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| | 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]]. |
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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.
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| The second shows the [[TE simple badness|TE simple badnesses]] aka relative errors in a certain JI subgroup for edos up to 99.
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| == 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 |
| ! colspan="8" |Relative Errors (Percent) | | ! colspan="8" | Relative Errors (Percent) |
| |- | | |- |
| ! 3/1 | | ! 3/1 |
| Line 1,010: |
Line 1,005: |
| |} | | |} |
|
| |
|
| == List of TE simple badnesses for small edos == | | == See also == |
| Notes:
| | * Relative errors of small ed-''p''<span/>'s: |
| # [[Patent val]] mapping is used throughout.
| | ** [[Relative errors of small EDTs]] |
| # Each edo is TE-optimally stretched.
| | ** [[Relative errors of small EDFs]] |
| # [[Graham Breed]]'s definition is used, scaled by 100.
| | ** [[Relative errors of small ED5s]] |
| {| class="wikitable sortable mw-collapsible" style="text-align:right"
| | ** [[Relative errors of small ED6s]] |
| ! rowspan="2" | Edo
| | * [[Relative errors of small equal temperaments]] |
| ! 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 ==
| |
| | |
| * [[EDO]] | |
| * [[Relative error]] | |
| * [[Relative Errors of Small EDTs]] | |
| * [[Relative Errors of Small EDFs]] | |
| * [[Relative Errors of Small ED6s]] | |
|
| |
|
| [[Category:EDO theory pages]] | | [[Category:EDO theory pages]] |
| [[category:list]] | | [[Category:Tables]] |
| [[category:table]]
| |
The following table 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 odd limits higher than 23. The relative errors of other intervals can be derived easily since they follow the additive rule.
| EDO
|
Relative Errors (Percent)
|
| 3/1
|
5/1
|
7/1
|
11/1
|
13/1
|
17/1
|
19/1
|
23/1
|
| 1
|
41.50
|
-32.19
|
19.26
|
-45.94
|
29.96
|
-8.75
|
-24.79
|
47.64
|
| 2
|
-16.99
|
35.61
|
38.53
|
8.11
|
-40.09
|
-17.49
|
-49.59
|
-4.71
|
| 3
|
24.51
|
3.42
|
-42.21
|
-37.83
|
-10.13
|
-26.24
|
25.62
|
42.93
|
| 4
|
-33.99
|
-28.77
|
-22.94
|
16.23
|
19.82
|
-34.99
|
0.83
|
-9.42
|
| 5
|
7.52
|
39.04
|
-3.68
|
-29.72
|
49.78
