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

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Created page with "Shown below are approximate partially delta-rational tetrads spanning an interval < octave, in edos < 24, with least-squares error < 0.0015. All delta..."
 
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|-
|-
|5
|5
|(0, 1, 3, 4)
|0, 1, 3, 4
|[2, 3]
| +2+?+3
|0.00113
|0.00113
|-
|-
|6
|6
|(0, 1, 3, 5)
|0, 1, 3, 5
|[1, 3]
| +1+?+3
|0.00006
|0.00006
|-
|-
|6
|6
|(0, 2, 3, 4)
|0, 2, 3, 4
|[3, 2]
| +3+?+2
|0.00006
|0.00006
|-
|-
|7
|7
|(0, 3, 5, 6)
|0, 3, 5, 6
|[2, 1]
| +2+?+1
|0.00145
|0.00145
|-
|-
|7
|7
|(0, 1, 4, 5)
|0, 1, 4, 5
|[2, 3]
| +2+?+3
|0.00071
|0.00071
|-
|-
|7
|7
|(0, 2, 4, 6)
|0, 2, 4, 6
|[2, 3]
| +2+?+3
|0.00149
|0.00149
|-
|-
|8
|8
|(0, 1, 4, 6)
|0, 1, 4, 6
|[1, 3]
| +1+?+3
|0.00119
|0.00119
|-
|-
|8
|8
|(0, 4, 5, 6)
|0, 4, 5, 6
|[3, 1]
| +3+?+1
|0.00104
|0.00104
|-
|-
|8
|8
|(0, 2, 4, 5)
|0, 2, 4, 5
|[3, 2]
| +3+?+2
|0.00119
|0.00119
|-
|-
|9
|9
|(0, 1, 5, 7)
|0, 1, 5, 7
|[1, 3]
| +1+?+3
|0.00138
|0.00138
|-
|-
|9
|9
|(0, 1, 5, 6)
|0, 1, 5, 6
|[2, 3]
| +2+?+3
|0.00118
|0.00118
|-
|-
|9
|9
|(0, 2, 4, 5)
|0, 2, 4, 5
|[3, 2]
| +3+?+2
|0.00133
|0.00133
|-
|-
|10
|10
|(0, 3, 7, 8)
|0, 3, 7, 8
|[2, 1]
| +2+?+1
|0.00068
|0.00068
|-
|-
|10
|10
|(0, 1, 6, 7)
|0, 1, 6, 7
|[2, 3]
| +2+?+3
|0.00055
|0.00055
|-
|-
|10
|10
|(0, 2, 6, 8)
|0, 2, 6, 8
|[2, 3]
| +2+?+3
|0.00113
|0.00113
|-
|-
|11
|11
|(0, 3, 7, 9)
|0, 3, 7, 9
|[1, 1]
| +1+?+1
|0.00040
|0.00040
|-
|-
|11
|11
|(0, 4, 5, 8)
|0, 4, 5, 8
|[1, 1]
| +1+?+1
|0.00087
|0.00087
|-
|-
|11
|11
|(0, 2, 4, 7)
|0, 2, 4, 7
|[1, 2]
| +1+?+2
|0.00036
|0.00036
|-
|-
|11
|11
|(0, 3, 6, 10)
|0, 3, 6, 10
|[1, 2]
| +1+?+2
|0.00090
|0.00090
|-
|-
|11
|11
|(0, 1, 6, 8)
|0, 1, 6, 8
|[1, 3]
| +1+?+3
|0.00027
|0.00027
|-
|-
|11
|11
|(0, 1, 6, 7)
|0, 1, 6, 7
|[2, 3]
| +2+?+3
|0.00128
|0.00128
|-
|-
|11
|11
|(0, 4, 6, 7)
|0, 4, 6, 7
|[3, 1]
| +3+?+1
|0.00043
|0.00043
|-
|-
|11
|11
|(0, 2, 5, 6)
|0, 2, 5, 6
|[3, 2]
| +3+?+2
|0.00026
|0.00026
|-
|-
|12
|12
|(0, 2, 6, 10)
|0, 2, 6, 10
|[1, 3]
| +1+?+3
|0.00006
|0.00006
|-
|-
|12
|12
|(0, 3, 8, 9)
|0, 3, 8, 9
|[2, 1]
| +2+?+1
|0.00014
|0.00014
|-
|-
|12
|12
|(0, 6, 9, 11)
|0, 6, 9, 11
|[2, 1]
| +2+?+1
|0.00077
|0.00077
|-
|-
|12
|12
|(0, 1, 7, 8)
|0, 1, 7, 8
|[2, 3]
| +2+?+3
|0.00005
|0.00005
|-
|-
|12
|12
|(0, 2, 7, 9)
|0, 2, 7, 9
|[2, 3]
| +2+?+3
|0.00010
|0.00010
|-
|-
|12
|12
|(0, 3, 7, 10)
|0, 3, 7, 10
|[2, 3]
| +2+?+3
|0.00016
|0.00016
|-
|-
|12
|12
|(0, 4, 7, 11)
|0, 4, 7, 11
|[2, 3]
| +2+?+3
|0.00021
|0.00021
|-
|-
|12
|12
|(0, 2, 5, 6)
|0, 2, 5, 6
|[3, 2]
| +3+?+2
|0.00145
|0.00145
|-
|-
|12
|12
|(0, 4, 6, 8)
|0, 4, 6, 8
|[3, 2]
| +3+?+2
|0.00006
|0.00006
|-
|-
|13
|13
|(0, 3, 8, 10)
|0, 3, 8, 10
|[1, 1]
| +1+?+1
|0.00062
|0.00062
|-
|-
|13
|13
|(0, 4, 6, 9)
|0, 4, 6, 9
|[1, 1]
| +1+?+1
|0.00065
|0.00065
|-
|-
|13
|13
|(0, 2, 5, 8)
|0, 2, 5, 8
|[1, 2]
| +1+?+2
|0.00057
|0.00057
|-
|-
|13
|13
|(0, 3, 7, 11)
|0, 3, 7, 11
|[1, 2]
| +1+?+2
|0.00067
|0.00067
|-
|-
|13
|13
|(0, 1, 7, 9)
|0, 1, 7, 9
|[1, 3]
| +1+?+3
|0.00026
|0.00026
|-
|-
|13
|13
|(0, 3, 6, 12)
|0, 3, 6, 12
|[1, 3]
| +1+?+3
|0.00037
|0.00037
|-
|-
|13
|13
|(0, 3, 9, 10)
|0, 3, 9, 10
|[2, 1]
| +2+?+1
|0.00118
|0.00118
|-
|-
|13
|13
|(0, 5, 6, 8)
|0, 5, 6, 8
|[2, 1]
| +2+?+1
|0.00147
|0.00147
|-
|-
|13
|13
|(0, 1, 7, 8)
|0, 1, 7, 8
|[2, 3]
| +2+?+3
|0.00126
|0.00126
|-
|-
|13
|13
|(0, 1, 8, 9)
|0, 1, 8, 9
|[2, 3]
| +2+?+3
|0.00085
|0.00085
|-
|-
|13
|13
|(0, 4, 7, 8)
|0, 4, 7, 8
|[3, 1]
| +3+?+1
|0.00021
|0.00021
|-
|-
|13
|13
|(0, 2, 6, 7)
|0, 2, 6, 7
|[3, 2]
| +3+?+2
|0.00025
|0.00025
|-
|-
|13
|13
|(0, 6, 7, 10)
|0, 6, 7, 10
|[3, 2]
| +3+?+2
|0.00038
|0.00038
|-
|-
|14
|14
|(0, 3, 9, 11)
|0, 3, 9, 11
|[1, 1]
| +1+?+1
|0.00138
|0.00138
|-
|-
|14
|14
|(0, 2, 5, 8)
|0, 2, 5, 8
