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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 < 0.0015. 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
!Steps
!Delta signature
!Least-squares error
|-
|5
|0, 1, 3, 4
| +2+?+3
|0.00113
|-
|6
|0, 1, 3, 5
| +1+?+3
|0.00006
|-
|6
|0, 2, 3, 4
| +3+?+2
|0.00006
|-
|7
|0, 3, 5, 6
| +2+?+1
|0.00145
|-
|7
|0, 1, 4, 5
| +2+?+3
|0.00071
|-
|7
|0, 2, 4, 6
| +2+?+3
|0.00149
|-
|8
|0, 1, 4, 6
| +1+?+3
|0.00119
|-
|8
|0, 4, 5, 6
| +3+?+1
|0.00104
|-
|8
|0, 2, 4, 5
| +3+?+2
|0.00119
|-
|9
|0, 1, 5, 7
| +1+?+3
|0.00138
|-
|9
|0, 1, 5, 6
| +2+?+3
|0.00118
|-
|9
|0, 2, 4, 5
| +3+?+2
|0.00133
|-
|10
|0, 3, 7, 8
| +2+?+1
|0.00068
|-
|10
|0, 1, 6, 7
| +2+?+3
|0.00055
|-
|10
|0, 2, 6, 8
| +2+?+3
|0.00113
|-
|11
|0, 3, 7, 9
| +1+?+1
|0.00040
|-
|11
|0, 4, 5, 8
| +1+?+1
|0.00087
|-
|11
|0, 2, 4, 7
| +1+?+2
|0.00036
|-
|11
|0, 3, 6, 10
| +1+?+2
|0.00090
|-
|11
|0, 1, 6, 8
| +1+?+3
|0.00027
|-
|11
|0, 1, 6, 7
| +2+?+3
|0.00128
|-
|11
|0, 4, 6, 7
| +3+?+1
|0.00043
|-
|11
|0, 2, 5, 6
| +3+?+2
|0.00026
|-
|12
|0, 2, 6, 10
| +1+?+3
|0.00006
|-
|12
|0, 3, 8, 9
| +2+?+1
|0.00014
|-
|12
|0, 6, 9, 11
| +2+?+1
|0.00077
|-
|12
|0, 1, 7, 8
| +2+?+3
|0.00005
|-
|12
|0, 2, 7, 9
| +2+?+3
|0.00010
|-
|12
|0, 3, 7, 10
| +2+?+3
|0.00016
|-
|12
|0, 4, 7, 11
| +2+?+3
|0.00021
|-
|12
|0, 2, 5, 6
| +3+?+2
|0.00145
|-
|12
|0, 4, 6, 8
| +3+?+2
|0.00006
|-
|13
|0, 3, 8, 10
| +1+?+1
|0.00062
|-
|13
|0, 4, 6, 9
| +1+?+1
|0.00065
|-
|13
|0, 2, 5, 8
| +1+?+2
|0.00057
|-
|13
|0, 3, 7, 11
| +1+?+2
|0.00067
|-
|13
|0, 1, 7, 9
| +1+?+3
|0.00026
|-
|13
|0, 3, 6, 12
| +1+?+3
|0.00037
|-
|13
|0, 3, 9, 10
| +2+?+1
|0.00118
|-
|13
|0, 5, 6, 8
| +2+?+1
|0.00147
|-
|13
|0, 1, 7, 8
| +2+?+3
|0.00126
|-
|13
|0, 1, 8, 9
| +2+?+3
|0.00085
|-
|13
|0, 4, 7, 8
| +3+?+1
|0.00021
|-
|13
|0, 2, 6, 7
| +3+?+2
|0.00025
|-
|13
|0, 6, 7, 10
| +3+?+2
|0.00038
|-
|14
|0, 3, 9, 11
| +1+?+1
|0.00138
|-
|14
|0, 2, 5, 8
| +1+?+2
|0.00125
|-
|14
|0, 1, 8, 10
| +1+?+3
|0.00073
|-
|14
|0, 2, 7, 11
| +1+?+3
|0.00076
|-
|14
|0, 3, 9, 10
| +2+?+1
|0.00054
|-
|14
|0, 5, 6, 8
| +2+?+1
|0.00023
|-
|14
|0, 6, 10, 12
| +2+?+1
|0.00145
|-
|14
|0, 1, 8, 9