|
-43.73
|
-23.96
|
38.22
|
| 6
|
49.02
|
6.84
|
15.59
|
24.34
|
-20.26
|
47.52
|
-48.76
|
-14.14
|
| 7
|
-9.47
|
-25.35
|
34.85
|
-21.60
|
9.69
|
38.78
|
26.45
|
33.51
|
| 8
|
32.03
|
42.46
|
-45.88
|
32.45
|
39.65
|
30.03
|
1.66
|
-18.85
|
| 9
|
-26.47
|
10.26
|
-26.62
|
-13.49
|
-30.40
|
21.28
|
-23.13
|
28.79
|
| 10
|
15.04
|
-21.93
|
-7.35
|
40.57
|
-0.44
|
12.54
|
-47.93
|
-23.56
|
| 11
|
-43.46
|
45.88
|
11.91
|
-5.37
|
29.52
|
3.79
|
27.28
|
24.08
|
| 12
|
-1.96
|
13.69
|
31.17
|
48.68
|
-40.53
|
-4.96
|
2.49
|
-28.27
|
| 13
|
39.55
|
-18.51
|
-49.56
|
2.74
|
-10.57
|
-13.70
|
-22.31
|
19.37
|
| 14
|
-18.95
|
49.30
|
-30.30
|
-43.20
|
19.38
|
-22.45
|
-47.10
|
-32.99
|
| 15
|
22.56
|
17.11
|
-11.03
|
10.85
|
49.34
|
-31.19
|
28.11
|
14.66
|
| 16
|
-35.94
|
-15.08
|
8.23
|
-35.09
|
-20.70
|
-39.94
|
3.32
|
-37.70
|
| 17
|
5.56
|
-47.28
|
27.50
|
18.97
|
9.25
|
-48.69
|
-21.48
|
9.94
|
| 18
|
47.07
|
20.53
|
46.76
|
-26.98
|
39.21
|
42.57
|
-46.27
|
-42.41
|
| 19
|
-11.43
|
-11.66
|
-33.97
|
27.08
|
-30.84
|
33.82
|
28.94
|
5.23
|
| 20
|
30.07
|
-43.86
|
-14.71
|
-18.86
|
-0.88
|
25.07
|
4.14
|
-47.12
|
| 21
|
-28.42
|
23.95
|
4.55
|
35.19
|
29.08
|
16.33
|
-20.65
|
0.52
|
| 22
|
13.08
|
-8.24
|
23.82
|
-10.75
|
-40.97
|
7.58
|
-45.44
|
48.16
|
| 23
|
-45.41
|
-40.43
|
43.08
|
43.31
|
-11.01
|
-1.16
|
29.77
|
-4.19
|
| 24
|
-3.91
|
27.37
|
-37.65
|
-2.64
|
18.94
|
-9.91
|
4.97
|
43.45
|
| 25
|
37.59
|
-4.82
|
-18.39
|
-48.58
|
48.90
|
-18.66
|
-19.82
|
-8.90
|
| 26
|
-20.90
|
-37.01
|
0.88
|
5.48
|
-21.14
|
-27.40
|
-44.61
|
38.74
|
| 27
|
20.60
|
30.79
|
20.14
|
-40.47
|
8.81
|
-36.15
|
30.60
|
-13.62
|
| 28
|
-37.90
|
-1.40
|
39.41
|
13.59
|
38.77
|
-44.90
|
5.80
|
34.03
|
| 29
|
3.61
|
-33.59
|
-41.33
|
-32.35
|
-31.28
|
46.36
|
-18.99
|
-18.33
|
| 30
|
45.11
|
34.22
|
-22.06
|
21.71
|
-1.32
|
37.61
|
-43.78
|
29.31
|
| 31
|
-13.38
|
2.02
|
-2.80
|
-24.24
|
28.64
|
28.87
|
31.42
|
-23.04
|
| 32
|
28.12
|
-30.17
|
16.46
|
29.82
|
-41.41
|
20.12
|
6.63
|
24.60
|
| 33
|
-30.38
|
37.64
|
35.73
|
-16.12
|
-11.45
|
11.37
|
-18.16
|
-27.75
|
| 34
|
11.13
|
5.44
|
-45.01
|
37.93
|
18.50
|
2.63
|
-42.95
|
19.89
|
| 35
|
-47.37
|
-26.75
|
-25.74
|
-8.01
|
48.46
|
-6.12
|
32.25
|
-32.47
|
| 36
|
-5.87
|
41.06
|
-6.48
|
46.05
|
-21.58
|
-14.87
|
7.46
|
15.18
|
| 37
|
35.64