|[1, 2]
| +1+?+2
|0.00125
|0.00125
|-
|-
|14
|14
|(0, 1, 8, 10)
|0, 1, 8, 10
|[1, 3]
| +1+?+3
|0.00073
|0.00073
|-
|-
|14
|14
|(0, 2, 7, 11)
|0, 2, 7, 11
|[1, 3]
| +1+?+3
|0.00076
|0.00076
|-
|-
|14
|14
|(0, 3, 9, 10)
|0, 3, 9, 10
|[2, 1]
| +2+?+1
|0.00054
|0.00054
|-
|-
|14
|14
|(0, 5, 6, 8)
|0, 5, 6, 8
|[2, 1]
| +2+?+1
|0.00023
|0.00023
|-
|-
|14
|14
|(0, 6, 10, 12)
|0, 6, 10, 12
|[2, 1]
| +2+?+1
|0.00145
|0.00145
|-
|-
|14
|14
|(0, 1, 8, 9)
|0, 1, 8, 9
|[2, 3]
| +2+?+3
|0.00034
|0.00034
|-
|-
|14
|14
|(0, 2, 8, 10)
|0, 2, 8, 10
|[2, 3]
| +2+?+3
|0.00071
|0.00071
|-
|-
|14
|14
|(0, 3, 8, 11)
|0, 3, 8, 11
|[2, 3]
| +2+?+3
|0.00109
|0.00109
|-
|-
|14
|14
|(0, 4, 8, 12)
|0, 4, 8, 12
|[2, 3]
| +2+?+3
|0.00149
|0.00149
|-
|-
|14
|14
|(0, 4, 7, 8)
|0, 4, 7, 8
|[3, 1]
| +3+?+1
|0.00084
|0.00084
|-
|-
|14
|14
|(0, 5, 12, 13)
|0, 5, 12, 13
|[3, 1]
| +3+?+1
|0.00116
|0.00116
|-
|-
|14
|14
|(0, 8, 9, 11)
|0, 8, 9, 11
|[3, 1]
| +3+?+1
|0.00036
|0.00036
|-
|-
|14
|14
|(0, 2, 6, 7)
|0, 2, 6, 7
|[3, 2]
| +3+?+2
|0.00069
|0.00069
|-
|-
|14
|14
|(0, 4, 7, 9)
|0, 4, 7, 9
|[3, 2]
| +3+?+2
|0.00076
|0.00076
|-
|-
|15
|15
|(0, 3, 9, 11)
|0, 3, 9, 11
|[1, 1]
| +1+?+1
|0.00112
|0.00112
|-
|-
|15
|15
|(0, 4, 7, 10)
|0, 4, 7, 10
|[1, 1]
| +1+?+1
|0.00142
|0.00142
|-
|-
|15
|15
|(0, 2, 6, 9)
|0, 2, 6, 9
|[1, 2]
| +1+?+2
|0.00104
|0.00104
|-
|-
|15
|15
|(0, 3, 8, 12)
|0, 3, 8, 12
|[1, 2]
| +1+?+2
|0.00146
|0.00146
|-
|-
|15
|15
|(0, 4, 5, 11)
|0, 4, 5, 11
|[1, 2]
| +1+?+2
|0.00143
|0.00143
|-
|-
|15
|15
|(0, 1, 8, 10)
|0, 1, 8, 10
|[1, 3]
| +1+?+3
|0.00053
|0.00053
|-
|-
|15
|15
|(0, 1, 9, 11)
|0, 1, 9, 11
|[1, 3]
| +1+?+3
|0.00147
|0.00147
|-
|-
|15
|15
|(0, 2, 8, 12)
|0, 2, 8, 12
|[1, 3]
| +1+?+3
|0.00101
|0.00101
|-
|-
|15
|15
|(0, 3, 7, 13)
|0, 3, 7, 13
|[1, 3]
| +1+?+3
|0.00138
|0.00138
|-
|-
|15
|15
|(0, 3, 10, 11)
|0, 3, 10, 11
|[2, 1]
| +2+?+1
|0.00048
|0.00048
|-
|-
|15
|15
|(0, 5, 6, 8)
|0, 5, 6, 8
|[2, 1]
| +2+?+1
|0.00147
|0.00147
|-
|-
|15
|15
|(0, 6, 11, 13)
|0, 6, 11, 13
|[2, 1]
| +2+?+1
|0.00081
|0.00081
|-
|-
|15
|15
|(0, 8, 9, 12)
|0, 8, 9, 12
|[2, 1]
| +2+?+1
|0.00117
|0.00117
|-
|-
|15
|15
|(0, 1, 8, 9)
|0, 1, 8, 9
|[2, 3]
| +2+?+3
|0.00121
|0.00121
|-
|-
|15
|15
|(0, 1, 9, 10)
|0, 1, 9, 10
|[2, 3]
| +2+?+3
|0.00036
|0.00036
|-
|-
|15
|15
|(0, 2, 9, 11)
|0, 2, 9, 11
|[2, 3]
| +2+?+3
|0.00074
|0.00074
|-
|-
|15
|15
|(0, 3, 9, 12)
|0, 3, 9, 12
|[2, 3]
| +2+?+3
|0.00113
|0.00113
|-
|-
|15
|15
|(0, 4, 8, 9)
|0, 4, 8, 9
|[3, 1]
| +3+?+1
|0.00053
|0.00053
|-
|-
|15
|15
|(0, 5, 13, 14)
|0, 5, 13, 14
|[3, 1]
| +3+?+1
|0.00028
|0.00028
|-
|-
|15
|15
|(0, 2, 6, 7)
|0, 2, 6, 7
|[3, 2]
| +3+?+2
|0.00137
|0.00137
|-
|-
|15
|15
|(0, 2, 7, 8)
|0, 2, 7, 8
|[3, 2]
| +3+?+2
|0.00052
|0.00052
|-
|-
|15
|15
|(0, 4, 7, 9)
|0, 4, 7, 9
|[3, 2]
| +3+?+2
|0.00099
|0.00099
|-
|-
|15
|15
|(0, 6, 8, 11)
|0, 6, 8, 11
|[3, 2]
| +3+?+2
|0.00141
|0.00141
|-
|-
|16
|16
|(0, 3, 10, 12)
|0, 3, 10, 12
|[1, 1]
| +1+?+1
|0.00046
|0.00046
|-
|-
|16
|16
|(0, 4, 7, 10)
|0, 4, 7, 10
|[1, 1]
| +1+?+1
|0.00072
|0.00072
|-
|-
|16
|16
|(0, 2, 6, 9)
|0, 2, 6, 9
|[1, 2]
| +1+?+2
|0.00042
|0.00042
|-
|-
|16
|16
|(0, 3, 9, 13)
|0, 3, 9, 13
|[1, 2]
| +1+?+2
|0.00075
|0.00075
|-
|-
|16
|16
|(0, 1, 8, 10)
|0, 1, 8, 10
|[1, 3]
| +1+?+3
|0.00145
|0.00145
|-
|-
|16
|16
|(0, 1, 9, 11)
|0, 1, 9, 11
|[1, 3]
| +1+?+3
|0.00025
|0.00025
|-
|-
|16
|16
|(0, 2, 3, 8)
|0, 2, 3, 8
|[1, 3]
| +1+?+3
|0.00118
|0.00118
|-
|-
|16
|16
|(0, 2, 8, 12)
|0, 2, 8, 12
|[1, 3]
| +1+?+3
|0.00119
|0.00119
|-
|-
|16
|16
|(0, 3, 4, 11)
|0, 3, 4, 11
|[1, 3]
| +1+?+3
|0.00148
|0.00148
|-
|-
|16
|16
|(0, 3, 8, 14)
|0, 3, 8, 14
|[1, 3]
| +1+?+3
|0.00103
|0.00103
|-
|-
|16
|16
|(0, 3, 10, 11)
|0, 3, 10, 11
|[2, 1]
| +2+?+1
|0.00074
|0.00074
|-
|-
|16
|16
|(0, 3, 11, 12)
|0, 3, 11, 12
|[2, 1]
| +2+?+1
|0.00127
|0.00127
|-
|-
|16
|16