| +2+?+3
|0.00034
|-
|14
|0, 2, 8, 10
| +2+?+3
|0.00071
|-
|14
|0, 3, 8, 11
| +2+?+3
|0.00109
|-
|14
|0, 4, 8, 12
| +2+?+3
|0.00149
|-
|14
|0, 4, 7, 8
| +3+?+1
|0.00084
|-
|14
|0, 5, 12, 13
| +3+?+1
|0.00116
|-
|14
|0, 8, 9, 11
| +3+?+1
|0.00036
|-
|14
|0, 2, 6, 7
| +3+?+2
|0.00069
|-
|14
|0, 4, 7, 9
| +3+?+2
|0.00076
|-
|15
|0, 3, 9, 11
| +1+?+1
|0.00112
|-
|15
|0, 4, 7, 10
| +1+?+1
|0.00142
|-
|15
|0, 2, 6, 9
| +1+?+2
|0.00104
|-
|15
|0, 3, 8, 12
| +1+?+2
|0.00146
|-
|15
|0, 4, 5, 11
| +1+?+2
|0.00143
|-
|15
|0, 1, 8, 10
| +1+?+3
|0.00053
|-
|15
|0, 1, 9, 11
| +1+?+3
|0.00147
|-
|15
|0, 2, 8, 12
| +1+?+3
|0.00101
|-
|15
|0, 3, 7, 13
| +1+?+3
|0.00138
|-
|15
|0, 3, 10, 11
| +2+?+1
|0.00048
|-
|15
|0, 5, 6, 8
| +2+?+1
|0.00147
|-
|15
|0, 6, 11, 13
| +2+?+1
|0.00081
|-
|15
|0, 8, 9, 12
| +2+?+1
|0.00117
|-
|15
|0, 1, 8, 9
| +2+?+3
|0.00121
|-
|15
|0, 1, 9, 10
| +2+?+3
|0.00036
|-
|15
|0, 2, 9, 11
| +2+?+3
|0.00074
|-
|15
|0, 3, 9, 12
| +2+?+3
|0.00113
|-
|15
|0, 4, 8, 9
| +3+?+1
|0.00053
|-
|15
|0, 5, 13, 14
| +3+?+1
|0.00028
|-
|15
|0, 2, 6, 7
| +3+?+2
|0.00137
|-
|15
|0, 2, 7, 8
| +3+?+2
|0.00052
|-
|15
|0, 4, 7, 9
| +3+?+2
|0.00099
|-
|15
|0, 6, 8, 11
| +3+?+2
|0.00141
|-
|16
|0, 3, 10, 12
| +1+?+1
|0.00046
|-
|16
|0, 4, 7, 10
| +1+?+1
|0.00072
|-
|16
|0, 2, 6, 9
| +1+?+2
|0.00042
|-
|16
|0, 3, 9, 13
| +1+?+2
|0.00075
|-
|16
|0, 1, 8, 10
| +1+?+3
|0.00145
|-
|16
|0, 1, 9, 11
| +1+?+3
|0.00025
|-
|16
|0, 2, 3, 8
| +1+?+3
|0.00118
|-
|16
|0, 2, 8, 12
| +1+?+3
|0.00119
|-
|16
|0, 3, 4, 11
| +1+?+3
|0.00148
|-
|16
|0, 3, 8, 14
| +1+?+3
|0.00103
|-
|16
|0, 3, 10, 11
| +2+?+1
|0.00074
|-
|16
|0, 3, 11, 12
| +2+?+1
|0.00127
|-
|16
|0, 5, 7, 9
| +2+?+1
|0.00109
|-
|16
|0, 8, 9, 12
| +2+?+1
|0.00143
|-
|16
|0, 1, 9, 10
| +2+?+3
|0.00050
|-
|16
|0, 1, 10, 11
| +2+?+3
|0.00091
|-
|16
|0, 2, 9, 11
| +2+?+3
|0.00102
|-
|16
|0, 4, 8, 9
| +3+?+1
|0.00031
|-
|16
|0, 5, 14, 15
| +3+?+1
|0.00040
|-
|16
|0, 8, 10, 12
| +3+?+1
|0.00104
|-
|16
|0, 9, 13, 15
| +3+?+1
|0.00001
|-
|16
|0, 2, 7, 8
| +3+?+2
|0.00024
|-
|16
|0, 2, 8, 9
| +3+?+2
|0.00145
|-
|16
|0, 4, 8, 10
| +3+?+2
|0.00119
|-
|16
|0, 5, 13, 15
| +3+?+2
|0.00146
|-
|16
|0, 6, 8, 11
