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
|}
|}


Revision as of 14:49, 21 July 2020

This article contains two lists. The first shows relative errors of the first 9 prime harmonics for 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 second shows the 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

Edo Relative Errors (Percent)
2/1 3/1 5/1 7/1 11/1 13/1 17/1 19/1 23/1
1 0.00 41.50 -32.19 19.26 -45.94 29.96 -8.75 -24.79 47.64
2 0.00 -16.99 35.61 38.53 8.11 -40.09 -17.49 -49.59 -4.71
3 0.00 24.51 3.42 -42.21 -37.83 -10.13 -26.24 25.62 42.93
4 0.00 -33.99 -28.77 -22.94 16.23 19.82 -34.99 0.83 -9.42
5 0.00 7.52 39.04 -3.68 -29.72 49.78 -43.73 -23.96 38.22
6 0.00 49.02 6.84 15.59 24.34 -20.26 47.52 -48.76 -14.14
7 0.00 -9.47 -25.35 34.85 -21.60 9.69 38.78 26.45 33.51
8 0.00 32.03 42.46 -45.88 32.45 39.65 30.03 1.66 -18.85
9 0.00 -26.47 10.26 -26.62 -13.49 -30.40 21.28 -23.13 28.79
10 0.00 15.04 -21.93 -7.35 40.57 -0.44 12.54 -47.93 -23.56
11 0.00 -43.46 45.88 11.91 -5.37 29.52 3.79 27.28 24.08
12 0.00 -1.96 13.69 31.17 48.68 -40.53 -4.96 2.49 -28.27
13 0.00 39.55 -18.51 -49.56 2.74 -10.57 -13.70 -22.31 19.37
14 0.00 -18.95 49.30 -30.30 -43.20 19.38 -22.45 -47.10 -32.99
15 0.00 22.56 17.11 -11.03 10.85 49.34 -31.19 28.11 14.66
16 0.00 -35.94 -15.08 8.23 -35.09 -20.70 -39.94 3.32 -37.70
17 0.00 5.56 -47.28 27.50 18.97 9.25 -48.69 -21.48 9.94
18 0.00 47.07 20.53 46.76 -26.98 39.21 42.57 -46.27 -42.41
19 0.00 -11.43 -11.66 -33.97 27.08 -30.84 33.82 28.94 5.23
20 0.00 30.07 -43.86 -14.71 -18.86 -0.88 25.07 4.14 -47.12
21 0.00 -28.42 23.95 4.55 35.19 29.08 16.33 -20.65 0.52
22 0.00 13.08 -8.24 23.82 -10.75 -40.97 7.58 -45.44 48.16
23 0.00 -45.41 -40.43 43.08 43.31 -11.01 -1.16 29.77 -4.19
24 0.00 -3.91 27.37 -37.65 -2.64 18.94 -9.91 4.97 43.45
25 0.00 37.59 -4.82 -18.39 -48.58 48.90 -18.66 -19.82 -8.90
26 0.00 -20.90 -37.01 0.88 5.48 -21.14 -27.40 -44.61 38.74
27 0.00 20.60 30.79 20.14 -40.47 8.81 -36.15 30.60 -13.62
28 0.00 -37.90 -1.40 39.41 13.59 38.77 -44.90 5.80 34.03
29 0.00 3.61 -33.59 -41.33 -32.35 -31.28 46.36 -18.99 -18.33
30 0.00 45.11 34.22 -22.06 21.71 -1.32 37.61 -43.78 29.31
31 0.00 -13.38 2.02 -2.80 -24.24 28.64 28.87 31.42 -23.04
32 0.00 28.12 -30.17 16.46 29.82 -41.41 20.12 6.63 24.60
33 0.00 -30.38 37.64 35.73 -16.12 -11.45 11.37 -18.16 -27.75
34 0.00 11.13 5.44 -45.01 37.93 18.50 2.63 -42.95 19.89
35 0.00 -47.37 -26.75 -25.74 -8.01 48.46 -6.12 32.25 -32.47
36 0.00 -5.87 41.06 -6.48 46.05 -21.58 -14.87 7.46 15.18
37 0.00 35.64 8.87 12.79 0.10 8.37 -23.61 -17.33 -37.18
38 0.00 -22.86 -23.33 32.05 -45.84 38.33 -32.36 -42.12 10.46
39 0.00 18.65 44.48 -48.68 8.22 -31.71 -41.11 33.08 -41.89
40 0.00 -39.85 12.29 -29.42 -37.73 -1.76 -49.85 8.29 5.75
41 0.00 1.65 -19.91 -10.16 16.33 28.20 41.40 -16.50 -46.60
42 0.00 43.16 47.90 9.11 -29.61 -41.85 32.66 -41.30 1.04
43 0.00 -15.34 15.71 28.37 24.44 -11.89 23.91 33.91 48.68
44 0.00 26.16 -16.48 47.64 -21.50 18.07 15.16 9.12 -3.67
45 0.00 -32.33 -48.68 -33.10 32.56 48.02 6.42 -15.67 43.97
46 0.00 9.17 19.13 -13.83 -13.39 -22.02 -2.33 -40.47 -8.38
47 0.00 -49.32 -13.06 5.43 40.67 7.93 -11.08 34.74 39.26
48 0.00 -7.82 -45.25 24.70 -5.27 37.89 -19.82 9.95 -13.10
49 0.00 33.68 22.55 43.96 48.79 -32.15 -28.57 -14.84 34.55