|
8.87
|
12.79
|
0.10
|
8.37
|
-23.61
|
-17.33
|
-37.18
|
| 38
|
-22.86
|
-23.33
|
32.05
|
-45.84
|
38.33
|
-32.36
|
-42.12
|
10.46
|
| 39
|
18.65
|
44.48
|
-48.68
|
8.22
|
-31.71
|
-41.11
|
33.08
|
-41.89
|
| 40
|
-39.85
|
12.29
|
-29.42
|
-37.73
|
-1.76
|
-49.85
|
8.29
|
5.75
|
| 41
|
1.65
|
-19.91
|
-10.16
|
16.33
|
28.20
|
41.40
|
-16.50
|
-46.60
|
| 42
|
43.16
|
47.90
|
9.11
|
-29.61
|
-41.85
|
32.66
|
-41.30
|
1.04
|
| 43
|
-15.34
|
15.71
|
28.37
|
24.44
|
-11.89
|
23.91
|
33.91
|
48.68
|
| 44
|
26.16
|
-16.48
|
47.64
|
-21.50
|
18.07
|
15.16
|
9.12
|
-3.67
|
| 45
|
-32.33
|
-48.68
|
-33.10
|
32.56
|
48.02
|
6.42
|
-15.67
|
43.97
|
| 46
|
9.17
|
19.13
|
-13.83
|
-13.39
|
-22.02
|
-2.33
|
-40.47
|
-8.38
|
| 47
|
-49.32
|
-13.06
|
5.43
|
40.67
|
7.93
|
-11.08
|
34.74
|
39.26
|
| 48
|
-7.82
|
-45.25
|
24.70
|
-5.27
|
37.89
|
-19.82
|
9.95
|
-13.10
|
| 49
|
33.68
|
22.55
|
43.96
|
48.79
|
-32.15
|
-28.57
|
-14.84
|
34.55
|
| 50
|
-24.81
|
-9.64
|
-36.77
|
2.84
|
-2.20
|
-37.31
|
-39.64
|
-17.81
|
| 51
|
16.69
|
-41.83
|
-17.51
|
-43.10
|
27.76
|
-46.06
|
35.57
|
29.83
|
| 52
|
-41.81
|
25.97
|
1.75
|
10.96
|
-42.29
|
45.19
|
10.78
|
-22.52
|
| 53
|
-0.30
|
-6.22
|
21.02
|
-34.99
|
-12.33
|
36.45
|
-14.02
|
25.12
|
| 54
|
41.20
|
-38.41
|
40.28
|
19.07
|
17.63
|
27.70
|
-38.81
|
-27.23
|
| 55
|
-17.29
|
29.40
|
-40.45
|
-26.87
|
47.58
|
18.95
|
36.40
|
20.41
|
| 56
|
24.21
|
-2.80
|
-21.19
|
27.18
|
-22.46
|
10.21
|
11.61
|
-31.95
|
| 57
|
-34.29
|
-34.99
|
-1.92
|
-18.76
|
7.49
|
1.46
|
-13.19
|
15.70
|
| 58
|
7.22
|
32.82
|
17.34
|
35.30
|
37.45
|
-7.28
|
-37.98
|
-36.66
|
| 59
|
48.72
|
0.62
|
36.61
|
-10.65
|
-32.59
|
-16.03
|
37.23
|
10.98
|
| 60
|
-9.78
|
-31.57
|
-44.13
|
43.41
|
-2.64
|
-24.78
|
12.43
|
-41.37
|
| 61
|
31.73
|
36.24
|
-24.87
|
-2.53
|
27.32
|
-33.52
|
-12.36
|
6.27
|
| 62
|
-26.77
|
4.05
|
-5.60
|
-48.48
|
-42.73
|
-42.27
|
-37.15
|
-46.08
|
| 63
|
14.74
|
-28.15
|
13.66
|
5.58
|
-12.77
|
48.98
|
38.06
|
1.56
|
| 64
|
-43.76
|
39.66
|
32.93
|
-40.36
|
17.19
|
40.24
|
13.26
|
49.20
|
| 65
|
-2.26
|
7.47
|
-47.81
|
13.69
|
47.14
|
31.49
|
-11.53
|
-3.15
|
| 66
|
39.25
|
-24.73
|
-28.54
|
-32.25
|
-22.90
|
22.75
|
-36.32
|
44.49
|
| 67
|
-19.25
|
43.08
|
-9.28
|
21.81
|
7.05
|
14.00
|
38.89
|
-7.87
|
| 68
|
22.25
|
10.89
|
9.99
|
-24.14
|
37.01