| +3+?+2
|0.00103
|-
|17
|0, 3, 10, 12
| +1+?+1
|0.00137
|-
|17
|0, 5, 6, 10
| +1+?+1
|0.00006
|-
|17
|0, 6, 11, 15
| +1+?+1
|0.00014
|-
|17
|0, 2, 7, 10
| +1+?+2
|0.00129
|-
|17
|0, 4, 6, 12
| +1+?+2
|0.00013
|-
|17
|0, 4, 11, 16
| +1+?+2
|0.00007
|-
|17
|0, 1, 9, 11
| +1+?+3
|0.00067
|-
|17
|0, 1, 10, 12
| +1+?+3
|0.00087
|-
|17
|0, 2, 3, 8
| +1+?+3
|0.00020
|-
|17
|0, 2, 9, 13
| +1+?+3
|0.00024
|-
|17
|0, 3, 4, 11
| +1+?+3
|0.00046
|-
|17
|0, 4, 8, 16
| +1+?+3
|0.00090
|-
|17
|0, 3, 11, 12
| +2+?+1
|0.00007
|-
|17
|0, 5, 7, 9
| +2+?+1
|0.00003
|-
|17
|0, 6, 12, 14
| +2+?+1
|0.00000
|-
|17
|0, 9, 13, 16
| +2+?+1
|0.00040
|-
|17
|0, 1, 9, 10
| +2+?+3
|0.00114
|-
|17
|0, 1, 10, 11
| +2+?+3
|0.00007
|-
|17
|0, 1, 11, 12
| +2+?+3
|0.00133
|-
|17
|0, 2, 10, 12
| +2+?+3
|0.00014
|-
|17
|0, 3, 10, 13
| +2+?+3
|0.00022
|-
|17
|0, 4, 10, 14
| +2+?+3
|0.00029
|-
|17
|0, 5, 10, 15
| +2+?+3
|0.00037
|-
|17
|0, 6, 10, 16
| +2+?+3
|0.00046
|-
|17
|0, 4, 8, 9
| +3+?+1
|0.00095
|-
|17
|0, 4, 9, 10
| +3+?+1
|0.00070
|-
|17
|0, 5, 14, 15
| +3+?+1
|0.00119
|-
|17
|0, 5, 15, 16
| +3+?+1
|0.00092
|-
|17
|0, 8, 10, 12
| +3+?+1
|0.00057
|-
|17
|0, 2, 7, 8
| +3+?+2
|0.00082
|-
|17
|0, 2, 8, 9
| +3+?+2
|0.00065
|-
|17
|0, 4, 8, 10
| +3+?+2
|0.00023
|-
|17
|0, 5, 14, 16
| +3+?+2
|0.00025
|-
|17
|0, 7, 13, 16
| +3+?+2
|0.00055
|-
|17
|0, 8, 9, 13
| +3+?+2
|0.00092
|-
|18
|0, 3, 11, 13
| +1+?+1
|0.00010
|-
|18
|0, 4, 8, 11
| +1+?+1
|0.00007
|-
|18
|0, 5, 6, 10
| +1+?+1
|0.00145
|-
|18
|0, 5, 14, 17
| +1+?+1
|0.00137
|-
|18
|0, 2, 7, 10
| +1+?+2
|0.00009
|-
|18
|0, 3, 4, 9
| +1+?+2
|0.00113
|-
|18
|0, 3, 10, 14
| +1+?+2
|0.00007
|-
|18
|0, 5, 8, 15
| +1+?+2
|0.00149
|-
|18
|0, 1, 9, 11
| +1+?+3
|0.00137
|-
|18
|0, 1, 10, 12
| +1+?+3
|0.00003
|-
|18
|0, 1, 11, 13
| +1+?+3
|0.00136
|-
|18
|0, 2, 3, 8
| +1+?+3
|0.00056
|-
|18
|0, 2, 9, 13
| +1+?+3
|0.00141
|-
|18
|0, 2, 10, 14
| +1+?+3
|0.00138
|-
|18
|0, 3, 9, 15
| +1+?+3
|0.00006
|-
|18
|0, 4, 5, 14
| +1+?+3
|0.00078
|-
|18
|0, 3, 11, 12
| +2+?+1
|0.00084
|-
|18
|0, 3, 12, 13
| +2+?+1
|0.00073
|-
|18
|0, 5, 7, 9
| +2+?+1
|0.00089
|-
|18
|0, 6, 13, 15
| +2+?+1
|0.00141
|-
|18
|0, 8, 10, 13
| +2+?+1
|0.00027
