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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|relative errors]] 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. Also by that rule, however, finding large errors with such ''p''/1 harmonies will not suffice that the edo does a poor approximation in the ''p''-limit overall. One must inspect every relevant interval to be sure of that. The second list comes in naturally for showing the root-mean-squared relative errors of a certain JI subgroup, and may be used as a criterion. 
This article contains two lists. The first shows [[Relative error|relative errors]] 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.  


== List of Relative Errors of Prime Harmonies for Small Edos ==
The second shows the [[TE simple badness|TE simple badnesses]] aka relative errors in a certain JI subgroup for edos up to 99. 
 
== 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 1,108: Line 1,110:
|}
|}


== List of RMS Relative Errors of JI Subgroups for Small Edos ==
== List of TE simple badnesses for small edos ==
Notes:   
Notes:   
# Patent val mapping is used throughout.   
# [[Patent val]] mapping is used throughout.   
# Octave equivalence is assumed. For example, the [[5-odd-limit]] takes account of 1/1, 3/1, 5/1, 5/3 and their octave inverses.
# Each edo is TE-optimally stretched.  
# The weight of intervals is determined by the [[tonality diamond]]. For example, the [[9-odd-limit]] takes account of 3/1 twice.  
# [[Graham Breed]]'s definition is used, scaled by 100.  
{| class="wikitable sortable mw-collapsible" style="text-align:right"
{| class="wikitable sortable mw-collapsible" style="text-align:right"
! rowspan="2" | Edo
! rowspan="2" | Edo
! colspan="11" | Root Mean Squared Relative Errors (Percent)
! colspan="8" | TE simple badness × 100
|-
|-
! 3 Odd Limit
! 3 Limit
! 5 Odd Limit
! 5 Limit
! 7 Odd Limit
! 7 Limit
! 9 Odd Limit
! 11 Limit
! 11 Odd Limit
! 13 Limit
! 13 Odd Limit
! 17 Limit
! 15 Odd Limit
! 19 Limit
! 17 Odd Limit
! 23 Limit
! 19 Odd Limit
! 21 Odd Limit
! 23 Odd Limit
|-
|-
| 1
| 1
| 29.35
| 13.09
| 42.66
| 16.61
| 38.25
| 14.43
| 54.88
| 14.79
| 61.68
| 13.75
| 57.87
| 12.83
| 54.17
| 12.25
| 51.99
| 11.95
| 51.57
| 53.79
| 53.35
|-
|-
| 2
| 2
| 12.02
| 5.36