|(0, 5, 7, 9)
|0, 5, 7, 9
|[2, 1]
| +2+?+1
|0.00109
|0.00109
|-
|-
|16
|16
|(0, 8, 9, 12)
|0, 8, 9, 12
|[2, 1]
| +2+?+1
|0.00143
|0.00143
|-
|-
|16
|16
|(0, 1, 9, 10)
|0, 1, 9, 10
|[2, 3]
| +2+?+3
|0.00050
|0.00050
|-
|-
|16
|16
|(0, 1, 10, 11)
|0, 1, 10, 11
|[2, 3]
| +2+?+3
|0.00091
|0.00091
|-
|-
|16
|16
|(0, 2, 9, 11)
|0, 2, 9, 11
|[2, 3]
| +2+?+3
|0.00102
|0.00102
|-
|-
|16
|16
|(0, 4, 8, 9)
|0, 4, 8, 9
|[3, 1]
| +3+?+1
|0.00031
|0.00031
|-
|-
|16
|16
|(0, 5, 14, 15)
|0, 5, 14, 15
|[3, 1]
| +3+?+1
|0.00040
|0.00040
|-
|-
|16
|16
|(0, 8, 10, 12)
|0, 8, 10, 12
|[3, 1]
| +3+?+1
|0.00104
|0.00104
|-
|-
|16
|16
|(0, 9, 13, 15)
|0, 9, 13, 15
|[3, 1]
| +3+?+1
|0.00001
|0.00001
|-
|-
|16
|16
|(0, 2, 7, 8)
|0, 2, 7, 8
|[3, 2]
| +3+?+2
|0.00024
|0.00024
|-
|-
|16
|16
|(0, 2, 8, 9)
|0, 2, 8, 9
|[3, 2]
| +3+?+2
|0.00145
|0.00145
|-
|-
|16
|16
|(0, 4, 8, 10)
|0, 4, 8, 10
|[3, 2]
| +3+?+2
|0.00119
|0.00119
|-
|-
|16
|16
|(0, 5, 13, 15)
|0, 5, 13, 15
|[3, 2]
| +3+?+2
|0.00146
|0.00146
|-
|-
|16
|16
|(0, 6, 8, 11)
|0, 6, 8, 11
|[3, 2]
| +3+?+2
|0.00103
|0.00103
|-
|-
|17
|17
|(0, 3, 10, 12)
|0, 3, 10, 12
|[1, 1]
| +1+?+1
|0.00137
|0.00137
|-
|-
|17
|17
|(0, 5, 6, 10)
|0, 5, 6, 10
|[1, 1]
| +1+?+1
|0.00006
|0.00006
|-
|-
|17
|17
|(0, 6, 11, 15)
|0, 6, 11, 15
|[1, 1]
| +1+?+1
|0.00014
|0.00014
|-
|-
|17
|17
|(0, 2, 7, 10)
|0, 2, 7, 10
|[1, 2]
| +1+?+2
|0.00129
|0.00129
|-
|-
|17
|17
|(0, 4, 6, 12)
|0, 4, 6, 12
|[1, 2]
| +1+?+2
|0.00013
|0.00013
|-
|-
|17
|17
|(0, 4, 11, 16)
|0, 4, 11, 16
|[1, 2]
| +1+?+2
|0.00007
|0.00007
|-
|-
|17
|17
|(0, 1, 9, 11)
|0, 1, 9, 11
|[1, 3]
| +1+?+3
|0.00067
|0.00067
|-
|-
|17
|17
|(0, 1, 10, 12)
|0, 1, 10, 12
|[1, 3]
| +1+?+3
|0.00087
|0.00087
|-
|-
|17
|17
|(0, 2, 3, 8)
|0, 2, 3, 8
|[1, 3]
| +1+?+3
|0.00020
|0.00020
|-
|-
|17
|17
|(0, 2, 9, 13)
|0, 2, 9, 13
|[1, 3]
| +1+?+3
|0.00024
|0.00024
|-
|-
|17
|17
|(0, 3, 4, 11)
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|-
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|-
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|-
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|-
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|-
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|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
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|-
|-
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|-
|-
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|-
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|-
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|-
|-
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|-
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|-
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|-
|-
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|-
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|-
|-
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|-
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|-
|-
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|-
|-
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|-
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|-
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|-
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|-
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|-
|-
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|-
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|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|20
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|-
|-
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|-
|-
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|20
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|-
|-
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|20
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|-