|-
|18
|0, 11, 12, 16
| +2+?+1
|0.00042
|-
|18
|0, 1, 10, 11
| +2+?+3
|0.00058
|-
|18
|0, 1, 11, 12
| +2+?+3
|0.00052
|-
|18
|0, 2, 10, 12
| +2+?+3
|0.00118
|-
|18
|0, 2, 11, 13
| +2+?+3
|0.00107
|-
|18
|0, 4, 8, 9
| +3+?+1
|0.00144
|-
|18
|0, 4, 9, 10
| +3+?+1
|0.00001
|-
|18
|0, 5, 15, 16
| +3+?+1
|0.00057
|-
|18
|0, 5, 16, 17
| +3+?+1
|0.00132
|-
|18
|0, 8, 11, 13
| +3+?+1
|0.00139
|-
|18
|0, 9, 14, 16
| +3+?+1
|0.00056
|-
|18
|0, 2, 7, 8
| +3+?+2
|0.00126
|-
|18
|0, 2, 8, 9
| +3+?+2
|0.00003
|-
|18
|0, 2, 9, 10
| +3+?+2
|0.00137
|-
|18
|0, 4, 8, 10
| +3+?+2
|0.00133
|-
|18
|0, 4, 9, 11
| +3+?+2
|0.00141
|-
|18
|0, 5, 15, 17
| +3+?+2
|0.00070
|-
|18
|0, 6, 9, 12
| +3+?+2
|0.00006
|-
|18
|0, 9, 13, 17
| +3+?+2
|0.00091
|-
|19
|0, 3, 11, 13
| +1+?+1
|0.00150
|-
|19
|0, 3, 12, 14
| +1+?+1
|0.00093
|-
|19
|0, 4, 8, 11
| +1+?+1
|0.00130
|-
|19
|0, 5, 15, 18
| +1+?+1
|0.00011
|-
|19
|0, 6, 12, 16
| +1+?+1
|0.00074
|-
|19
|0, 8, 9, 15
| +1+?+1
|0.00051
|-
|19
|0, 2, 7, 10
| +1+?+2
|0.00085
|-
|19
|0, 2, 8, 11
| +1+?+2
|0.00142
|-
|19
|0, 3, 4, 9
| +1+?+2
|0.00009
|-
|19
|0, 3, 11, 15
| +1+?+2
|0.00138
|-
|19
|0, 4, 7, 13
| +1+?+2
|0.00068
|-
|19
|0, 6, 10, 18
| +1+?+2
|0.00052
|-
|19
|0, 1, 10, 12
| +1+?+3
|0.00074
|-
|19
|0, 1, 11, 13
| +1+?+3
|0.00048
|-
|19
|0, 2, 3, 8
| +1+?+3
|0.00115
|-
|19
|0, 2, 4, 9
| +1+?+3
|0.00135
|-
|19
|0, 2, 10, 14
| +1+?+3
|0.00024
|-
|19
|0, 3, 5, 12
| +1+?+3
|0.00066
|-
|19
|0, 4, 5, 14
| +1+?+3
|0.00148
|-
|19
|0, 4, 9, 17
| +1+?+3
|0.00021
|-
|19
|0, 3, 12, 13
| +2+?+1
|0.00018
|-
|19
|0, 3, 13, 14
| +2+?+1
|0.00125
|-
|19
|0, 5, 8, 10
| +2+?+1
|0.00086
|-
|19
|0, 6, 13, 15
| +2+?+1
|0.00048
|-
|19
|0, 9, 14, 17
| +2+?+1
|0.00105
|-
|19
|0, 1, 10, 11
| +2+?+3
|0.00108
|-
|19
|0, 1, 11, 12
| +2+?+3
|0.00011
|-
|19
|0, 1, 12, 13
| +2+?+3
|0.00089
|-
|19
|0, 2, 11, 13
| +2+?+3
|0.00023
|-
|19
|0, 3, 11, 14
| +2+?+3
|0.00035
|-
|19
|0, 4, 11, 15
| +2+?+3
|0.00048
|-
|19
|0, 5, 11, 16
| +2+?+3
|0.00061
|-
|19
|0, 6, 11, 17
| +2+?+3
|0.00074
|-
|19
|0, 7, 11, 18
| +2+?+3
|0.00088
|-
|19
|0, 4, 9, 10
| +3+?+1
|0.00053
|-
|19
|0, 4, 10, 11
| +3+?+1
|0.00079
|-
|19
|0, 5, 16, 17
| +3+?+1
|0.00006
|-
|19