| 31.00
| 10.69
| 33.35
| 10.66
| 40.44
| 9.58
| 36.97
| 10.37
| 40.91
| 9.82
| 39.38
| 10.07
| 38.05
| 9.50
| 41.60
| 41.18
| 39.43
|-
|-
| 3
| 3
| 17.33
| 7.73
| 15.33
| 6.97
| 34.23
| 10.80
| 42.69
| 10.68
| 45.56
| 9.76
| 42.45
| 9.17
| 42.08
| 9.04
| 41.59
| 9.20
| 41.08
| 39.93
| 41.80
|-
|-
| 4
| 4
| 24.03
| 10.72
| 21.13
| 8.79
| 18.34
| 7.73
| 31.02
| 9.20
| 37.61
| 9.67
| 40.74
| 9.02
| 43.75
| 8.67
| 41.62
| 8.22
| 40.86
| 41.54
| 40.21
|-
|-
| 5
| 5
| 5.32
| 2.37
| 23.91
| 7.08
| 23.81
| 7.15
| 21.44
| 8.41
| 29.27
| 8.72
| 35.10
| 9.61
| 36.78
| 9.34
| 43.55
| 9.11
| 43.62
| 41.59
| 41.82
|-
|-
| 6
| 6
| 34.66
| 15.46
| 30.66
| 13.94
| 26.61
| 12.32
| 51.22
| 11.08
| 47.03
| 11.52
| 50.72
| 10.79
| 49.62
| 11.89
| 47.53
| 11.51
| 56.32
| 56.32
| 56.23
|-
|-
| 7
| 7
| 6.70
| 2.99
| 14.79
| 4.46
| 31.20
| 8.72
| 29.90
| 8.06
| 28.86
| 7.57
| 27.93
| 7.97
| 29.75
| 7.72
| 34.97
| 7.55
| 35.45
| 35.34
| 35.97
|-
|-
| 8
| 8
| 22.65
| 10.10
| 25.55
| 9.11
| 48.63
| 14.89
| 54.11
| 13.41
| 49.94
| 12.35
| 47.16
| 11.44
| 50.14
| 10.92
| 47.27
| 10.81
| 46.42
| 47.29
| 48.19
|-
|-
| 9
| 9
| 18.71
| 8.35
| 21.88
| 9.09
| 22.98
| 8.21
| 31.51
| 7.37
| 28.92
| 6.83
| 27.45
| 7.37
| 25.73
| 6.91
| 30.28
| 7.32
| 28.94
| 31.48
| 35.50
|-
|-
| 10
| 10
| 10.63
| 4.74
| 21.47
| 7.73
| 18.85
| 6.79
| 25.42
| 7.83
| 30.45
| 7.19
| 28.61
| 6.68
| 27.65
| 7.58
| 26.22
| 7.34
| 34.04
| 32.56
| 32.73
|-
|-
| 11
| 11
| 30.73
| 13.71
| 51.59
| 19.34
| 45.19
| 17.01
| 65.23
| 15.22
| 59.74
| 14.29
| 59.17
| 13.23
| 55.52
| 12.52
| 52.52
| 11.88
| 51.64
| 50.73
| 49.81
|-
|-
| 12
| 12
| 1.38
| 0.62
| 9.84
| 3.11
| 18.74
| 4.94
| 18.70
| 5.99
| 27.49
| 8.35
| 37.31
| 7.88
| 34.98
| 7.40
| 33.43
| 7.47
| 31.75
| 31.76
| 33.51
|-
|-
| 13
| 13
| 27.97
| 12.48
| 34.24
| 14.02
| 45.60
| 15.79
| 63.59
| 14.13
| 58.18
| 12.94
| 54.71
| 12.03
| 51.65
| 11.34
| 49.64
| 10.84
| 48.56
| 46.59
| 45.14
|-
|-
| 14
| 14
| 13.40
| 5.98
| 40.68
| 13.72
| 43.05
| 13.32
| 44.08
| 12.86
| 44.41
| 12.12
| 44.22
| 11.31
| 45.23
| 10.99
| 43.44
| 10.44
| 44.75
| 45.54
| 44.25
|-
|-
| 15
| 15
| 15.95
| 7.12
| 13.59
| 5.81
| 18.95
| 6.97
| 27.35
| 6.25
| 25.06
| 6.65
| 29.02
| 7.73
| 28.80
| 7.29
| 35.91
| 6.88
| 34.47
| 32.94
| 31.54
|-
|-
| 16
| 16
| 25.41
| 11.34
| 20.84
| 9.53