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|-
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|20
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|-
|-
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|20
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|-
|-
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|20
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|-
|-
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|20
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|-
|-
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|20
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|-
|-
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|20
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|-
|-
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|20
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|-
|-
|20
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
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|-
|-
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|-
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|-
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|-
|-
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|-
|-
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|-
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|-
|-
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|-
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|-
|-
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|-
|-
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|-
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|-
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|-
|-
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|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|0, 6, 15, 17
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|-
|-
|22
|22
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|0, 8, 12, 15
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|0.00090
|-
|-
|22
|22
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|0, 9, 16, 19
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|0.00013
|-
|-
|22
|22
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|0, 11, 14, 18
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|-
|-
|22
|22
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|0, 12, 17, 21
|[2, 1]
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|0.00018
|-
|-
|22
|22
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|-
|-
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|22
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|-
|-
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|22
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|-
|-
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|22
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|0, 4, 5, 10
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|-
|-
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|-
|-
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|-
|-
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|0, 6, 13, 19
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|-
|-
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|-
|-
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|(0, 7, 13, 20)
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|[2, 3]
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|-
|-
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|(0, 8, 13, 21)
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|-
|-
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|0, 4, 10, 11
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|0.00063
|-
|-
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|(0, 4, 11, 12)
|0, 4, 11, 12
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|-
|-
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|(0, 4, 12, 13)
