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== Delta-rational harmony ==
== Delta-rational harmony ==
The tables below show chords that approximate 3-integer-limit [[delta-rational]] chords with least-squares error less than 0.0011.
The tables below show chords that approximate 3-integer-limit [[delta-rational]] chords with least-squares error less than 0.001.


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=== Fully delta-rational triads ===
=== Fully delta-rational triads ===
{| class="wikitable"
|(0,1,2)
|[1, 1]
|0.00021
|-
|(0,1,3)
|[1, 2]
|0.00048
|-
|(0,1,4)
|[1, 3]
|0.00078
|-
|(0,2,3)
|[2, 1]
|0.00039
|-
|(0,2,4)
|[1, 1]
|0.00087
|-
|(0,3,4)
|[3, 1]
|0.00056
|-
|(0,3,11)
|[1, 3]
|0.00007
|-
|(0,5,8)
|[3, 2]
|0.00084
|-
|(0,8,18)
|[2, 3]
|0.00082
|-
|(0,9,20)
|[2, 3]
|0.00076
|-
|(0,12,17)
|[2, 1]
|0.00048
|-
|(0,13,20)
|[3, 2]
|0.00063
|-
|(0,15,21)
|[2, 1]
|0.00063
|-
|(0,16,28)
|[1, 1]
|0.00082
|-
|(0,18,25)
|[2, 1]
|0.00081
|-
|(0,18,31)
|[1, 1]
|0.00058
|-
|(0,19,24)
|[3, 1]
|0.00095
|}
=== Partially delta-rational tetrads ===
=== Partially delta-rational tetrads ===
{| class="wikitable"
|(0,1,2,3)
|[1, 1]
|0.00053
|-
|(0,1,2,4)
|[1, 2]
|0.00094
|-
|(0,1,3,4)
|[1, 1]
|0.00080
|-
|(0,1,17,18)
|[2, 3]
|0.00073
|-
|(0,1,17,19)
|[1, 3]
|0.00071
|-
|(0,1,18,19)
|[2, 3]
|0.00042
|-
|(0,1,18,20)
|[1, 3]
|0.00032
|-
|(0,1,19,20)
|[2, 3]
|0.00010
|-
|(0,1,19,21)
|[1, 3]
|0.00008
|-
|(0,1,20,21)
|[2, 3]
|0.00023
|-
|(0,1,20,22)
|[1, 3]
|0.00049
|-
|(0,1,21,22)
|[2, 3]
|0.00056
|-
|(0,1,21,23)
|[1, 3]
|0.00091
|-
|(0,1,22,23)
|[2, 3]
|0.00090
|-
|(0,1,31,32)
|[1, 2]
|0.00071
|-
|(0,2,3,4)
|[2, 1]
|0.00077
|-
|(0,2,6,11)
|[1, 3]
|0.00094
|-
|(0,2,7,12)
|[1, 3]
|0.00013
|-
|(0,2,8,13)
|[1, 3]
|0.00069
|-
|(0,2,12,13)
|[3, 2]
|0.00083
|-
|(0,2,12,15)
|[1, 2]
|0.00087
|-
|(0,2,13,14)
|[3, 2]
|0.00045
|-
|(0,2,13,16)
|[1, 2]
|0.00014
|-
|(0,2,14,15)
|[3, 2]
|0.00008
|-
|(0,2,14,17)
|[1, 2]
|0.00060
|-
|(0,2,15,16)
|[3, 2]
|0.00031