| 23.76
| 9.91
| 40.61
| 8.98
| 37.62
| 8.22
| 34.90
| 7.67
| 34.95
| 7.67
| 33.39
| 7.26
| 34.53
| 32.93
| 31.86
|-
|-
| 17
| 17
| 3.93
| 1.76
| 33.53
| 10.52
| 38.55
| 11.30
| 35.46
| 10.51
| 33.98
| 9.65
| 31.63
| 9.88
| 36.39
| 9.32
| 40.08
| 8.88
| 38.50
| 40.44
| 39.15
|-
|-
| 18
| 18
| 33.28
| 14.85
| 27.25
| 12.45
| 27.87
| 10.91
| 44.68
| 13.03
| 54.53
| 11.90
| 50.68
| 11.02
| 50.32
| 12.37
| 47.53
| 12.77
| 57.22
| 60.69
| 65.40
|-
|-
| 19
| 19
| 8.08
| 3.61
| 7.70
| 3.02
| 17.42
| 4.35
| 16.32
| 6.79
| 27.15
| 6.47
| 27.40
| 7.40
| 26.15
| 7.56
| 32.36
| 7.17
| 34.49
| 36.87
| 35.68
|-
|-
| 20
| 20
| 21.27
| 9.49
| 42.93
| 15.46
| 37.69
| 13.58
| 50.84
| 12.26
| 48.27
| 11.21
| 44.72
| 10.75
| 42.45
| 10.07
| 41.57
| 9.99
| 39.45
| 37.96
| 41.45
|-
|-
| 21
| 21
| 20.10
| 8.97
| 30.27
| 11.67
| 26.48
| 10.27
| 39.94
| 10.30
| 43.95
| 9.76
| 43.78
| 9.06
| 41.04
| 8.80
| 39.33
| 8.31
| 38.55
| 38.00
| 36.40
|-
|-
| 22
| 22
| 9.25
| 4.13
| 12.42
| 4.94
| 17.34
| 5.23
| 18.87
| 5.33
| 20.68
| 6.89
| 30.63
| 6.42
| 28.72
| 6.99
| 27.24
| 7.57
| 32.68
| 35.13
| 38.42
|-
|-
| 23
| 23
| 32.11
| 14.33
| 28.76
| 11.79
| 50.48
| 16.76
| 63.98
| 17.03
| 69.09
| 15.55
| 64.00
| 14.44
| 68.54
| 13.91
| 65.37
| 13.12
| 65.64
| 62.83
| 60.29
|-
|-
| 24
| 24
| 2.76
| 1.23
| 19.68
| 6.22
| 32.65
| 8.95
| 29.30
| 8.01
| 26.76
| 7.66
| 27.28
| 7.14
| 27.93
| 6.70
| 26.88
| 7.02
| 25.56
| 29.95
| 33.86
|-
|-
| 25
| 25
| 26.58
| 11.86
| 26.81
| 11.70
| 29.35
| 11.76
| 48.26
| 12.70
| 56.30
| 12.57
| 56.12
| 11.89
| 53.32
| 11.30
| 52.49
| 10.68
| 51.55
| 49.34
| 47.78
|-
|-
| 26
| 26
| 14.78
| 6.59
| 21.43
| 6.96
| 22.30
| 7.43
| 25.31
| 7.51
| 26.66
| 6.86
| 24.84
| 6.37
| 30.29
| 6.17
| 28.68
| 7.45
| 28.82
| 27.54
| 36.02
|-
|-
| 27
| 27
| 14.57
| 6.50
| 18.11
| 6.19
| 15.80
| 5.40
| 19.33
| 9.37
| 37.61
| 8.58
| 34.85
| 9.13
| 37.55
| 8.70
| 42.45
| 8.41
| 41.14
| 40.85
| 40.71
|-
|-
| 28
| 28
| 26.80
| 11.95
| 24.81
| 11.13
| 38.67
| 13.62
| 55.10
| 12.46
| 52.53
| 12.19
| 54.37
| 12.00
| 53.56
| 11.25
| 53.12
| 10.92
| 50.95
| 48.81
| 49.68
|-
|-
| 29
| 29
| 2.55
| 1.14
| 23.69
| 7.41
| 28.09
| 7.91
| 28.84
| 7.15
| 28.27
| 6.54
| 27.23
| 8.94
| 26.06
| 8.36
| 38.29
| 7.89
| 36.43
| 36.16
| 34.64
|-
|-
| 30
| 30
| 31.90
| 14.23
| 27.18
| 11.62
| 37.90
