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Relative errors of small EDOs: Difference between revisions

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This article contains two lists. The first shows [[relative error]]s of the first 9 prime harmonics for [[EDO|EDOs]] up to 99. There is no point for showing higher primes because no EDO under 99 is consistent up to them. For other intervals, the relative error follows the additive rule, so they can be derived easily.  
The following table shows [[relative error]]s of the first 9 prime harmonics for [[edo]]s up to 99. There is no point for showing higher primes because no edo under 99 is [[consistent]] up to odd limits higher than 23. The relative errors of other intervals can be derived easily since they follow the [[Relative interval error #Computation|additive rule]].  


The second shows the [[TE simple badness]]es aka relative errors in a certain JI subgroup for EDOs up to 99. 
__TOC__
== List of relative errors of prime harmonics for small EDOs ==
{| class="wikitable sortable mw-collapsible" style="text-align:right"
{| class="wikitable sortable mw-collapsible" style="text-align:right"
! rowspan="2" | EDO
! rowspan="2" | EDO
Line 1,007: Line 1,003:
|  45.52
|  45.52
|  16.74
|  16.74
|}
== List of TE simple badnesses for small EDOs ==
Notes: 
# [[Patent val]] mapping is used throughout.
# Each EDO is TE-optimally stretched.
# [[Graham Breed]]'s definition is used, scaled by 100. 
{| class="wikitable sortable mw-collapsible" style="text-align:right"
! rowspan="2" | EDO
! colspan="8" | TE simple badness × 100
|-
! 3 Limit
! 5 Limit
! 7 Limit
! 11 Limit
! 13 Limit
! 17 Limit
! 19 Limit
! 23 Limit
|-
| 1
| 13.09
| 16.61
| 14.43
| 14.79
| 13.75
| 12.83
| 12.25
| 11.95
|-
| 2
| 5.36
| 10.69
| 10.66
| 9.58
| 10.37
| 9.82
| 10.07
| 9.50
|-
| 3
| 7.73
| 6.97
| 10.80
| 10.68
| 9.76
| 9.17
| 9.04
| 9.20
|-
| 4
| 10.72
| 8.79
| 7.73
| 9.20
| 9.67
| 9.02
| 8.67
| 8.22
|-
| 5
| 2.37
| 7.08
| 7.15
| 8.41
| 8.72
| 9.61
| 9.34
| 9.11
|-
| 6
| 15.46
| 13.94
| 12.32
| 11.08
| 11.52
| 10.79
| 11.89
| 11.51
|-
| 7
| 2.99
| 4.46
| 8.72
| 8.06
| 7.57
| 7.97
| 7.72
| 7.55
|-
| 8
| 10.10
| 9.11
| 14.89
| 13.41
| 12.35
| 11.44
| 10.92
| 10.81
|-
| 9
| 8.35
