+?+3
|0.00078
|-
|18
|0,4,8,11
| +1+?+1
|0.00007
|-
|18
|0,4,9,10
| +3+?+1
|0.00001
|-
|18
|0,5,7,9
| +2+?+1
|0.00089
|-
|18
|0,5,15,16
| +3+?+1
|0.00057
|-
|18
|0,5,15,17
| +3+?+2
|0.00070
|-
|18
|0,6,9,12
| +3+?+2
|0.00006
|-
|18
|0,8,10,13
| +2+?+1
|0.00027
|-
|18
|0,9,13,17
| +3+?+2
|0.00091
|-
|18
|0,9,14,16
| +3+?+1
|0.00056
|-
|18
|0,11,12,16
| +2+?+1
|0.00042
|-
|19
|0,1,10,12
| +1+?+3
|0.00074
|-
|19
|0,1,11,12
| +2+?+3
|0.00011
|-
|19
|0,1,11,13
| +1+?+3
|0.00048
|-
|19
|0,1,12,13
| +2+?+3
|0.00089
|-
|19
|0,2,7,10
| +1+?+2
|0.00085
|-
|19
|0,2,8,9
| +3+?+2
|0.00046
|-
|19
|0,2,9,10
| +3+?+2
|0.00073
|-
|19
|0,2,10,14
| +1+?+3
|0.00024
|-
|19
|0,2,11,13
| +2+?+3
|0.00023
|-
|19
|0,3,4,9
| +1+?+2
|0.00009
|-
|19
|0,3,5,12
| +1+?+3
|0.00066
|-
|19
|0,3,11,14
| +2+?+3
|0.00035
|-
|19
|0,3,12,13
| +2+?+1
|0.00018
|-
|19
|0,3,12,14
| +1+?+1
|0.00093
|-
|19
|0,4,7,13
| +1+?+2
|0.00068
|-
|19
|0,4,9,10
| +3+?+1
|0.00053
|-
|19
|0,4,9,11
| +3+?+2
|0.00024
|-
|19
|0,4,9,17
| +1+?+3
|0.00021
|-
|19
|0,4,10,11
| +3+?+1
|0.00079
|-
|19
|0,4,11,15
| +2+?+3
|0.00048
|-
|19
|0,5,8,10
| +2+?+1
|0.00086
|-
|19
|0,5,11,16
| +2+?+3
|0.00061
|-
|19
|0,5,15,18
| +1+?+1
|0.00011
|-
|19
|0,5,16,17
| +3+?+1
|0.00006
|-
|19
|0,6,10,18
| +1+?+2
|0.00052
|-
|19
|0,6,11,17
| +2+?+3
|0.00074
|-
|19
|0,6,12,16
| +1+?+1
|0.00074
|-
|19
|0,6,13,15
| +2+?+1
|0.00048
|-
|19
|0,7,11,18
| +2+?+3
|0.00088
|-
|19
|0,7,14,17
| +3+?+2
|0.00078
|-
|19
|0,8,9,15
| +1+?+1
|0.00051
|-
|19
|0,8,10,14
| +3+?+2
|0.00022
|-
|19
|0,8,11,13
| +3+?+1
|0.00007
|-
|19
|0,9,15,17
| +3+?+1
|0.00088
|-
|20
|0,1,11,12
| +2+?+3
|0.00061
|-
|20
|0,1,11,13
| +1+?+3
|0.00021
|-
|20
|0,1,12,13
| +2+?+3
|0.00027
|-
|20
|0,1,12,14
| +1+?+3
|0.00090
|-
|20
|0,2,4,9
| +1+?+3
|0.00061
|-
|20
|0,2,8,9
| +3+?+2
|0.00084
|-
|20
|0,2,8,11
| +1+?+2
|0.00042
|-
|20
|0,2,9,10
| +3+?+2
|0.00021
|-
|20
|0,2,11,15
| +1+?+3
|0.00072
|-
|20
|0,2,12,14
| +2+?+3
|0.00055
|-
|20
|0,3,4,9
| +1+?+2
|0.00073
|-
|20
|0,3,5,12
| +1+?+3
|0.00066
|-
|20
|0,3,10,16
| +1+?+3
|0.00055
|-
|20
|0,3,11,15
| +1+?+2
|0.00058
|-
|20
|0,3,12,13
| +2+?+1
|0.00089
|-
|20
|0,3,12,14
| +1+?+1
|0.00045
|-
|20
|0,3,12,15
| +2+?+3
|0.00084
|-
|20
|0,3,13,14
| +2+?+1
|0.00037
|-
|20
|0,4,5,10
| +2+?+3
|0.00095
|-
|20