| 13.94
| 54.71
| 12.51
| 50.11
| 11.87
| 48.64
| 11.02
| 52.35
| 11.82
| 49.44
| 11.15
| 56.78
| 54.14
| 51.88
|-
|-
| 31
| 31
| 9.46
| 4.22
| 9.67
| 4.20
| 8.39
| 3.70
| 15.13
| 3.84
| 16.20
| 5.35
| 24.64
| 5.75
| 23.22
| 5.93
| 26.82
| 5.89
| 29.15
| 28.68
| 28.86
|-
|-
| 32
| 32
| 19.88
| 8.87
| 33.66
| 12.60
| 30.98
| 11.07
| 40.68
| 10.18
| 38.04
| 10.85
| 45.48
| 10.13
| 42.83
| 9.47
| 40.79
| 9.00
| 38.70
| 39.73
| 38.37
|-
|-
| 33
| 33
| 21.48
| 9.58
| 39.34
| 14.46
| 39.71
| 13.86
| 53.83
| 12.72
| 49.58
| 11.71
| 45.99
| 10.87
| 43.50
| 10.30
| 41.64
| 9.91
| 40.02
| 38.37
| 37.93
|-
|-
| 34
| 34
| 7.87
| 3.51
| 6.42
| 2.92
| 31.44
| 8.67
| 32.66
| 9.26
| 36.26
| 8.59
| 34.20
| 7.96
| 32.30
| 8.36
| 30.55
| 8.01
| 36.09
| 37.48
| 36.77
|-
|-
| 35
| 35
| 33.49
| 14.94
| 27.42
| 12.31
| 23.76
| 10.85
| 44.83
| 10.54
| 44.04
| 13.06
| 57.61
| 12.22
| 59.14
| 12.27
| 56.64
| 11.61
| 59.15
| 60.36
| 57.86
|-
|-
| 36
| 36
| 4.15
| 1.85
| 29.52
| 9.33
| 27.89
| 8.63
| 27.14
| 8.76
| 33.46
| 8.96
| 34.81
| 8.63
| 35.32
| 8.08
| 35.03
| 7.62
| 33.23
| 32.64
| 31.49
|-
|-
| 37
| 37
| 25.20
| 11.24
| 21.42
| 9.82
| 18.60
| 8.70
| 36.26
| 8.37
| 35.75
| 7.78
| 33.72
| 8.21
| 33.63
| 8.13
| 37.80
| 8.42
| 38.79
| 39.54
| 43.41
|-
|-
| 38
| 38
| 16.16
| 7.21
| 15.40
| 6.04
| 31.97
| 9.96
| 37.24
| 9.76
| 38.40
| 10.64
| 45.06
| 10.02
| 45.49
| 9.62
| 43.64
| 9.30
| 42.83
| 42.40
| 41.91
|-
|-
| 39
| 39
| 13.18
| 5.88
| 25.79
| 7.89
| 48.19
| 13.78
| 47.12
| 12.34
| 43.03
| 12.08
| 44.87
| 11.86
| 50.25
| 11.42
| 52.82
| 11.21
| 51.45
| 51.48
| 52.56
|-
|-
| 40
| 40
| 28.18
| 12.57
| 31.47
| 13.28
| 29.94
| 11.62
| 45.70
| 10.48
| 42.07
| 9.99
| 41.23
| 9.43
| 38.58
| 9.38
| 37.96
| 9.18
| 39.19
| 41.56
| 41.99
|-
|-
| 41
| 41
| 1.17
| 0.52
| 13.85
| 4.31
| 12.25
| 3.76
| 12.44
| 4.51
| 15.99
| 5.29
| 20.85
| 6.00
| 21.84
| 5.90
| 27.57
| 6.59
| 27.66
| 26.76
| 31.80
|-
|-
| 42
| 42
| 30.52
| 13.61
| 30.48
| 11.60
| 29.43
| 11.45
| 43.52
| 13.33
| 53.12
| 14.24
| 59.59
| 13.22
| 65.77
| 13.36
| 62.08
| 12.64
| 65.55
| 63.88
| 61.75
|-
|-
| 43
| 43
| 10.85
| 4.84
| 17.93
| 6.75
| 23.24
| 7.56
| 29.85
| 7.08
| 30.23
| 6.85
| 29.04
| 6.49
| 27.17
| 6.35
| 27.50
| 6.45
| 29.04
| 27.80
| 31.12
|-
|-
| 44
| 44
| 18.50
| 8.25
| 24.83
| 9.89
| 34.67