| 9.09
| 8.21
| 7.37
| 6.83
| 7.37
| 6.91
| 7.32
|-
| 10
| 4.74
| 7.73
| 6.79
| 7.83
| 7.19
| 6.68
| 7.58
| 7.34
|-
| 11
| 13.71
| 19.34
| 17.01
| 15.22
| 14.29
| 13.23
| 12.52
| 11.88
|-
| 12
| 0.62
| 3.11
| 4.94
| 5.99
| 8.35
| 7.88
| 7.40
| 7.47
|-
| 13
| 12.48
| 14.02
| 15.79
| 14.13
| 12.94
| 12.03
| 11.34
| 10.84
|-
| 14
| 5.98
| 13.72
| 13.32
| 12.86
| 12.12
| 11.31
| 10.99
| 10.44
|-
| 15
| 7.12
| 5.81
| 6.97
| 6.25
| 6.65
| 7.73
| 7.29
| 6.88
|-
| 16
| 11.34
| 9.53
| 9.91
| 8.98
| 8.22
| 7.67
| 7.67
| 7.26
|-
| 17
| 1.76
| 10.52
| 11.30
| 10.51
| 9.65
| 9.88
| 9.32
| 8.88
|-
| 18
| 14.85
| 12.45
| 10.91
| 13.03
| 11.90
| 11.02
| 12.37
| 12.77
|-
| 19
| 3.61
| 3.02
| 4.35
| 6.79
| 6.47
| 7.40
| 7.56
| 7.17
|-
| 20
| 9.49
| 15.46
| 13.58
| 12.26
| 11.21
| 10.75
| 10.07
| 9.99
|-
| 21
| 8.97
| 11.67
| 10.27
| 10.30
| 9.76
| 9.06
| 8.80
| 8.31
|-
| 22
| 4.13
| 4.94
| 5.23
| 5.33
| 6.89
| 6.42
| 6.99
| 7.57
|-
| 23
| 14.33
| 11.79
| 16.76
| 17.03
| 15.55
| 14.44
| 13.91
| 13.12
|-
| 24
| 1.23
| 6.22
| 8.95
| 8.01
| 7.66
| 7.14
| 6.70
| 7.02
|-
| 25
| 11.86
| 11.70
| 11.76
| 12.70
| 12.57
| 11.89
| 11.30
| 10.68
|-
| 26
| 6.59
| 6.96
| 7.43
| 7.51
| 6.86
| 6.37
| 6.17
| 7.45
|-
| 27
| 6.50
| 6.19
| 5.40
| 9.37
| 8.58
| 9.13
| 8.70
| 8.41
|-
| 28
| 11.95
| 11.13
| 13.62
| 12.46
| 12.19
| 12.00
| 11.25
| 10.92
|-
| 29
| 1.14
| 7.41
| 7.91
| 7.15
| 6.54
| 8.94
| 8.36
| 7.89
|-
| 30
| 14.23
| 11.62
| 13.94
| 12.51
| 11.87
| 11.02
| 11.82
| 11.15
|-
| 31
| 4.22
| 4.20
| 3.70
| 3.84
| 5.35
| 5.75
| 5.93
| 5.89
|-
| 32
| 8.87
| 12.60
| 11.07
| 10.18
| 10.85
| 10.13
| 9.47
| 9.00
|-
| 33
| 9.58
| 14.46
| 13.86
| 12.72
| 11.71
| 10.87
| 10.30
| 9.91
|-
| 34
| 3.51
| 2.92
| 8.67
| 9.26
| 8.59
| 7.96
| 8.36
| 8.01
|-
| 35
| 14.94
| 12.31
| 10.85
| 10.54
| 13.06
| 12.22
| 12.27
| 11.61
|-
| 36
| 1.85
| 9.33
| 8.63
| 8.76
| 8.96
| 8.63
| 8.08
| 7.62
|-
| 37
| 11.24
| 9.82
| 8.70
| 8.37
| 7.78
| 8.21
| 8.13
| 8.42
|-
| 38
| 7.21
| 6.04
| 9.96
| 9.76
| 10.64
| 10.02
| 9.62
| 9.30
|-
| 39
| 5.88
| 7.89
| 13.78
| 12.34
| 12.08
| 11.86
| 11.42
| 11.21
|-
| 40
| 12.57
| 13.28
| 11.62
| 10.48
| 9.99
| 9.43
| 9.38
| 9.18
|-
| 41
| 0.52
| 4.31
| 3.76
| 4.51
| 5.29
| 6.00
| 5.90
| 6.59
|-
| 42
| 13.61
| 11.60
| 11.45
| 13.33