|0,4,9,10
| +3+?+1
|0.00096
|-
|20
|0,4,9,11
| +3+?+2
|0.00070
|-
|20
|0,4,9,12
| +1+?+1
|0.00056
|-
|20
|0,4,10,11
| +3+?+1
|0.00021
|-
|20
|0,4,13,18
| +1+?+2
|0.00020
|-
|20
|0,5,6,12
| +2+?+3
|0.00037
|-
|20
|0,5,7,11
| +1+?+1
|0.00018
|-
|20
|0,5,8,10
| +2+?+1
|0.00007
|-
|20
|0,5,9,19
| +1+?+3
|0.00054
|-
|20
|0,5,16,18
| +3+?+2
|0.00075
|-
|20
|0,5,16,19
| +1+?+1
|0.00090
|-
|20
|0,5,17,18
| +3+?+1
|0.00034
|-
|20
|0,6,10,13
| +3+?+2
|0.00055
|-
|20
|0,6,14,16
| +2+?+1
|0.00068
|-
|20
|0,7,15,18
| +3+?+2
|0.00079
|-
|20
|0,8,11,13
| +3+?+1
|0.00098
|-
|20
|0,8,11,14
| +2+?+1
|0.00044
|-
|20
|0,9,15,17
| +3+?+1
|0.00090
|-
|20
|0,9,15,18
| +2+?+1
|0.00084
|-
|20
|0,10,11,16
| +3+?+2
|0.00056
|-
|20
|0,11,13,17
| +2+?+1
|0.00086
|-
|20
|0,12,13,16
| +3+?+1
|0.00002
|-
|20
|0,13,16,19
| +3+?+1
|0.00072
|-
|21
|0,1,11,13
| +1+?+3
|0.00077
|-
|21
|0,1,12,13
| +2+?+3
|0.00023
|-
|21
|0,1,12,14
| +1+?+3
|0.00022
|-
|21
|0,1,13,14
| +2+?+3
|0.00058
|-
|21
|0,2,4,9
| +1+?+3
|0.00001
|-
|21
|0,2,8,11
| +1+?+2
|0.00038
|-
|21
|0,2,9,10
| +3+?+2
|0.00021
|-
|21
|0,2,10,11
| +3+?+2
|0.00076
|-
|21
|0,2,11,15
| +1+?+3
|0.00054
|-
|21
|0,2,12,14
| +2+?+3
|0.00046
|-
|21
|0,3,11,17
| +1+?+3
|0.00079
|-
|21
|0,3,12,15
| +2+?+3
|0.00071
|-
|21
|0,3,12,16
| +1+?+2
|0.00063
|-
|21
|0,3,13,14
| +2+?+1
|0.00034
|-
|21
|0,3,13,15
| +1+?+1
|0.00042
|-
|21
|0,3,14,15
| +2+?+1
|0.00082
|-
|21
|0,4,5,10
| +2+?+3
|0.00004
|-
|21
|0,4,6,15
| +1+?+3
|0.00053
|-
|21
|0,4,9,12
| +1+?+1
|0.00060
|-
|21
|0,4,10,11
| +3+?+1
|0.00025
|-
|21
|0,4,10,12
| +3+?+2
|0.00053
|-
|21
|0,4,10,18
| +1+?+3
|0.00092
|-
|21
|0,4,11,12
| +3+?+1
|0.00083
|-
|21
|0,4,12,16
| +2+?+3
|0.00096
|-
|21
|0,5,7,11
| +1+?+1
|0.00093
|-
|21
|0,5,8,10
| +2+?+1
|0.00057
|-
|21
|0,5,17,18
| +3+?+1
|0.00069
|-
|21
|0,5,17,19
| +3+?+2
|0.00001
|-
|21
|0,5,18,19
| +3+?+1
|0.00067
|-
|21
|0,6,7,14
| +2+?+3
|0.00050
|-
|21
|0,6,7,16
| +1+?+2
|0.00091
|-
|21
|0,6,10,13
| +3+?+2
|0.00078
|-
|21
|0,6,14,16
| +2+?+1
|0.00079
|-
|21
|0,8,11,14
| +2+?+1
|0.00096
|-
|21
|0,8,11,15
| +3+?+2
|0.00093
|-
|21
|0,8,12,14
| +3+?+1
|0.00046
|-
|21
|0,9,15,19
| +3+?+2
|0.00062
|-
|21
|0,9,16,18
| +3+?+1
|0.00029
|-
|21
|0,14,15,20
| +2+?+1
|0.00046
|-
|22
|0,1,12,13
| +2+?+3
|0.00063
|-
|22
|0,1,12,14
| +1+?+3