| 10.45
| 37.73
| 10.66
| 41.36
| 9.74
| 38.33
| 9.02
| 35.94
| 8.46
| 33.89
| 8.11
| 32.23
| 39.18
| 38.59
|-
|-
| 45
| 45
| 22.86
| 10.20
| 28.60
| 9.75
| 25.05
| 8.49
| 30.33
| 11.84
| 45.42
| 13.50
| 55.24
| 12.72
| 60.43
| 11.90
| 58.39
| 12.03
| 55.42
| 56.13
| 59.79
|-
|-
| 46
| 46
| 6.49
| 2.89
| 11.05
| 3.45
| 17.16
| 5.12
| 17.47
| 5.20
| 19.10
| 5.42
| 21.65
| 5.02
| 24.29
| 5.62
| 23.04
| 5.30
| 28.49
| 27.19
| 26.15
|-
|-
| 47
| 47
| 34.88
| 15.56
| 29.51
| 13.54
| 30.18
| 13.24
| 54.85
| 14.39
| 62.76
| 13.38
| 59.63
| 12.39
| 59.97
| 12.20
| 56.72
| 11.98
| 58.62
| 57.15
| 59.00
|-
|-
| 48
| 48
| 5.53
| 2.47
| 27.93
| 8.27
| 35.48
| 10.25
| 32.10
| 9.22
| 29.36
| 9.84
| 35.49
| 9.20
| 41.00
| 8.71
| 39.01
| 8.23
| 37.90
| 37.47
| 36.00
|-
|-
| 49
| 49
| 23.82
| 10.63
| 19.82
| 8.69
| 23.09
| 7.87
| 31.61
| 7.11
| 29.96
| 10.12
| 43.69
| 10.85
| 43.20
| 10.67
| 48.35
| 10.09
| 48.67
| 52.04
| 49.97
|-
|-
| 50
| 50
| 17.55
| 7.83
| 14.44
| 6.62
| 19.91
| 6.39
| 25.32
| 6.76
| 27.15
| 6.54
| 26.58
| 6.19
| 26.14
| 5.90
| 25.91
| 5.62
| 25.78
| 29.12
| 28.10
|-
|-
| 51
| 51
| 11.80
| 5.27
| 34.81
| 11.79
| 30.66
| 10.34
| 37.05
| 9.93
| 40.21
| 10.23
| 41.37
| 9.89
| 40.00
| 10.15
| 41.66
| 10.01
| 44.12
| 42.12
| 42.63
|-
|-
| 52
| 52
| 29.56
| 13.19
| 39.49
| 15.75
| 34.47
| 13.86
| 54.80
| 12.69
| 52.54
| 12.08
| 50.56
| 12.33
| 47.31
| 11.62
| 52.73
| 11.02
| 50.88
| 50.14
| 48.19
|-
|-
| 53
| 53
| 0.21
| 0.10
| 4.05
| 1.22
| 14.63
| 3.81
| 13.30
| 5.65
| 23.32
| 5.22
| 22.02
| 6.05
| 20.62
| 5.76
| 26.78
| 5.75
| 26.05
| 26.47
| 27.14
|-
|-
| 54
| 54
| 29.13
| 13.00
| 45.97
| 17.51
| 46.54
| 15.92
| 58.09
| 14.24
| 53.13
| 13.01
| 49.29
| 12.05
| 47.08
| 12.31
| 44.50
| 12.02
| 49.35
| 54.18
| 55.25
|-
|-
| 55
| 55
| 12.23
| 5.46
| 27.26
| 9.63
| 36.05
| 10.57
| 35.80
| 9.63
| 33.53
| 10.83
| 43.84
| 10.23
| 41.88
| 10.02
| 40.75
| 9.52
| 41.83
| 46.81
| 45.74
|-
|-
| 56
| 56
| 17.12
| 7.64
| 17.15
| 7.50
| 22.83
| 8.38
| 34.14
| 7.90
| 32.50
| 7.95
| 34.74
| 7.37
| 33.13
| 6.90
| 31.24
| 7.07
| 29.65
| 28.40
| 31.56
|-
|-
| 57
| 57
| 24.24
| 10.82
| 23.10
| 9.06
| 23.84
| 9.30
| 35.77
| 8.47
| 33.01
| 8.68
| 34.87
| 8.41
| 39.51
| 7.92
| 39.42
| 7.98
| 37.70
| 36.33
| 38.15
|-
|-
| 58
| 58
| 2.28
| 5.89
| 5.10
| 5.10
| 19.91