|0, 4, 12, 13
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|-
|-
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|0, 5, 18, 19
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|0.00030
|-
|-
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|(0, 5, 19, 20)
|0, 5, 19, 20
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|0.00094
|-
|-
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|(0, 7, 8, 10)
|0, 7, 8, 10
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|-
|-
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|22
|(0, 8, 12, 14)
|0, 8, 12, 14
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|0.00043
|-
|-
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|0, 9, 16, 18
|[3, 1]
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|0.00111
|0.00111
|-
|-
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|(0, 9, 17, 19)
|0, 9, 17, 19
|[3, 1]
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|0.00127
|-
|-
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|0, 12, 14, 17
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|0.00064
|-
|-
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|22
|(0, 13, 17, 20)
|0, 13, 17, 20
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|0.00044
|-
|-
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|22
|(0, 2, 8, 9)
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|0.00139
|-
|-
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|(0, 2, 9, 10)
|0, 2, 9, 10
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|-
|-
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|22
|(0, 2, 10, 11)
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|-
|-
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|0.00122
|-
|-
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|-
|-
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|0, 5, 18, 20
|[3, 2]
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|-
|-
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|0, 6, 11, 14
|[3, 2]
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|0.00094
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|-
|-
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|0, 7, 16, 19
|[3, 2]
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|-
|-
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|(0, 8, 11, 15)
|0, 8, 11, 15
|[3, 2]
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|0.00074
|-
|-
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|(0, 10, 12, 17)
|0, 10, 12, 17
|[3, 2]
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|0.00135
|-
|-
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|23
|(0, 1, 2, 3)
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|[1, 1]
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|-
|-
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|23
|(0, 3, 14, 16)
|0, 3, 14, 16
|[1, 1]
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|-
|-
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|23
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|0, 4, 10, 13
|[1, 1]
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|0.00012
|-
|-
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|23
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|0, 5, 8, 12
|[1, 1]
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|-
|-
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|[1, 1]
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|-
|-
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|0, 7, 12, 17
|[1, 1]
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|0.00079
|-
|-
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|0, 8, 17, 22
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|-
|-
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|-
|-