|0.00033
|-
|22
|0,1,13,14
| +2+?+3
|0.00010
|-
|22
|0,1,13,15
| +1+?+3
|0.00058
|-
|22
|0,1,14,15
| +2+?+3
|0.00084
|-
|22
|0,2,4,9
| +1+?+3
|0.00048
|-
|22
|0,2,9,10
| +3+?+2
|0.00055
|-
|22
|0,2,9,12
| +1+?+2
|0.00063
|-
|22
|0,2,10,11
| +3+?+2
|0.00032
|-
|22
|0,2,12,16
| +1+?+3
|0.00027
|-
|22
|0,2,13,15
| +2+?+3
|0.00020
|-
|22
|0,3,5,10
| +1+?+2
|0.00060
|-
|22
|0,3,6,13
| +1+?+3
|0.00021
|-
|22
|0,3,11,17
| +1+?+3
|0.00094
|-
|22
|0,3,12,16
| +1+?+2
|0.00091
|-
|22
|0,3,13,14
| +2+?+1
|0.00090
|-
|22
|0,3,13,15
| +1+?+1
|0.00067
|-
|22
|0,3,13,16
| +2+?+3
|0.00030
|-
|22
|0,3,14,15
| +2+?+1
|0.00013
|-
|22
|0,4,5,10
| +2+?+3
|0.00084
|-
|22
|0,4,8,14
| +1+?+2
|0.00036
|-
|22
|0,4,10,11
| +3+?+1
|0.00063
|-
|22
|0,4,10,12
| +3+?+2
|0.00026
|-
|22
|0,4,10,13
| +1+?+1
|0.00088
|-
|22
|0,4,11,12
| +3+?+1
|0.00034
|-
|22
|0,4,11,19
| +1+?+3
|0.00074
|-
|22
|0,4,13,17
| +2+?+3
|0.00040
|-
|22
|0,5,9,11
| +2+?+1
|0.00070
|-
|22
|0,5,13,18
| +2+?+3
|0.00051
|-
|22
|0,5,17,20
| +1+?+1
|0.00072
|-
|22
|0,5,18,19
| +3+?+1
|0.00030
|-
|22
|0,5,18,20
| +3+?+2
|0.00060
|-
|22
|0,5,19,20
| +3+?+1
|0.00094
|-
|22
|0,6,11,14
| +3+?+2
|0.00094
|-
|22
|0,6,12,20
| +1+?+2
|0.00090
|-
|22
|0,6,13,19
| +2+?+3
|0.00063
|-
|22
|0,6,14,18
| +1+?+1
|0.00040
|-
|22
|0,6,15,17
| +2+?+1
|0.00019
|-
|22
|0,7,8,10
| +3+?+1
|0.00099
|-
|22
|0,7,8,16
| +2+?+3
|0.00063
|-
|22
|0,7,9,19
| +1+?+2
|0.00071
|-
|22
|0,7,13,20
| +2+?+3
|0.00074
|-
|22
|0,7,16,19
| +3+?+2
|0.00025
|-
|22
|0,8,10,16
| +1+?+1
|0.00087
|-
|22
|0,8,11,15
| +3+?+2
|0.00074
|-
|22
|0,8,12,14
| +3+?+1
|0.00043
|-
|22
|0,8,12,15
| +2+?+1
|0.00090
|-
|22
|0,8,13,21
| +2+?+3
|0.00086
|-
|22
|0,9,16,19
| +2+?+1
|0.00013
|-
|22
|0,10,13,20
| +1+?+1
|0.00076
|-
|22
|0,12,14,17
| +3+?+1
|0.00064
|-
|22
|0,12,17,21
| +2+?+1
|0.00018
|-
|22
|0,13,17,20
| +3+?+1
|0.00044
|-
|23
|0,1,12,13
| +2+?+3
|0.00095
|-
|23
|0,1,12,14
| +1+?+3
|0.00078
|-
|23
|0,1,13,14
| +2+?+3
|0.00030
|-
|23
|0,1,13,15
| +1+?+3
|0.00004
|-
|23
|0,1,14,15
| +2+?+3
|0.00037
|-
|23
|0,1,14,16
| +1+?+3
|0.00089
|-
|23
|0,2,4,9
| +1+?+3
|0.00088
|-
|23
|0,2,5,10
| +1+?+3
|0.00081
|-
|23
|0,2,9,10
| +3+?+2
|0.00082
|-
|23
|0,2,9,12
| +1+?+2
|0.00006
|-
|23
|0,2,10,11
| +3+?+2
|0.00004
|-
|23
|0,2,11,12
| +3+?+2
|0.00077