| 4.83
| 17.42
| 4.56
| 15.58
| 5.33
| 18.00
| 7.07
| 19.28
| 7.72
| 20.19
| 23.33
| 33.00
| 31.76
| 36.48
|-
|-
| 59
| 59
| 34.45
| 15.37
| 32.27
| 14.43
| 30.56
| 12.55
| 50.92
| 12.56
| 52.75
| 13.10
| 57.52
| 12.56
| 55.52
| 11.85
| 55.24
| 11.19
| 52.96
| 56.85
| 54.79
|-
|-
| 60
| 60
| 6.91
| 3.08
| 18.66
| 5.56
| 24.63
| 6.23
| 22.05
| 10.22
| 39.47
| 9.44
| 36.74
| 8.77
| 37.51
| 8.54
| 35.74
| 8.26
| 35.78
| 38.17
| 37.90
|-
|-
| 61
| 61
| 22.44
| 10.01
| 22.80
| 8.59
| 35.17
| 11.66
| 43.33
| 10.84
| 41.50
| 9.93
| 38.74
| 10.38
| 42.93
| 9.95
| 48.09
| 9.39
| 47.45
| 45.38
| 43.57
|-
|-
| 62
| 62
| 18.93
| 8.44
| 19.34
| 8.40
| 16.79
| 7.40
| 30.27
| 7.67
| 32.40
| 7.28
| 31.75
| 6.83
| 29.71
| 6.40
| 29.11
| 6.09
| 27.98
| 26.75
| 26.58
|-
|-
| 63
| 63
| 10.42
| 4.65
| 25.16
| 8.77
| 24.46
| 8.00
| 27.48
| 7.17
| 25.09
| 6.73
| 24.99
| 7.50
| 24.64
| 7.41
| 31.49
| 7.03
| 32.75
| 32.14
| 31.01
|-
|-
| 64
| 64
| 30.94
| 13.80
| 48.18
| 18.41
| 46.71
| 17.26
| 67.95
| 16.16
| 63.84
| 14.96
| 61.41
| 14.36
| 57.55
| 13.46
| 58.80
| 13.07
| 56.33
| 53.79
| 55.53
|-
|-
| 65
| 65
| 1.60
| 0.71
| 5.88
| 1.94
| 30.76
| 7.82
| 27.73
| 7.65
| 28.10
| 8.94
| 36.84
| 8.68
| 34.49
| 8.23
| 35.00
| 7.77
| 33.99
| 39.13
| 37.48
|-
|-
| 66
| 66
| 27.75
| 12.38
| 37.25
| 14.83
| 38.19
| 14.37
| 57.61
| 13.50
| 57.72
| 12.47
| 55.24
| 11.84
| 52.04
| 11.36
| 49.84
| 11.32
| 50.46
| 48.27
| 49.12
|-
|-
| 67
| 67
| 13.61
| 6.07
| 36.85
| 12.62
| 33.61
| 11.18
| 38.37
| 10.24
| 37.73
| 9.35
| 35.12
| 8.67
| 34.59
| 8.44
| 32.93
| 8.10
| 34.44
| 36.06
| 34.88
|-
|-
| 68
| 68
| 15.74
| 7.02
| 12.85
| 5.84
| 11.15
| 5.19
| 21.53
| 6.84
| 29.47
| 6.75
| 30.25
| 6.34
| 29.63
| 5.93
| 28.40
| 5.81
| 26.95
| 26.60
| 27.00
|-
|-
| 69
| 69
| 25.63
| 11.43
| 21.03
| 9.40
| 34.80
| 12.23
| 48.35
| 12.30
| 51.43
| 11.48
| 48.76
| 10.67
| 49.79
| 9.98
| 47.53
| 9.41
| 45.20
| 43.31
| 41.50
|-
|-
| 70
| 70
| 3.72
| 1.66
| 29.41
| 8.76
| 31.86
| 8.63
| 29.66
| 9.73
| 33.73
| 9.37
| 32.60
| 9.21
| 35.45
| 9.62
| 36.02
| 9.20
| 40.23
| 42.36
| 41.42
|-
|-
| 71
| 71
| 33.07
| 14.75
| 27.67
| 12.71
| 40.14
| 14.95
| 60.61
| 13.52
| 55.78
| 12.34
| 51.65
| 12.20
| 50.91
| 11.49
| 53.28
| 11.25
| 50.91
| 48.80
| 49.64
|-
|-
| 72
| 72
| 8.29
| 3.70
| 10.49
| 3.56
| 9.28
| 3.09