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|0.00094
|-
|-
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|0.00146
|-
|-
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|[1, 2]
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|-
|-
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|0, 2, 10, 13
|[1, 2]
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|0.00149
|-
|-
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|[1, 2]
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|-
|-
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|(0, 3, 13, 17)
|0, 3, 13, 17
|[1, 2]
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|0.00013
|-
|-
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|(0, 4, 15, 20)
|0, 4, 15, 20
|[1, 2]
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|0.00027
|-
|-
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|23
|(0, 5, 6, 14)
|0, 5, 6, 14
|[1, 2]
| +1+?+2
|0.00058
|0.00058
|-
|-
|23
|23
|(0, 5, 11, 18)
|0, 5, 11, 18
|[1, 2]
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|0.00078
|0.00078
|-
|-
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|(0, 6, 8, 17)
|0, 6, 8, 17
|[1, 2]
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|-
|-
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|(0, 8, 11, 22)
|0, 8, 11, 22
|[1, 2]
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|-
|-
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|0.00078
|-
|-
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|-
|-
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|[1, 3]
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|-
|-
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|(0, 2, 4, 9)
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|-
|-
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|23
|(0, 2, 5, 10)
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|-
|-
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|(0, 2, 12, 16)
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|[1, 3]
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|0.00074
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|-
|-
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|-
|-
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|[1, 3]
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|-
|-
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|[1, 3]
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|-
|-
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|[1, 3]
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|-
|-
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|-
|-
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|-
|-
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|(0, 5, 11, 21)
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|-
|-
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|0.00071
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|-
|-
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|23
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|-
|-
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|(0, 5, 9, 11)
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|-
|-
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|23
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|[2, 1]
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|-
|-
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|-
|-
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|23
|(0, 8, 12, 15)
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|-
|-
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|23
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|[2, 1]
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|0.00144
|-
|-
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|23
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|0.00078
|-