|-
|23
|0,2,12,16
| +1+?+3
|0.00074
|-
|23
|0,2,13,15
| +2+?+3
|0.00061
|-
|23
|0,2,13,17
| +1+?+3
|0.00096
|-
|23
|0,2,14,16
| +2+?+3
|0.00075
|-
|23
|0,3,5,10
| +1+?+2
|0.00007
|-
|23
|0,3,6,13
| +1+?+3
|0.00074
|-
|23
|0,3,12,18
| +1+?+3
|0.00021
|-
|23
|0,3,13,16
| +2+?+3
|0.00094
|-
|23
|0,3,13,17
| +1+?+2
|0.00013
|-
|23
|0,3,14,15
| +2+?+1
|0.00044
|-
|23
|0,3,14,16
| +1+?+1
|0.00007
|-
|23
|0,3,15,16
| +2+?+1
|0.00051
|-
|23
|0,4,7,16
| +1+?+3
|0.00012
|-
|23
|0,4,10,11
| +3+?+1
|0.00093
|-
|23
|0,4,10,12
| +3+?+2
|0.00092
|-
|23
|0,4,10,13
| +1+?+1
|0.00012
|-
|23
|0,4,11,12
| +3+?+1
|0.00006
|-
|23
|0,4,11,13
| +3+?+2
|0.00073
|-
|23
|0,4,12,13
| +3+?+1
|0.00084
|-
|23
|0,4,15,20
| +1+?+2
|0.00027
|-
|23
|0,5,6,14
| +1+?+2
|0.00058
|-
|23
|0,5,7,13
| +2+?+3
|0.00039
|-
|23
|0,5,7,18
| +1+?+3
|0.00076
|-
|23
|0,5,8,12
| +1+?+1
|0.00024
|-
|23
|0,5,9,11
| +2+?+1
|0.00011
|-
|23
|0,5,11,18
| +1+?+2
|0.00078
|-
|23
|0,5,11,21
| +1+?+3
|0.00062
|-
|23
|0,5,18,20
| +3+?+2
|0.00099
|-
|23
|0,5,18,21
| +1+?+1
|0.00008
|-
|23
|0,5,19,20
| +3+?+1
|0.00002
|-
|23
|0,6,7,20
| +1+?+3
|0.00071
|-
|23
|0,6,8,15
| +2+?+3
|0.00077
|-
|23
|0,6,8,17
| +1+?+2
|0.00005
|-
|23
|0,6,11,14
| +3+?+2
|0.00020
|-
|23
|0,6,15,17
| +2+?+1
|0.00098
|-
|23
|0,7,8,10
| +3+?+1
|0.00054
|-
|23
|0,7,12,17
| +1+?+1
|0.00079
|-
|23
|0,7,17,20
| +3+?+2
|0.00088
|-
|23
|0,8,9,18
| +2+?+3
|0.00015
|-
|23
|0,8,11,22
| +1+?+2
|0.00093
|-
|23
|0,8,12,15
| +2+?+1
|0.00031
|-
|23
|0,8,13,15
| +3+?+1
|0.00072
|-
|23
|0,8,17,22
| +1+?+1
|0.00068
|-
|23
|0,9,15,21
| +1+?+1
|0.00006
|-
|23
|0,9,16,20
| +3+?+2
|0.00014
|-
|23
|0,9,17,19
| +3+?+1
|0.00011
|-
|23
|0,10,12,17
| +3+?+2
|0.00063
|-
|23
|0,11,12,20
| +1+?+1
|0.00094
|-
|23
|0,11,14,18
| +2+?+1
|0.00078
|-
|23
|0,11,16,21
| +3+?+2
|0.00087
|-
|23
|0,12,14,17
| +3+?+1
|0.00065
|-
|23
|0,13,16,22
| +3+?+2
|0.00081
|-
|23
|0,14,16,21
| +2+?+1
|0.00064
|}
[[Category:Tables]][[Category:Tetrads]]
[[Category:Tables]][[Category:Tetrads]]

Latest revision as of 23:40, 17 December 2024

Shown below are approximate partially delta-rational tetrads with signature +a+?+b spanning an interval < octave, in edos < 24, with least-squares error < 0.001. All delta signatures are in the 3-integer limit ignoring the +? term.