| 11.02
| 2.96
| 10.44
| 3.82
| 18.07
| 3.59
| 17.94
| 4.57
| 17.66
| 5.60
| 22.25
| 21.50
| 27.66
|-
|-
| 73
| 73
| 21.05
| 9.39
| 29.00
| 9.56
| 28.01
| 9.59
| 33.03
| 8.65
| 31.46
| 9.62
| 36.71
| 10.93
| 42.68
| 10.60
| 51.07
| 10.47
| 50.59
| 48.62
| 49.68
|-
|-
| 74
| 74
| 20.31
| 9.06
| 27.07
| 10.80
| 29.50
| 10.83
| 43.48
| 9.69
| 39.96
| 9.02
| 38.83
| 9.36
| 36.48
| 9.06
| 39.27
| 8.88
| 38.77
| 37.14
| 38.34
|-
|-
| 75
| 75
| 9.04
| 4.03
| 15.74
| 5.85
| 30.96
| 8.36
| 28.93
| 10.29
| 40.99
| 10.36
| 43.48
| 9.98
| 41.03
| 9.51
| 41.78
| 9.57
| 41.39
| 43.06
| 44.95
|-
|-
| 76
| 76
| 32.33
| 14.42
| 30.79
| 12.07
| 26.85
| 10.57
| 41.29
| 11.84
| 46.68
| 11.01
| 43.62
| 12.28
| 49.21
| 12.13
| 57.43
| 11.98
| 58.19
| 59.67
| 60.83
|-
|-
| 77
| 77
| 2.98
| 1.33
| 15.70
| 5.04
| 19.26
| 5.59
| 17.88
| 6.66
| 25.03
| 6.25
| 24.22
| 6.42
| 24.99
| 6.03
| 26.92
| 6.03
| 25.86
| 26.01
| 27.38
|-
|-
| 78
| 78
| 26.37
| 11.76
| 29.24
| 12.37
| 25.60
| 10.95
| 44.46
| 9.80
| 40.65
| 9.14
| 38.52
| 8.47
| 36.07
| 9.09
| 34.09
| 8.57
| 40.15
| 39.44
| 37.77
|-
|-
| 79
| 79
| 14.99
| 6.69
| 24.96
| 7.84
| 34.25
| 10.49
| 35.51
| 9.43
| 33.09
| 8.66
| 31.45
| 8.64
| 35.72
| 9.55
| 37.20
| 9.10
| 44.52
| 43.00
| 42.02
|-
|-
| 80
| 80
| 14.35
| 6.40
| 15.16
| 5.59
| 20.73
| 5.68
| 21.46
| 5.17
| 19.59
| 6.01
| 23.04
| 6.12
| 24.26
| 5.78
| 25.19
| 5.56
| 23.99
| 28.19
| 27.47
|-
|-
| 81
| 81
| 27.01
| 12.05
| 23.34
| 10.67
| 25.10
| 9.49
| 38.39
| 8.65
| 35.52
| 10.05
| 43.31
| 9.45
| 41.97
| 8.94
| 40.27
| 8.50
| 38.75
| 43.37
| 41.87
|-
|-
| 82
| 82
| 2.34
| 1.04
| 27.71
| 8.62
| 24.51
| 7.52
| 24.88
| 9.02
| 31.98
| 8.92
| 35.80
| 8.26
| 35.92
| 7.82
| 33.94
| 7.62
| 33.32
| 31.78
| 31.60
|-
|-
| 83
| 83
| 31.69
| 14.14
| 26.14
| 11.58
| 27.44
| 11.68
| 47.40
| 11.82
| 49.48
| 11.53
| 49.59
| 11.44
| 52.72
| 10.90
| 54.79
| 11.25
| 52.81
| 51.10
| 56.03
|-
|-
| 84
| 84
| 9.68
| 4.32
| 8.10
| 3.72
| 16.38
| 5.39
| 21.35
| 7.02
| 31.18
| 6.50
| 29.69
| 7.05
| 29.65
| 6.70
| 32.25
| 6.32
| 31.74
| 30.33
| 29.05
|-
|-
| 85
| 85
| 19.67
| 8.78
| 37.18
| 13.57
| 40.58
| 12.98
| 45.47
| 11.80
| 43.11
| 11.37
| 43.13
| 11.76
| 42.21
| 11.08
| 47.43
| 10.84
| 45.48
| 49.49
| 49.63
|-
|-
| 86
| 86
| 21.69
| 9.68
| 35.85
| 13.50
| 40.91
| 13.06
| 46.50