| 14.24
| 13.22
| 13.36
| 12.64
|-
| 43
| 4.84
| 6.75
| 7.56
| 7.08
| 6.85
| 6.49
| 6.35
| 6.45
|-
| 44
| 8.25
| 9.89
| 10.45
| 10.66
| 9.74
| 9.02
| 8.46
| 8.11
|-
| 45
| 10.20
| 9.75
| 8.49
| 11.84
| 13.50
| 12.72
| 11.90
| 12.03
|-
| 46
| 2.89
| 3.45
| 5.12
| 5.20
| 5.42
| 5.02
| 5.62
| 5.30
|-
| 47
| 15.56
| 13.54
| 13.24
| 14.39
| 13.38
| 12.39
| 12.20
| 11.98
|-
| 48
| 2.47
| 8.27
| 10.25
| 9.22
| 9.84
| 9.20
| 8.71
| 8.23
|-
| 49
| 10.63
| 8.69
| 7.87
| 7.11
| 10.12
| 10.85
| 10.67
| 10.09
|-
| 50
| 7.83
| 6.62
| 6.39
| 6.76
| 6.54
| 6.19
| 5.90
| 5.62
|-
| 51
| 5.27
| 11.79
| 10.34
| 9.93
| 10.23
| 9.89
| 10.15
| 10.01
|-
| 52
| 13.19
| 15.75
| 13.86
| 12.69
| 12.08
| 12.33
| 11.62
| 11.02
|-
| 53
| 0.10
| 1.22
| 3.81
| 5.65
| 5.22
| 6.05
| 5.76
| 5.75
|-
| 54
| 13.00
| 17.51
| 15.92
| 14.24
| 13.01
| 12.05
| 12.31
| 12.02
|-
| 55
| 5.46
| 9.63
| 10.57
| 9.63
| 10.83
| 10.23
| 10.02
| 9.52
|-
| 56
| 7.64
| 7.50
| 8.38
| 7.90
| 7.95
| 7.37
| 6.90
| 7.07
|-
| 57
| 10.82
| 9.06
| 9.30
| 8.47
| 8.68
| 8.41
| 7.92
| 7.98
|-
| 58
| 2.28
| 5.89
| 5.10
| 4.83
| 4.56
| 5.33
| 7.07
| 7.72
|-
| 59
| 15.37
| 14.43
| 12.55
| 12.56
| 13.10
| 12.56
| 11.85
| 11.19
|-
| 60
| 3.08
| 5.56
| 6.23
| 10.22
| 9.44
| 8.77
| 8.54
| 8.26
|-
| 61
| 10.01
| 8.59
| 11.66
| 10.84
| 9.93
| 10.38
| 9.95
| 9.39
|-
| 62
| 8.44
| 8.40
| 7.40
| 7.67
| 7.28
| 6.83
| 6.40
| 6.09
|-
| 63
| 4.65
| 8.77
| 8.00
| 7.17
| 6.73
| 7.50
| 7.41
| 7.03
|-
| 64
| 13.80
| 18.41
| 17.26
| 16.16
| 14.96
| 14.36
| 13.46
| 13.07
|-
| 65
| 0.71
| 1.94
| 7.82
| 7.65
| 8.94
| 8.68
| 8.23
| 7.77
|-
| 66
| 12.38
| 14.83
| 14.37
| 13.50
| 12.47
| 11.84
| 11.36
| 11.32
|-
| 67
| 6.07
| 12.62
| 11.18
| 10.24
| 9.35
| 8.67
| 8.44
| 8.10
|-
| 68
| 7.02
| 5.84
| 5.19
| 6.84
| 6.75
| 6.34
| 5.93
| 5.81
|-
| 69
| 11.43
| 9.40
| 12.23
| 12.30
| 11.48
| 10.67
| 9.98
| 9.41
|-
| 70
| 1.66
| 8.76
| 8.63
| 9.73
| 9.37
| 9.21
| 9.62
| 9.20
|-
| 71
| 14.75
| 12.71
| 14.95
| 13.52
| 12.34
| 12.20
| 11.49
| 11.25
|-
| 72
| 3.70
| 3.56
| 3.09
| 2.96
| 3.82
| 3.59
| 4.57
| 5.60
|-
| 73
| 9.39
| 9.56
| 9.59
| 8.65
| 9.62
| 10.93
| 10.60
| 10.47
|-
| 74
| 9.06
| 10.80
| 10.83
| 9.69
| 9.02
| 9.36
| 9.06
| 8.88
|-
| 75
| 4.03
| 5.85
| 8.36
| 10.29
| 10.36
| 9.98
| 9.51