|0, 8, 11, 13
| +3+?+1
|0.00007
|-
|19
|0, 9, 15, 17
| +3+?+1
|0.00088
|-
|19
|0, 2, 8, 9
| +3+?+2
|0.00046
|-
|19
|0, 2, 9, 10
| +3+?+2
|0.00073
|-
|19
|0, 4, 9, 11
| +3+?+2
|0.00024
|-
|19
|0, 5, 16, 18
| +3+?+2
|0.00146
|-
|19
|0, 7, 14, 17
| +3+?+2
|0.00078
|-
|19
|0, 8, 10, 14
| +3+?+2
|0.00022
|-
|20
|0, 1, 2, 3
| +1+?+1
|0.00146
|-
|20
|0, 3, 12, 14
| +1+?+1
|0.00045
|-
|20
|0, 4, 9, 12
| +1+?+1
|0.00056
|-
|20
|0, 5, 7, 11
| +1+?+1
|0.00018
|-
|20
|0, 5, 16, 19
| +1+?+1
|0.00090
|-
|20
|0, 6, 13, 17
| +1+?+1
|0.00126
|-
|20
|0, 7, 11, 16
| +1+?+1
|0.00142
|-
|20
|0, 10, 12, 19
| +1+?+1
|0.00112
|-
|20
|0, 2, 8, 11
| +1+?+2
|0.00042
|-
|20
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|-
|23
|0, 3, 13, 16
| +2+?+3
|0.00094
|-
|23
|0, 3, 14, 17
| +2+?+3
|0.00114
|-
|23
|0, 4, 6, 11
| +2+?+3
|0.00131
|-
|23
|0, 4, 13, 17
| +2+?+3
|0.00127
|-
|23
|0, 5, 7, 13
| +2+?+3
|0.00039
|-
|23
|0, 6, 8, 15
| +2+?+3
|0.00077
|-
|23
|0, 8, 9, 18
| +2+?+3
|0.00015
|-
|23
|0, 4, 10, 11
| +3+?+1
|0.00093
|-
|23
|0, 4, 11, 12
| +3+?+1
|0.00006
|-
|23
|0, 4, 12, 13
| +3+?+1
|0.00084
|-
|23
|0, 5, 18, 19
| +3+?+1
|0.00109
|-
|23
|0, 5, 19, 20
| +3+?+1
|0.00002
|-
|23
|0, 5, 20, 21
| +3+?+1
|0.00116
|-
|23
|0, 7, 8, 10
| +3+?+1
|0.00054
|-
|23
|0, 8, 12, 14
| +3+?+1
|0.00116
|-
|23
|0, 8, 13, 15
| +3+?+1
|0.00072
|-
|23
|0, 9, 17, 19
| +3+?+1
|0.00011
|-
|23
|0, 12, 14, 17
| +3+?+1
|0.00065
|-
|23
|0, 13, 17, 20
| +3+?+1
|0.00133
|-
|23
|0, 2, 9, 10
| +3+?+2
|0.00082
|-
|23
|0, 2, 10, 11
| +3+?+2
|0.00004
|-
|23
|0, 2, 11, 12
| +3+?+2
|0.00077
|-
|23
|0, 4, 10, 12
| +3+?+2
|0.00092
|-
|23
|0, 4, 11, 13
| +3+?+2
|0.00073
|-
|23
|0, 5, 18, 20
| +3+?+2
|0.00099
|-
|23
|0, 5, 19, 21
| +3+?+2
|0.00110
|-
|23
|0, 6, 11, 14
| +3+?+2
|0.00020
|-
|23
|0, 7, 17, 20
| +3+?+2
|0.00088
|-
|23
|0, 8, 12, 16
| +3+?+2
|0.00139
|-
|23
|0, 9, 16, 20
| +3+?+2
|0.00014
|-
|23
|0, 10, 12, 17
| +3+?+2
|0.00063
|-
|23
|0, 11, 16, 21
| +3+?+2
|0.00087
|-
|23
|0, 13, 16, 22
| +3+?+2
|0.00081
|}
 
[[Category:Tables]][[Category:Tetrads]]
[[Category:Tables]][[Category:Tetrads]]
Retrieved from "https://en.xen.wiki/w/Partially_delta-rational_tetrads_in_small_edos"