|-
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|23
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|-
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|23
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|[2, 3]
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|-
|-
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|23
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|0.00030
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|-
|-
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|23
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|-
|-
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|23
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|-
|-
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|23
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|-
|-
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|23
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|-
|-
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|23
|(0, 3, 4, 8)
|0, 3, 4, 8
|[2, 3]
| +2+?+3
|0.00126
|0.00126
|-
|-
|23
|23
|(0, 3, 13, 16)
|0, 3, 13, 16
|[2, 3]
| +2+?+3
|0.00094
|0.00094
|-
|-
|23
|23
|(0, 3, 14, 17)
|0, 3, 14, 17
|[2, 3]
| +2+?+3
|0.00114
|0.00114
|-
|-
|23
|23
|(0, 4, 6, 11)
|0, 4, 6, 11
|[2, 3]
| +2+?+3
|0.00131
|0.00131
|-
|-
|23
|23
|(0, 4, 13, 17)
|0, 4, 13, 17
|[2, 3]
| +2+?+3
|0.00127
|0.00127
|-
|-
|23
|23
|(0, 5, 7, 13)
|0, 5, 7, 13
|[2, 3]
| +2+?+3
|0.00039
|0.00039
|-
|-
|23
|23
|(0, 6, 8, 15)
|0, 6, 8, 15
|[2, 3]
| +2+?+3
|0.00077
|0.00077
|-
|-
|23
|23
|(0, 8, 9, 18)
|0, 8, 9, 18
|[2, 3]
| +2+?+3
|0.00015
|0.00015
|-
|-
|23
|23
|(0, 4, 10, 11)
|0, 4, 10, 11
|[3, 1]
| +3+?+1
|0.00093
|0.00093
|-
|-
|23
|23
|(0, 4, 11, 12)
|0, 4, 11, 12
|[3, 1]
| +3+?+1
|0.00006
|0.00006
|-
|-
|23
|23
|(0, 4, 12, 13)
|0, 4, 12, 13
|[3, 1]
| +3+?+1
|0.00084
|0.00084
|-
|-
|23
|23
|(0, 5, 18, 19)
|0, 5, 18, 19
|[3, 1]
| +3+?+1
|0.00109
|0.00109
|-
|-
|23
|23
|(0, 5, 19, 20)
|0, 5, 19, 20
|[3, 1]
| +3+?+1
|0.00002
|0.00002
|-
|-
|23
|23
|(0, 5, 20, 21)
|0, 5, 20, 21
|[3, 1]
| +3+?+1
|0.00116
|0.00116
|-
|-
|23
|23
|(0, 7, 8, 10)
|0, 7, 8, 10
|[3, 1]
| +3+?+1
|0.00054
|0.00054
|-
|-
|23
|23
|(0, 8, 12, 14)
|0, 8, 12, 14
|[3, 1]
| +3+?+1
|0.00116
|0.00116
|-
|-
|23
|23
|(0, 8, 13, 15)
|0, 8, 13, 15
|[3, 1]
| +3+?+1
|0.00072
|0.00072
|-
|-
|23
|23
|(0, 9, 17, 19)
|0, 9, 17, 19
|[3, 1]
| +3+?+1
|0.00011
|0.00011
|-
|-
|23
|23
|(0, 12, 14, 17)
|0, 12, 14, 17
|[3, 1]
| +3+?+1
|0.00065
|0.00065
|-
|-
|23
|23
|(0, 13, 17, 20)
|0, 13, 17, 20
|[3, 1]
| +3+?+1
|0.00133
|0.00133
|-
|-
|23
|23
|(0, 2, 9, 10)
|0, 2, 9, 10
|[3, 2]
| +3+?+2
|0.00082
|0.00082
|-
|-
|23
|23
|(0, 2, 10, 11)
|0, 2, 10, 11
|[3, 2]
| +3+?+2
|0.00004
|0.00004
|-
|-
|23
|23
|(0, 2, 11, 12)
|0, 2, 11, 12
|[3, 2]
| +3+?+2
|0.00077
|0.00077
|-
|-
|23
|23
|(0, 4, 10, 12)
|0, 4, 10, 12
|[3, 2]
| +3+?+2
|0.00092
|0.00092
|-
|-
|23
|23
|(0, 4, 11, 13)
|0, 4, 11, 13
|[3, 2]
| +3+?+2
|0.00073
|0.00073
|-
|-
|23
|23
|(0, 5, 18, 20)
|0, 5, 18, 20
|[3, 2]
| +3+?+2
|0.00099
|0.00099
|-
|-
|23
|23
|(0, 5, 19, 21)
|0, 5, 19, 21
|[3, 2]
| +3+?+2
|0.00110
|0.00110
|-
|-
|23
|23
|(0, 6, 11, 14)
|0, 6, 11, 14
|[3, 2]
| +3+?+2
|0.00020
|0.00020
|-
|-
|23
|23
|(0, 7, 17, 20)
|0, 7, 17, 20
|[3, 2]
| +3+?+2
|0.00088
|0.00088
|-
|-
|23
|23
|(0, 8, 12, 16)
|0, 8, 12, 16
|[3, 2]
| +3+?+2
|0.00139
|0.00139
|-
|-
|23
|23
|(0, 9, 16, 20)
|0, 9, 16, 20
|[3, 2]
| +3+?+2
|0.00014
|0.00014
|-
|-
|23
|23
|(0, 10, 12, 17)
|0, 10, 12, 17
|[3, 2]
| +3+?+2
|0.00063
|0.00063
|-
|-
|23
|23
|(0, 11, 16, 21)
|0, 11, 16, 21
|[3, 2]
| +3+?+2
|0.00087
|0.00087
|-
|-
|23
|23
|(0, 13, 16, 22)
|0, 13, 16, 22
|[3, 2]
| +3+?+2
|0.00081
|0.00081
|}
|}

Revision as of 13:15, 10 September 2024

Shown below are approximate partially delta-rational tetrads 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.