|-
|(0,2,16,17)
|[3, 2]
|0.00071
|-
|(0,2,18,20)
|[2, 3]
|0.00084
|-
|(0,2,18,22)
|[1, 3]
|0.00024
|-
|(0,2,19,21)
|[2, 3]
|0.00020
|-
|(0,2,19,23)
|[1, 3]
|0.00058
|-
|(0,2,20,22)
|[2, 3]
|0.00046
|-
|(0,3,4,5)
|[3, 1]
|0.00097
|-
|(0,3,5,9)
|[2, 3]
|0.00010
|-
|(0,3,6,10)
|[2, 3]
|0.00090
|-
|(0,3,7,12)
|[1, 2]
|0.00074
|-
|(0,3,8,13)
|[1, 2]
|0.00037
|-
|(0,3,10,17)
|[1, 3]
|0.00009
|-
|(0,3,17,23)
|[1, 3]
|0.00096
|-
|(0,3,18,22)
|[1, 2]
|0.00088
|-
|(0,3,18,24)
|[1, 3]
|0.00027
|-
|(0,3,19,20)
|[2, 1]
|0.00059
|-
|(0,3,19,21)
|[1, 1]
|0.00063
|-
|(0,3,19,22)
|[2, 3]
|0.00030
|-
|(0,3,19,23)
|[1, 2]
|0.00023
|-
|(0,3,20,21)
|[2, 1]
|0.00014
|-
|(0,3,20,22)
|[1, 1]
|0.00015
|-
|(0,3,20,23)
|[2, 3]
|0.00070
|-
|(0,3,21,22)
|[2, 1]
|0.00032
|-
|(0,3,21,23)
|[1, 1]
|0.00095
|-
|(0,3,22,23)
|[2, 1]
|0.00078
|-
|(0,3,27,32)
|[1, 3]
|0.00004
|-
|(0,4,5,12)
|[1, 2]
|0.00026
|-
|(0,4,6,16)
|[1, 3]
|0.00066
|-
|(0,4,8,13)
|[2, 3]
|0.00023
|-
|(0,4,11,20)
|[1, 3]
|0.00023
|-
|(0,4,13,14)
|[3, 1]
|0.00091
|-
|(0,4,13,19)
|[1, 2]
|0.00048
|-
|(0,4,14,15)
|[3, 1]
|0.00050
|-
|(0,4,14,16)
|[3, 2]
|0.00055
|-
|(0,4,14,17)
|[1, 1]
|0.00021
|-
|(0,4,15,16)
|[3, 1]
|0.00009
|-
|(0,4,15,17)
|[3, 2]
|0.00023
|-
|(0,4,15,18)
|[1, 1]
|0.00085
|-
|(0,4,16,17)
|[3, 1]
|0.00034
|-
|(0,4,17,18)
|[3, 1]
|0.00077
|-
|(0,4,17,25)
|[1, 3]
|0.00043
|-
|(0,4,19,23)
|[2, 3]
|0.00041
|-
|(0,4,20,24)
|[2, 3]
|0.00094
|-
|(0,4,22,27)
|[1, 2]
|0.00020
|-
|(0,4,24,31)
|[1, 3]
|0.00022
|-
|(0,5,6,9)
|[3, 2]
|0.00003
|-
|(0,5,7,10)
|[3, 2]
|0.00097
|-
|(0,5,7,19)
|[1, 3]
|0.00004
|-
|(0,5,9,17)
|[1, 2]
|0.00017
|-
|(0,5,10,16)
|[2, 3]
|0.00019
|-
|(0,5,11,13)
|[2, 1]
|0.00087
|-
|(0,5,11,15)
|[1, 1]
|0.00018
|-
|(0,5,12,14)
|[2, 1]
|0.00011
|-
|(0,5,12,23)
|[1, 3]
|0.00067
|-
|(0,5,13,15)
|[2, 1]
|0.00067
|-
|(0,5,16,23)
|[1, 2]
|0.00008
|-
|(0,5,17,27)
|[1, 3]
|0.00055
|-
|(0,5,19,24)
|[2, 3]
|0.00051
|-
|(0,5,22,31)
|[1, 3]
|0.00057
|-
|(0,5,24,30)
|[1, 2]
|0.00036
|-