50 0.00 -24.81 -9.64 -36.77 2.84 -2.20 -37.31 -39.64 -17.81
51 0.00 16.69 -41.83 -17.51 -43.10 27.76 -46.06 35.57 29.83
52 0.00 -41.81 25.97 1.75 10.96 -42.29 45.19 10.78 -22.52
53 0.00 -0.30 -6.22 21.02 -34.99 -12.33 36.45 -14.02 25.12
54 0.00 41.20 -38.41 40.28 19.07 17.63 27.70 -38.81 -27.23
55 0.00 -17.29 29.40 -40.45 -26.87 47.58 18.95 36.40 20.41
56 0.00 24.21 -2.80 -21.19 27.18 -22.46 10.21 11.61 -31.95
57 0.00 -34.29 -34.99 -1.92 -18.76 7.49 1.46 -13.19 15.70
58 0.00 7.22 32.82 17.34 35.30 37.45 -7.28 -37.98 -36.66
59 0.00 48.72 0.62 36.61 -10.65 -32.59 -16.03 37.23 10.98
60 0.00 -9.78 -31.57 -44.13 43.41 -2.64 -24.78 12.43 -41.37
61 0.00 31.73 36.24 -24.87 -2.53 27.32 -33.52 -12.36 6.27
62 0.00 -26.77 4.05 -5.60 -48.48 -42.73 -42.27 -37.15 -46.08
63 0.00 14.74 -28.15 13.66 5.58 -12.77 48.98 38.06 1.56
64 0.00 -43.76 39.66 32.93 -40.36 17.19 40.24 13.26 49.20
65 0.00 -2.26 7.47 -47.81 13.69 47.14 31.49 -11.53 -3.15
66 0.00 39.25 -24.73 -28.54 -32.25 -22.90 22.75 -36.32 44.49
67 0.00 -19.25 43.08 -9.28 21.81 7.05 14.00 38.89 -7.87
68 0.00 22.25 10.89 9.99 -24.14 37.01 5.25 14.09 39.78
69 0.00 -36.24 -21.30 29.25 29.92 -33.03 -3.49 -10.70 -12.58
70 0.00 5.26 46.50 48.52 -16.02 -3.08 -12.24 -35.49 35.07
71 0.00 46.77 14.31 -32.22 38.04 26.88 -20.99 39.71 -17.29
72 0.00 -11.73 -17.88 -12.96 -7.91 -43.17 -29.73 14.92 30.35
73 0.00 29.77 49.92 6.31 46.15 -13.21 -38.48 -9.87 -22.00
74 0.00 -28.72 17.73 25.57 0.21 16.75 -47.23 -34.66 25.64
75 0.00 12.78 -14.46 44.84 -45.74 46.70 44.03 40.54 -26.71
76 0.00 -45.72 -46.65 -35.90 8.32 -23.34 35.28 15.75 20.93
77 0.00 -4.21 21.15 -16.63 -37.62 6.61 26.54 -9.04 -31.43
78 0.00 37.29 -11.04 2.63 16.43 36.57 17.79 -33.83 16.22
79 0.00 -21.20 -43.23 21.90 -29.51 -33.47 9.04 41.37 -36.14
80 0.00 20.30 24.58 41.16 24.55 -3.52 0.30 16.58 11.50
81 0.00 -38.20 -7.62 -39.57 -21.40 26.44 -8.45 -8.21 -40.85
82 0.00 3.31 -39.81 -20.31 32.66 -43.61 -17.20 -33.01 6.79
83 0.00 44.81 28.00 -1.05 -13.28 -13.65 -25.94 42.20 -45.56
84 0.00 -13.69 -4.20 18.22 40.77 16.31 -34.69 17.41 2.08
85 0.00 27.82 -36.39 37.48 -5.17 46.26 -43.43 -7.38 49.72
86 0.00 -30.68 31.42 -43.25 48.89 -23.78 47.82 -32.18 -2.63
87 0.00 10.83 -0.77 -23.99 2.94 6.17 39.07 43.03 45.01
88 0.00 -47.67 -32.97 -4.72 -43.00 36.13 30.33 18.24 -7.35
89 0.00 -6.17 34.84 14.54 11.06 -33.91 21.58 -6.55 40.30
90 0.00 35.34 2.65 33.81 -34.88 -3.96 12.83 -31.35 -12.06
91 0.00 -23.16 -29.55 -46.93 19.17 26.00 4.09 43.86 35.59
92 0.00 18.34 38.26 -27.67 -26.77 -44.05 -4.66 19.07 -16.77
93 0.00 -40.15 6.07 -8.40 27.29 -14.09 -13.40 -5.73 30.87
94 0.00 1.35 -26.12 10.86 -18.66 15.87 -22.15 -30.52 -21.48
95 0.00 42.86 41.68 30.13 35.40 45.82 -30.90 44.69 26.16
96 0.00 -15.64 9.49 49.39 -10.54 -24.22 -39.64 19.90 -26.19
97 0.00 25.86 -22.70 -31.34 43.51 5.73 -48.39 -4.90 21.45
98 0.00 -32.63 45.10 -12.08 -2.43 35.69 42.86 -29.69 -30.91
99 0.00 8.87 12.91 7.19 -48.37 -34.35 34.12 45.52 16.74

List of TE simple badnesses for small edos

Notes:

  1. Patent val mapping is used throughout.
  2. Each edo is TE-optimally stretched.
  3. Graham Breed's definition is used, scaled by 100.
Edo 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

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