| 9.57
|-
| 76
| 14.42
| 12.07
| 10.57
| 11.84
| 11.01
| 12.28
| 12.13
| 11.98
|-
| 77
| 1.33
| 5.04
| 5.59
| 6.66
| 6.25
| 6.42
| 6.03
| 6.03
|-
| 78
| 11.76
| 12.37
| 10.95
| 9.80
| 9.14
| 8.47
| 9.09
| 8.57
|-
| 79
| 6.69
| 7.84
| 10.49
| 9.43
| 8.66
| 8.64
| 9.55
| 9.10
|-
| 80
| 6.40
| 5.59
| 5.68
| 5.17
| 6.01
| 6.12
| 5.78
| 5.56
|-
| 81
| 12.05
| 10.67
| 9.49
| 8.65
| 10.05
| 9.45
| 8.94
| 8.50
|-
| 82
| 1.04
| 8.62
| 7.52
| 9.02
| 8.92
| 8.26
| 7.82
| 7.62
|-
| 83
| 14.14
| 11.58
| 11.68
| 11.82
| 11.53
| 11.44
| 10.90
| 11.25
|-
| 84
| 4.32
| 3.72
| 5.39
| 7.02
| 6.50
| 7.05
| 6.70
| 6.32
|-
| 85
| 8.78
| 13.57
| 12.98
| 11.80
| 11.37
| 11.76
| 11.08
| 10.84
|-
| 86
| 9.68
| 13.50
| 13.06
| 14.03
| 12.95
| 12.94
| 12.35
| 11.64
|-
| 87
| 3.42
| 3.30
| 5.45
| 4.90
| 4.53
| 5.35
| 5.77
| 5.92
|-
| 88
| 15.04
| 12.29
| 12.05
| 10.79
| 12.68
| 12.94
| 12.56
| 11.88
|-
| 89
| 1.95
| 8.15
| 7.08
| 6.35
| 7.57
| 7.12
| 6.77
| 6.77
|-
| 90
| 11.15
| 10.25
| 9.07
| 11.10
| 10.39
| 9.62
| 9.75
| 9.33
|-
| 91
| 7.31
| 6.49
| 6.51
| 8.82
| 9.74
| 9.28
| 9.95
| 9.93
|-
| 92
| 5.79
| 6.91
| 10.24
| 10.40
| 10.83
| 10.03
| 9.52
| 9.06
|-
| 93
| 12.67
| 12.60
| 11.09
| 11.46
| 10.46
| 9.68
| 9.09
| 9.14
|-
| 94
| 0.43
| 5.52
| 5.74
| 5.35
| 5.48
| 5.28
| 5.24
| 4.99
|-
| 95
| 13.52
| 11.23
| 9.90
| 8.98
| 8.20
| 10.47
| 9.80
| 9.34
|-
| 96
| 4.93
| 5.86
| 9.86
| 9.14
| 8.90
| 8.96
| 8.59
| 8.28
|-
| 97
| 8.16
| 10.76
| 10.97
| 11.24
| 10.26
| 10.60
| 9.92
| 9.49
|-
| 98
| 10.29
| 16.34
| 14.25
| 12.75
| 12.32
| 11.92
| 11.54
| 11.15
|-
| 99
| 2.80
| 2.63
| 2.33
| 7.27
| 7.48
| 7.75
| 8.09
| 7.67
|}
|}


== See also ==
== See also ==
* [[EDO]]
* Relative errors of small ed-''p''<span/>'s:
* [[Relative error]]
** [[Relative errors of small EDTs]]
* [[Relative errors of small EDTs]]
** [[Relative errors of small EDFs]]
* [[Relative errors of small EDFs]]
** [[Relative errors of small ED5s]]
* [[Relative errors of small ED5s]]
** [[Relative errors of small ED6s]]
* [[Relative errors of small ED6s]]
* [[Relative errors of small equal temperaments]]


[[Category:EDO theory pages]]
[[Category:EDO theory pages]]
[[Category:Tables]]
[[Category:Tables]]
Retrieved from "https://en.xen.wiki/w/Relative_errors_of_small_EDOs"