| 14.03
| 56.12
| 12.95
| 52.46
| 12.94
| 49.39
| 12.35
| 53.13
| 11.64
| 51.87
| 56.60
| 54.32
|-
|-
| 87
| 87
| 7.66
| 3.42
| 7.49
| 3.30
| 17.95
| 5.45
| 21.45
| 4.90
| 19.59
| 4.53
| 18.27
| 5.35
| 17.46
| 5.77
| 22.87
| 5.92
| 26.46
| 27.06
| 29.54
|-
|-
| 88
| 88
| 33.71
| 15.04
| 28.19
| 12.29
| 27.93
| 12.05
| 48.75
| 10.79
| 44.65
| 12.68
| 55.03
| 12.94
| 57.31
| 12.56
| 61.03
| 11.88
| 60.92
| 59.39
| 57.26
|-
|-
| 89
| 89
| 4.36
| 1.95
| 25.53
| 8.15
| 22.32
| 7.08
| 23.87
| 6.35
| 21.94
| 7.57
| 28.68
| 7.12
| 29.76
| 6.77
| 29.05
| 6.77
| 28.11
| 26.83
| 29.08
|-
|-
| 90
| 90
| 24.99
| 11.15
| 22.73
| 10.25
| 23.56
| 9.07
| 36.52
| 11.10
| 47.19
| 10.39
| 45.01
| 9.62
| 43.48
| 9.75
| 41.05
| 9.33
| 44.05
| 47.93
| 47.32
|-
|-
| 91
| 91
| 16.38
| 7.31
| 17.95
| 6.49
| 23.77
| 6.51
| 24.47
| 8.82
| 33.89
| 9.74
| 39.10
| 9.28
| 40.72
| 9.95
| 39.76
| 9.93
| 45.62
| 49.78
| 51.74
|-
|-
| 92
| 92
| 12.97
| 5.79
| 22.10
| 6.91
| 34.33
| 10.24
| 34.93
| 10.40
| 38.20
| 10.83
| 43.31
| 10.03
| 48.59
| 9.52
| 46.07
| 9.06
| 44.10
| 42.54
| 41.62
|-
|-
| 93
| 93
| 28.39
| 12.67
| 29.00
| 12.60
| 25.18
| 11.09
| 45.40
| 11.46
| 49.64
| 10.46
| 45.97
| 9.68
| 43.85
| 9.09
| 41.39
| 9.14
| 39.58
| 39.96
| 42.98
|-
|-
| 94
| 94
| 0.96
| 0.43
| 17.88
| 5.52
| 19.42
| 5.74
| 17.71
| 5.35
| 18.34
| 5.48
| 19.87
| 5.28
| 21.42
| 5.24
| 21.61
| 4.99
| 22.84
| 23.45
| 23.13
|-
|-
| 95
| 95
| 30.30
| 13.52
| 28.19
| 11.23
| 24.44
| 9.90
| 38.98
| 8.98
| 35.67
| 8.20
| 33.18
| 10.47
| 37.32
| 9.80
| 48.98
| 9.34
| 46.57
| 46.63
| 45.03
|-
|-
| 96
| 96
| 11.06
| 4.93
| 14.65
| 5.86
| 33.96
| 9.86
| 38.60
| 9.14
| 35.89
| 8.90
| 35.36
| 8.96
| 33.10
| 8.59
| 35.08
| 8.28
| 35.27
| 37.11
| 36.83
|-
|-
| 97
| 97
| 18.29
| 8.16
| 28.06
| 10.76
| 31.37
| 10.97
| 43.50
| 11.24
| 44.67
| 10.26
| 41.44
| 10.60
| 38.92
| 9.92
| 44.81
| 9.49
| 42.64
| 40.78
| 39.81
|-
|-
| 98
| 98
| 23.07
| 10.29
| 45.07
| 16.34
| 40.28
| 14.25
| 51.63
| 12.75
| 47.45
| 12.32
| 49.69
| 11.92
| 47.15
| 11.54
| 48.80
| 11.15
| 48.28
| 49.40
| 48.41
|-
|-
| 99
| 99
| 6.27
| 2.80
| 7.63
| 2.63
| 6.60
| 2.33
| 8.38
| 7.27
| 31.37
| 7.48
| 33.58
| 7.75
| 33.84
| 8.09
| 35.67
| 7.67
| 38.51
| 36.92
| 35.54
|}
|}


Retrieved from "https://en.xen.wiki/w/Relative_errors_of_small_EDOs"