|
5.25
|
14.09
|
39.78
|
| 69
|
-36.24
|
-21.30
|
29.25
|
29.92
|
-33.03
|
-3.49
|
-10.70
|
-12.58
|
| 70
|
5.26
|
46.50
|
48.52
|
-16.02
|
-3.08
|
-12.24
|
-35.49
|
35.07
|
| 71
|
46.77
|
14.31
|
-32.22
|
38.04
|
26.88
|
-20.99
|
39.71
|
-17.29
|
| 72
|
-11.73
|
-17.88
|
-12.96
|
-7.91
|
-43.17
|
-29.73
|
14.92
|
30.35
|
| 73
|
29.77
|
49.92
|
6.31
|
46.15
|
-13.21
|
-38.48
|
-9.87
|
-22.00
|
| 74
|
-28.72
|
17.73
|
25.57
|
0.21
|
16.75
|
-47.23
|
-34.66
|
25.64
|
| 75
|
12.78
|
-14.46
|
44.84
|
-45.74
|
46.70
|
44.03
|
40.54
|
-26.71
|
| 76
|
-45.72
|
-46.65
|
-35.90
|
8.32
|
-23.34
|
35.28
|
15.75
|
20.93
|
| 77
|
-4.21
|
21.15
|
-16.63
|
-37.62
|
6.61
|
26.54
|
-9.04
|
-31.43
|
| 78
|
37.29
|
-11.04
|
2.63
|
16.43
|
36.57
|
17.79
|
-33.83
|
16.22
|
| 79
|
-21.20
|
-43.23
|
21.90
|
-29.51
|
-33.47
|
9.04
|
41.37
|
-36.14
|
| 80
|
20.30
|
24.58
|
41.16
|
24.55
|
-3.52
|
0.30
|
16.58
|
11.50
|
| 81
|
-38.20
|
-7.62
|
-39.57
|
-21.40
|
26.44
|
-8.45
|
-8.21
|
-40.85
|
| 82
|
3.31
|
-39.81
|
-20.31
|
32.66
|
-43.61
|
-17.20
|
-33.01
|
6.79
|
| 83
|
44.81
|
28.00
|
-1.05
|
-13.28
|
-13.65
|
-25.94
|
42.20
|
-45.56
|
| 84
|
-13.69
|
-4.20
|
18.22
|
40.77
|
16.31
|
-34.69
|
17.41
|
2.08
|
| 85
|
27.82
|
-36.39
|
37.48
|
-5.17
|
46.26
|
-43.43
|
-7.38
|
49.72
|
| 86
|
-30.68
|
31.42
|
-43.25
|
48.89
|
-23.78
|
47.82
|
-32.18
|
-2.63
|
| 87
|
10.83
|
-0.77
|
-23.99
|
2.94
|
6.17
|
39.07
|
43.03
|
45.01
|
| 88
|
-47.67
|
-32.97
|
-4.72
|
-43.00
|
36.13
|
30.33
|
18.24
|
-7.35
|
| 89
|
-6.17
|
34.84
|
14.54
|
11.06
|
-33.91
|
21.58
|
-6.55
|
40.30
|
| 90
|
35.34
|
2.65
|
33.81
|
-34.88
|
-3.96
|
12.83
|
-31.35
|
-12.06
|
| 91
|
-23.16
|
-29.55
|
-46.93
|
19.17
|
26.00
|
4.09
|
43.86
|
35.59
|
| 92
|
18.34
|
38.26
|
-27.67
|
-26.77
|
-44.05
|
-4.66
|
19.07
|
-16.77
|
| 93
|
-40.15
|
6.07
|
-8.40
|
27.29
|
-14.09
|
-13.40
|
-5.73
|
30.87
|
| 94
|
1.35
|
-26.12
|
10.86
|
-18.66
|
15.87
|
-22.15
|
-30.52
|
-21.48
|
| 95
|
42.86
|
41.68
|
30.13
|
35.40
|
45.82
|
-30.90
|
44.69
|
26.16
|
| 96
|
-15.64
|
9.49
|
49.39
|
-10.54
|
-24.22
|
-39.64
|
19.90
|
-26.19
|
| 97
|
25.86
|
-22.70
|
-31.34
|
43.51
|
5.73
|
-48.39
|
-4.90
|
21.45
|
| 98
|
-32.63
|
45.10
|
-12.08
|
-2.43
|
35.69
|
42.86
|
-29.69
|
-30.91
|
| 99
|
8.87
|
12.91
|
7.19
|
-48.37
|
-34.35
|
34.12
|
45.52
|
16.74
|
See also