edo chord delta signature least-squares error
6 0,1,3,5 +1+?+3 0.00006
6 0,2,3,4 +3+?+2 0.00006
7 0,1,4,5 +2+?+3 0.00071
10 0,1,6,7 +2+?+3 0.00055
10 0,3,7,8 +2+?+1 0.00068
11 0,1,6,8 +1+?+3 0.00027
11 0,2,4,7 +1+?+2 0.00036
11 0,2,5,6 +3+?+2 0.00026
11 0,3,6,10 +1+?+2 0.00090
11 0,3,7,9 +1+?+1 0.00040
11 0,4,5,8 +1+?+1 0.00087
11 0,4,6,7 +3+?+1 0.00043
12 0,1,7,8 +2+?+3 0.00005
12 0,2,6,10 +1+?+3 0.00006
12 0,2,7,9 +2+?+3 0.00010
12 0,3,7,10 +2+?+3 0.00016
12 0,3,8,9 +2+?+1 0.00014
12 0,4,6,8 +3+?+2 0.00006
12 0,4,7,11 +2+?+3 0.00021
12 0,6,9,11 +2+?+1 0.00077
13 0,1,7,9 +1+?+3 0.00026
13 0,1,8,9 +2+?+3 0.00085
13 0,2,5,8 +1+?+2 0.00057
13 0,2,6,7 +3+?+2 0.00025
13 0,3,6,12 +1+?+3 0.00037
13 0,3,7,11 +1+?+2 0.00067
13 0,3,8,10 +1+?+1 0.00062
13 0,4,6,9 +1+?+1 0.00065
13 0,4,7,8 +3+?+1 0.00021
13 0,6,7,10 +3+?+2 0.00038
14 0,1,8,9 +2+?+3 0.00034
14 0,1,8,10 +1+?+3 0.00073
14 0,2,6,7 +3+?+2 0.00069
14 0,2,7,11 +1+?+3 0.00076
14 0,2,8,10 +2+?+3 0.00071
14 0,3,9,10 +2+?+1 0.00054
14 0,4,7,8 +3+?+1 0.00084
14 0,4,7,9 +3+?+2 0.00076
14 0,5,6,8 +2+?+1 0.00023
14 0,8,9,11 +3+?+1 0.00036
15 0,1,8,10 +1+?+3 0.00053
15 0,1,9,10 +2+?+3 0.00036
15 0,2,7,8 +3+?+2 0.00052
15 0,2,9,11 +2+?+3 0.00074
15 0,3,10,11 +2+?+1 0.00048
15 0,4,7,9 +3+?+2 0.00099
15 0,4,8,9 +3+?+1 0.00053
15 0,5,13,14 +3+?+1 0.00028
15 0,6,11,13 +2+?+1 0.00081
16 0,1,9,10 +2+?+3 0.00050
16 0,1,9,11 +1+?+3 0.00025
16 0,1,10,11 +2+?+3 0.00091
16 0,2,6,9 +1+?+2 0.00042
16 0,2,7,8 +3+?+2 0.00024
16 0,3,9,13 +1+?+2 0.00075
16 0,3,10,11 +2+?+1 0.00074
16 0,3,10,12 +1+?+1 0.00046
16 0,4,7,10 +1+?+1 0.00072
16 0,4,8,9 +3+?+1 0.00031
16 0,5,14,15 +3+?+1 0.00040
16 0,9,13,15 +3+?+1 0.00001
17 0,1,9,11 +1+?+3 0.00067
17 0,1,10,11 +2+?+3 0.00007
17 0,1,10,12 +1+?+3 0.00087
17 0,2,3,8 +1+?+3 0.00020
17 0,2,7,8 +3+?+2 0.00082
17 0,2,8,9 +3+?+2 0.00065
17 0,2,9,13 +1+?+3 0.00024
17 0,2,10,12 +2+?+3 0.00014
17 0,3,4,11 +1+?+3 0.00046
17 0,3,10,13 +2+?+3 0.00022
17 0,3,11,12 +2+?+1 0.00007
17 0,4,6,12 +1+?+2 0.00013
17 0,4,8,9 +3+?+1 0.00095
17 0,4,8,10 +3+?+2 0.00023
17 0,4,8,16 +1+?+3 0.00090
17 0,4,9,10 +3+?+1 0.00070
17 0,4,10,14 +2+?+3 0.00029
17 0,4,11,16 +1+?+2 0.00007
17 0,5,6,10 +1+?+1 0.00006
17 0,5,7,9 +2+?+1 0.00003
17 0,5,10,15 +2+?+3 0.00037
17 0,5,14,16 +3+?+2 0.00025
17 0,5,15,16 +3+?+1 0.00092
17 0,6,10,16 +2+?+3 0.00046
17 0,6,11,15 +1+?+1 0.00014
17 0,6,12,14 +2+?+1 0.00000
17 0,7,13,16 +3+?+2 0.00055