|(0,5,25,26)
|[3, 1]
|0.00071
|-
|(0,5,25,27)
|[3, 2]
|0.00082
|-
|(0,5,25,28)
|[1, 1]
|0.00045
|-
|(0,5,26,27)
|[3, 1]
|0.00018
|-
|(0,5,26,28)
|[3, 2]
|0.00016
|-
|(0,5,26,29)
|[1, 1]
|0.00090
|-
|(0,5,27,28)
|[3, 1]
|0.00035
|-
|(0,5,28,29)
|[3, 1]
|0.00090
|-
|(0,6,7,17)
|[1, 2]
|0.00087
|-
|(0,6,8,22)
|[1, 3]
|0.00045
|-
|(0,6,9,14)
|[1, 1]
|0.00031
|-
|(0,6,11,18)
|[2, 3]
|0.00093
|-
|(0,6,12,21)
|[1, 2]
|0.00036
|-
|(0,6,12,25)
|[1, 3]
|0.00032
|-
|(0,6,15,18)
|[3, 2]
|0.00026
|-
|(0,6,16,19)
|[3, 2]
|0.00095
|-
|(0,6,16,28)
|[1, 3]
|0.00053
|-
|(0,6,18,26)
|[1, 2]
|0.00064
|-
|(0,6,19,25)
|[2, 3]
|0.00062
|-
|(0,6,20,24)
|[1, 1]
|0.00052
|-
|(0,6,21,23)
|[2, 1]
|0.00031
|-
|(0,6,21,32)
|[1, 3]
|0.00033
|-
|(0,6,22,24)
|[2, 1]
|0.00063
|-
|(0,6,25,32)
|[1, 2]
|0.00034
|-
|(0,7,8,14)
|[1, 1]
|0.00029
|-
|(0,7,8,24)
|[1, 3]
|0.00080
|-
|(0,7,9,11)
|[3, 1]
|0.00066
|-
|(0,7,9,12)
|[2, 1]
|0.00041
|-
|(0,7,9,13)
|[3, 2]
|0.00019
|-
|(0,7,10,12)
|[3, 1]
|0.00009
|-
|(0,7,10,13)
|[2, 1]
|0.00070
|-
|(0,7,11,13)
|[3, 1]
|0.00087
|-
|(0,7,12,27)
|[1, 3]
|0.00041
|-
|(0,7,16,30)
|[1, 3]
|0.00098
|-
|(0,7,17,22)
|[1, 1]
|0.00008
|-
|(0,7,19,26)
|[2, 3]
|0.00073
|-
|(0,7,20,29)
|[1, 2]
|0.00002
|-
|(0,7,23,26)
|[3, 2]
|0.00010
|-
|(0,7,28,32)
|[1, 1]
|0.00033
|-
|(0,7,29,31)
|[2, 1]
|0.00020
|-
|(0,7,30,32)
|[2, 1]
|0.00091
|-
|(0,8,12,29)
|[1, 3]
|0.00097
|-
|(0,8,13,22)
|[2, 3]
|0.00051
|-
|(0,8,15,21)
|[1, 1]
|0.00062
|-
|(0,8,15,31)
|[1, 3]
|0.00047
|-
|(0,8,16,18)
|[3, 1]
|0.00066
|-
|(0,8,16,19)
|[2, 1]
|0.00031
|-
|(0,8,16,20)
|[3, 2]
|0.00043
|-
|(0,8,16,27)
|[1, 2]
|0.00090
|-
|(0,8,17,19)
|[3, 1]
|0.00022
|-
|(0,8,17,20)
|[2, 1]
|0.00098
|-
|(0,8,19,27)
|[2, 3]
|0.00085
|-
|(0,8,24,29)
|[1, 1]
|0.00020
|-
|(0,9,11,16)
|[3, 2]
|0.00051
|-
|(0,9,13,20)
|[1, 1]
|0.00002
|-
|(0,9,14,24)
|[2, 3]
|0.00073
|-
|(0,9,18,30)
|[1, 2]
|0.00090
|-
|(0,9,19,28)
|[2, 3]
|0.00096
|-
|(0,9,21,27)
|[1, 1]
|0.00040
|-
|(0,9,22,24)
|[3, 1]
|0.00087
|-
|(0,9,22,25)