Edo Steps 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 0, 3, 4, 9 +1+?+2 0.00073
20 0, 3, 11, 15 +1+?+2 0.00058
20 0, 4, 7, 13 +1+?+2 0.00114
20 0, 4, 13, 18 +1+?+2 0.00020
20 0, 5, 9, 16 +1+?+2 0.00137
20 0, 7, 8, 18 +1+?+2 0.00105
20 0, 1, 10, 12 +1+?+3 0.00129
20 0, 1, 11, 13 +1+?+3 0.00021
20 0, 1, 12, 14 +1+?+3 0.00090
20 0, 2, 4, 9 +1+?+3 0.00061
20 0, 2, 11, 15 +1+?+3 0.00072
20 0, 3, 5, 12 +1+?+3 0.00066
20 0, 3, 10, 16 +1+?+3 0.00055
20 0, 4, 6, 15 +1+?+3 0.00137
20 0, 5, 6, 17 +1+?+3 0.00113
20 0, 5, 9, 19 +1+?+3 0.00054
20 0, 3, 12, 13 +2+?+1 0.00089
20 0, 3, 13, 14 +2+?+1 0.00037
20 0, 5, 8, 10 +2+?+1 0.00007
20 0, 6, 14, 16 +2+?+1 0.00068
20 0, 8, 11, 14 +2+?+1 0.00044
20 0, 9, 15, 18 +2+?+1 0.00084
20 0, 11, 13, 17 +2+?+1 0.00086
20 0, 1, 10, 11 +2+?+3 0.00147
20 0, 1, 11, 12 +2+?+3 0.00061
20 0, 1, 12, 13 +2+?+3 0.00027
20 0, 1, 13, 14 +2+?+3 0.00118
20 0, 2, 11, 13 +2+?+3 0.00125
20 0, 2, 12, 14 +2+?+3 0.00055
20 0, 3, 12, 15 +2+?+3 0.00084
20 0, 4, 5, 10 +2+?+3 0.00095
20 0, 4, 12, 16 +2+?+3 0.00113
20 0, 5, 6, 12 +2+?+3 0.00037
20 0, 5, 12, 17 +2+?+3 0.00144
20 0, 4, 9, 10 +3+?+1 0.00096
20 0, 4, 10, 11 +3+?+1 0.00021
20 0, 4, 11, 12 +3+?+1 0.00142
20 0, 5, 16, 17 +3+?+1 0.00115
20 0, 5, 17, 18 +3+?+1 0.00034
20 0, 8, 11, 13 +3+?+1 0.00098
20 0, 9, 15, 17 +3+?+1 0.00090
20 0, 12, 13, 16 +3+?+1 0.00002
20 0, 13, 16, 19 +3+?+1 0.00072
20 0, 2, 8, 9 +3+?+2 0.00084
20 0, 2, 9, 10 +3+?+2 0.00021
20 0, 2, 10, 11 +3+?+2 0.00129
20 0, 4, 9, 11 +3+?+2 0.00070
20 0, 5, 16, 18 +3+?+2 0.00075
20 0, 6, 10, 13 +3+?+2 0.00055
20 0, 7, 15, 18 +3+?+2 0.00079
20 0, 10, 11, 16 +3+?+2 0.00056
20 0, 11, 14, 19 +3+?+2 0.00129
21 0, 1, 2, 3 +1+?+1 0.00132
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