17 0,8,9,13 +3+?+2 0.00092
17 0,8,10,12 +3+?+1 0.00057
17 0,9,13,16 +2+?+1 0.00040
18 0,1,10,11 +2+?+3 0.00058
18 0,1,10,12 +1+?+3 0.00003
18 0,1,11,12 +2+?+3 0.00052
18 0,2,3,8 +1+?+3 0.00056
18 0,2,7,10 +1+?+2 0.00009
18 0,2,8,9 +3+?+2 0.00003
18 0,3,9,15 +1+?+3 0.00006
18 0,3,10,14 +1+?+2 0.00007
18 0,3,11,12 +2+?+1 0.00084
18 0,3,11,13 +1+?+1 0.00010
18 0,3,12,13 +2+?+1 0.00073
18 0,4,5,14 +1+?+3 0.00078
18 0,4,8,11 +1+?+1 0.00007
18 0,4,9,10 +3+?+1 0.00001
18 0,5,7,9 +2+?+1 0.00089
18 0,5,15,16 +3+?+1 0.00057
18 0,5,15,17 +3+?+2 0.00070
18 0,6,9,12 +3+?+2 0.00006
18 0,8,10,13 +2+?+1 0.00027
18 0,9,13,17 +3+?+2 0.00091
18 0,9,14,16 +3+?+1 0.00056
18 0,11,12,16 +2+?+1 0.00042
19 0,1,10,12 +1+?+3 0.00074
19 0,1,11,12 +2+?+3 0.00011
19 0,1,11,13 +1+?+3 0.00048
19 0,1,12,13 +2+?+3 0.00089
19 0,2,7,10 +1+?+2 0.00085
19 0,2,8,9 +3+?+2 0.00046
19 0,2,9,10 +3+?+2 0.00073
19 0,2,10,14 +1+?+3 0.00024
19 0,2,11,13 +2+?+3 0.00023
19 0,3,4,9 +1+?+2 0.00009
19 0,3,5,12 +1+?+3 0.00066
19 0,3,11,14 +2+?+3 0.00035
19 0,3,12,13 +2+?+1 0.00018
19 0,3,12,14 +1+?+1 0.00093
19 0,4,7,13 +1+?+2 0.00068
19 0,4,9,10 +3+?+1 0.00053
19 0,4,9,11 +3+?+2 0.00024
19 0,4,9,17 +1+?+3 0.00021
19 0,4,10,11 +3+?+1 0.00079
19 0,4,11,15 +2+?+3 0.00048
19 0,5,8,10 +2+?+1 0.00086
19 0,5,11,16 +2+?+3 0.00061
19 0,5,15,18 +1+?+1 0.00011
19 0,5,16,17 +3+?+1 0.00006
19 0,6,10,18 +1+?+2 0.00052
19 0,6,11,17 +2+?+3 0.00074
19 0,6,12,16 +1+?+1 0.00074
19 0,6,13,15 +2+?+1 0.00048
19 0,7,11,18 +2+?+3 0.00088
19 0,7,14,17 +3+?+2 0.00078
19 0,8,9,15 +1+?+1 0.00051
19 0,8,10,14 +3+?+2 0.00022
19 0,8,11,13 +3+?+1 0.00007
19 0,9,15,17 +3+?+1 0.00088
20 0,1,11,12 +2+?+3 0.00061
20 0,1,11,13 +1+?+3 0.00021
20 0,1,12,13 +2+?+3 0.00027
20 0,1,12,14 +1+?+3 0.00090
20 0,2,4,9 +1+?+3 0.00061
20 0,2,8,9 +3+?+2 0.00084
20 0,2,8,11 +1+?+2 0.00042
20 0,2,9,10 +3+?+2 0.00021
20 0,2,11,15 +1+?+3 0.00072
20 0,2,12,14 +2+?+3 0.00055
20 0,3,4,9 +1+?+2 0.00073
20 0,3,5,12 +1+?+3 0.00066
20 0,3,10,16 +1+?+3 0.00055
20 0,3,11,15 +1+?+2 0.00058
20 0,3,12,13 +2+?+1 0.00089
20 0,3,12,14 +1+?+1 0.00045
20 0,3,12,15 +2+?+3 0.00084
20 0,3,13,14 +2+?+1 0.00037
20 0,4,5,10 +2+?+3 0.00095
20 0,4,9,10 +3+?+1 0.00096
20 0,4,9,11 +3+?+2 0.00070
20 0,4,9,12 +1+?+1 0.00056
20 0,4,10,11 +3+?+1 0.00021
20 0,4,13,18 +1+?+2 0.00020
20 0,5,6,12 +2+?+3 0.00037
20 0,5,7,11 +1+?+1 0.00018
20 0,5,8,10 +2+?+1 0.00007
20 0,5,9,19 +1+?+3 0.00054