|[2, 1]
|0.00053
|-
|(0,9,22,26)
|[3, 2]
|0.00026
|-
|(0,9,23,25)
|[3, 1]
|0.00013
|-
|(0,9,23,26)
|[2, 1]
|0.00093
|-
|(0,10,11,26)
|[1, 2]
|0.00035
|-
|(0,10,11,32)
|[1, 3]
|0.00081
|-
|(0,10,12,20)
|[1, 1]
|0.00098
|-
|(0,10,14,18)
|[2, 1]
|0.00050
|-
|(0,10,14,25)
|[2, 3]
|0.00088
|-
|(0,10,15,29)
|[1, 2]
|0.00041
|-
|(0,10,16,21)
|[3, 2]
|0.00055
|-
|(0,10,19,32)
|[1, 2]
|0.00021
|-
|(0,10,27,31)
|[3, 2]
|0.00082
|-
|(0,10,28,30)
|[3, 1]
|0.00045
|-
|(0,10,28,31)
|[2, 1]
|0.00016
|-
|(0,10,29,31)
|[3, 1]
|0.00068
|-
|(0,11,12,18)
|[3, 2]
|0.00030
|-
|(0,11,13,16)
|[3, 1]
|0.00081
|-
|(0,11,14,17)
|[3, 1]
|0.00044
|-
|(0,11,16,31)
|[1, 2]
|0.00064
|-
|(0,11,17,25)
|[1, 1]
|0.00091
|-
|(0,11,19,23)
|[2, 1]
|0.00045
|-
|(0,11,21,26)
|[3, 2]
|0.00074
|-
|(0,12,15,24)
|[1, 1]
|0.00087
|-
|(0,12,15,28)
|[2, 3]
|0.00013
|-
|(0,12,17,23)
|[3, 2]
|0.00054
|-
|(0,12,18,21)
|[3, 1]
|0.00043
|-
|(0,12,19,22)
|[3, 1]
|0.00095
|-
|(0,12,23,27)
|[2, 1]
|0.00083
|-
|(0,12,26,31)
|[3, 2]
|0.00005
|-
|(0,13,14,24)
|[1, 1]
|0.00019
|-
|(0,13,17,22)
|[2, 1]
|0.00085
|-
|(0,13,21,27)
|[3, 2]
|0.00035
|-
|(0,13,22,25)
|[3, 1]
|0.00097
|-
|(0,13,23,26)
|[3, 1]
|0.00054
|-
|(0,13,28,32)
|[2, 1]
|0.00055
|-
|(0,14,17,24)
|[3, 2]
|0.00099
|-
|(0,14,18,28)
|[1, 1]
|0.00043
|-
|(0,14,21,26)
|[2, 1]
|0.00080
|-
|(0,14,25,31)
|[3, 2]
|0.00054
|-
|(0,14,27,30)
|[3, 1]
|0.00050
|-
|(0,15,16,20)
|[3, 1]
|0.00055
|-
|(0,15,17,28)
|[1, 1]
|0.00064
|-
|(0,15,21,28)
|[3, 2]
|0.00045
|-
|(0,15,22,32)
|[1, 1]
|0.00039
|-
|(0,16,18,26)
|[3, 2]
|0.00049
|-
|(0,16,19,25)
|[2, 1]
|0.00031
|-
|(0,16,20,24)
|[3, 1]
|0.00018
|-
|(0,16,25,32)
|[3, 2]
|0.00095
|-
|(0,17,22,28)
|[2, 1]
|0.00091
|-
|(0,17,23,27)
|[3, 1]
|0.00066
|-
|(0,18,27,31)
|[3, 1]
|0.00095
|-
|(0,19,21,28)
|[2, 1]
|0.00065
|-
|(0,20,24,31)
|[2, 1]
|0.00078
|-
|(0,21,22,32)
|[3, 2]
|0.00091
|-
|(0,22,27,32)
|[3, 1]
|0.00038
|}


== Instruments ==
== Instruments ==
Retrieved from "https://en.xen.wiki/w/33edo"