20 0,5,16,18 +3+?+2 0.00075
20 0,5,16,19 +1+?+1 0.00090
20 0,5,17,18 +3+?+1 0.00034
20 0,6,10,13 +3+?+2 0.00055
20 0,6,14,16 +2+?+1 0.00068
20 0,7,15,18 +3+?+2 0.00079
20 0,8,11,13 +3+?+1 0.00098
20 0,8,11,14 +2+?+1 0.00044
20 0,9,15,17 +3+?+1 0.00090
20 0,9,15,18 +2+?+1 0.00084
20 0,10,11,16 +3+?+2 0.00056
20 0,11,13,17 +2+?+1 0.00086
20 0,12,13,16 +3+?+1 0.00002
20 0,13,16,19 +3+?+1 0.00072
21 0,1,11,13 +1+?+3 0.00077
21 0,1,12,13 +2+?+3 0.00023
21 0,1,12,14 +1+?+3 0.00022
21 0,1,13,14 +2+?+3 0.00058
21 0,2,4,9 +1+?+3 0.00001
21 0,2,8,11 +1+?+2 0.00038
21 0,2,9,10 +3+?+2 0.00021
21 0,2,10,11 +3+?+2 0.00076
21 0,2,11,15 +1+?+3 0.00054
21 0,2,12,14 +2+?+3 0.00046
21 0,3,11,17 +1+?+3 0.00079
21 0,3,12,15 +2+?+3 0.00071
21 0,3,12,16 +1+?+2 0.00063
21 0,3,13,14 +2+?+1 0.00034
21 0,3,13,15 +1+?+1 0.00042
21 0,3,14,15 +2+?+1 0.00082
21 0,4,5,10 +2+?+3 0.00004
21 0,4,6,15 +1+?+3 0.00053
21 0,4,9,12 +1+?+1 0.00060
21 0,4,10,11 +3+?+1 0.00025
21 0,4,10,12 +3+?+2 0.00053
21 0,4,10,18 +1+?+3 0.00092
21 0,4,11,12 +3+?+1 0.00083
21 0,4,12,16 +2+?+3 0.00096
21 0,5,7,11 +1+?+1 0.00093
21 0,5,8,10 +2+?+1 0.00057
21 0,5,17,18 +3+?+1 0.00069
21 0,5,17,19 +3+?+2 0.00001
21 0,5,18,19 +3+?+1 0.00067
21 0,6,7,14 +2+?+3 0.00050
21 0,6,7,16 +1+?+2 0.00091
21 0,6,10,13 +3+?+2 0.00078
21 0,6,14,16 +2+?+1 0.00079
21 0,8,11,14 +2+?+1 0.00096
21 0,8,11,15 +3+?+2 0.00093
21 0,8,12,14 +3+?+1 0.00046
21 0,9,15,19 +3+?+2 0.00062
21 0,9,16,18 +3+?+1 0.00029
21 0,14,15,20 +2+?+1 0.00046
22 0,1,12,13 +2+?+3 0.00063
22 0,1,12,14 +1+?+3 0.00033
22 0,1,13,14 +2+?+3 0.00010
22 0,1,13,15 +1+?+3 0.00058
22 0,1,14,15 +2+?+3 0.00084
22 0,2,4,9 +1+?+3 0.00048
22 0,2,9,10 +3+?+2 0.00055
22 0,2,9,12 +1+?+2 0.00063
22 0,2,10,11 +3+?+2 0.00032
22 0,2,12,16 +1+?+3 0.00027
22 0,2,13,15 +2+?+3 0.00020
22 0,3,5,10 +1+?+2 0.00060
22 0,3,6,13 +1+?+3 0.00021
22 0,3,11,17 +1+?+3 0.00094
22 0,3,12,16 +1+?+2 0.00091
22 0,3,13,14 +2+?+1 0.00090
22 0,3,13,15 +1+?+1 0.00067
22 0,3,13,16 +2+?+3 0.00030
22 0,3,14,15 +2+?+1 0.00013
22 0,4,5,10 +2+?+3 0.00084
22 0,4,8,14 +1+?+2 0.00036
22 0,4,10,11 +3+?+1 0.00063
22 0,4,10,12 +3+?+2 0.00026
22 0,4,10,13 +1+?+1 0.00088
22 0,4,11,12 +3+?+1 0.00034
22 0,4,11,19 +1+?+3 0.00074
22 0,4,13,17 +2+?+3 0.00040
22 0,5,9,11 +2+?+1 0.00070
22 0,5,13,18 +2+?+3 0.00051
22 0,5,17,20 +1+?+1 0.00072
22 0,5,18,19 +3+?+1 0.00030
22 0,5,18,20 +3+?+2 0.00060
22 0,5,19,20 +3+?+1 0.00094
22 0,6,11,14 +3+?+2 0.00094
22 0,6,12,20 +1+?+2 0.00090
22 0,6,13,19 +2+?+3 0.00063
22 0,6,14,18 +1+?+1 0.00040
22 0,6,15,17 +2+?+1 0.00019
22 0,7,8,10 +3+?+1 0.00099
22 0,7,8,16 +2+?+3 0.00063
22 0,7,9,19 +1+?+2 0.00071
22 0,7,13,20 +2+?+3 0.00074
22 0,7,16,19 +3+?+2 0.00025
22 0,8,10,16 +1+?+1 0.00087
22 0,8,11,15 +3+?+2 0.00074
22 0,8,12,14 +3+?+1 0.00043
22 0,8,12,15 +2+?+1 0.00090
22 0,8,13,21 +2+?+3 0.00086
22 0,9,16,19 +2+?+1 0.00013
22 0,10,13,20 +1+?+1 0.00076
22 0,12,14,17 +3+?+1 0.00064
22 0,12,17,21 +2+?+1 0.00018
22 0,13,17,20 +3+?+1 0.00044
23 0,1,12,13 +2+?+3 0.00095
23 0,1,12,14 +1+?+3 0.00078
23 0,1,13,14 +2+?+3 0.00030
23 0,1,13,15 +1+?+3 0.00004
23 0,1,14,15 +2+?+3 0.00037
23 0,1,14,16 +1+?+3 0.00089
23 0,2,4,9 +1+?+3 0.00088
23 0,2,5,10 +1+?+3 0.00081
23 0,2,9,10 +3+?+2 0.00082
23 0,2,9,12 +1+?+2 0.00006
23 0,2,10,11 +3+?+2 0.00004
23 0,2,11,12 +3+?+2 0.00077
23 0,2,12,16 +1+?+3 0.00074
23 0,2,13,15 +2+?+3 0.00061
23 0,2,13,17 +1+?+3 0.00096
23 0,2,14,16 +2+?+3 0.00075
23 0,3,5,10 +1+?+2 0.00007
23 0,3,6,13 +1+?+3 0.00074
23 0,3,12,18 +1+?+3 0.00021
23 0,3,13,16 +2+?+3 0.00094
23 0,3,13,17 +1+?+2 0.00013
23 0,3,14,15 +2+?+1 0.00044
23 0,3,14,16 +1+?+1 0.00007
23 0,3,15,16 +2+?+1 0.00051
23 0,4,7,16 +1+?+3 0.00012
23 0,4,10,11 +3+?+1 0.00093
23 0,4,10,12 +3+?+2 0.00092
23 0,4,10,13 +1+?+1 0.00012
23 0,4,11,12 +3+?+1 0.00006
23 0,4,11,13 +3+?+2 0.00073
23 0,4,12,13 +3+?+1 0.00084
23 0,4,15,20 +1+?+2 0.00027
23 0,5,6,14 +1+?+2 0.00058
23 0,5,7,13 +2+?+3 0.00039
23 0,5,7,18 +1+?+3 0.00076
23 0,5,8,12 +1+?+1 0.00024
23 0,5,9,11 +2+?+1 0.00011
23 0,5,11,18 +1+?+2 0.00078
23 0,5,11,21 +1+?+3 0.00062
23 0,5,18,20 +3+?+2 0.00099
23 0,5,18,21 +1+?+1 0.00008
23 0,5,19,20 +3+?+1 0.00002
23 0,6,7,20 +1+?+3 0.00071
23 0,6,8,15 +2+?+3 0.00077
23 0,6,8,17 +1+?+2 0.00005
23 0,6,11,14 +3+?+2 0.00020
23 0,6,15,17 +2+?+1 0.00098
23 0,7,8,10 +3+?+1 0.00054
23 0,7,12,17 +1+?+1 0.00079
23 0,7,17,20 +3+?+2 0.00088
23 0,8,9,18 +2+?+3 0.00015
23 0,8,11,22 +1+?+2 0.00093
23 0,8,12,15 +2+?+1 0.00031
23 0,8,13,15 +3+?+1 0.00072
23 0,8,17,22 +1+?+1 0.00068
23 0,9,15,21 +1+?+1 0.00006
23 0,9,16,20 +3+?+2 0.00014
23 0,9,17,19 +3+?+1 0.00011
23 0,10,12,17 +3+?+2 0.00063
23 0,11,12,20 +1+?+1 0.00094
23 0,11,14,18 +2+?+1 0.00078
23 0,11,16,21 +3+?+2 0.00087
23 0,12,14,17 +3+?+1 0.00065
23 0,13,16,22 +3+?+2 0.00081
23 0,14,16,21 +2+?+1 0.00064
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