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Relative errors of small EDOs: Difference between revisions

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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]].


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. 
== List of Relative Errors of Prime Harmonies 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="9" | Relative Errors (Percent)
! colspan="8" | Relative Errors (Percent)
|-
|-
!  2/1
!  3/1
!  3/1
!  5/1
!  5/1
Line 19: Line 15:
|-
|-
|  1
|  1
|  0.00
|  41.50
|  41.50
| -32.19
| -32.19
Line 30: Line 25:
|-
|-
|  2
|  2
|  0.00
| -16.99
| -16.99
|  35.61
|  35.61
Line 41: Line 35:
|-
|-
|  3
|  3
|  0.00
|  24.51
|  24.51
|  3.42
|  3.42
Line 52: Line 45:
|-
|-
|  4
|  4
|  0.00
| -33.99
| -33.99
| -28.77
| -28.77
Line 63: Line 55:
|-
|-
|  5
|  5
|  0.00
|  7.52
|  7.52
|  39.04
|  39.04
Line 74: Line 65:
|-
|-
|  6
|  6
|  0.00
|  49.02
|  49.02
|  6.84
|  6.84
Line 85: Line 75:
|-
|-
|  7
|  7
|  0.00
|  -9.47
|  -9.47
| -25.35
| -25.35
Line 96: Line 85:
|-
|-
|  8
|  8
|  0.00
|  32.03
|  32.03
|  42.46
|  42.46
Line 107: Line 95:
|-
|-
|  9
|  9
|  0.00
| -26.47
| -26.47
|  10.26
|  10.26
Line 118: Line 105:
|-
|-
| 10
| 10
|  0.00
|  15.04
|  15.04
| -21.93
| -21.93
Line 129: Line 115:
|-
|-
| 11
| 11
|  0.00
| -43.46
| -43.46
|  45.88
|  45.88
Line 140: Line 125:
|-
|-
| 12
| 12
|  0.00
|  -1.96
|  -1.96
|  13.69
|  13.69
Line 151: Line 135:
|-
|-
| 13
| 13
|  0.00
|  39.55
|  39.55
| -18.51
| -18.51
Line 162: Line 145:
|-
|-
| 14
| 14
|  0.00
| -18.95
| -18.95
|  49.30
|  49.30
Line 173: Line 155:
|-
|-
| 15
| 15
|  0.00
|  22.56
|  22.56
|  17.11
|  17.11
Line 184: Line 165:
|-
|-
| 16
| 16
|  0.00
| -35.94
| -35.94
| -15.08
| -15.08
Line 195: Line 175:
|-
|-
| 17
| 17
|  0.00
|  5.56
|  5.56
| -47.28
| -47.28
Line 206: Line 185:
|-
|-
| 18
| 18
|  0.00
|  47.07
|  47.07
|  20.53
|  20.53
Line 217: Line 195:
|-
|-
| 19
| 19
|  0.00
| -11.43
| -11.43
| -11.66
| -11.66
Line 228: Line 205:
|-
|-
| 20
| 20
|  0.00
|  30.07
|  30.07
| -43.86
| -43.86
Line 239: Line 215:
|-
|-
| 21
| 21
|  0.00
| -28.42
| -28.42
|  23.95
|  23.95
Line 250: Line 225:
|-
|-
| 22
| 22
|  0.00
|  13.08
|  13.08
|  -8.24
|  -8.24
Line 261: Line 235:
|-
|-
| 23
| 23
|  0.00
| -45.41
| -45.41
| -40.43
| -40.43
Line 272: Line 245:
|-
|-
| 24
| 24
|  0.00
|  -3.91
|  -3.91
|  27.37
|  27.37
Line 283: Line 255:
|-
|-
| 25
| 25
|  0.00
|  37.59
|  37.59
|  -4.82
|  -4.82
Line 294: Line 265:
|-
|-
| 26
| 26
|  0.00
| -20.90
| -20.90
| -37.01
| -37.01
Line 305: Line 275:
|-
|-
| 27
| 27
|  0.00
|  20.60
|  20.60
|  30.79
|  30.79
Line 316: Line 285:
|-
|-
| 28
| 28
|  0.00
| -37.90
| -37.90
|  -1.40
|  -1.40
Line 327: Line 295:
|-
|-
| 29
| 29
|  0.00
|  3.61
|  3.61
| -33.59
| -33.59
Line 338: Line 305:
|-
|-
| 30
| 30
|  0.00
|  45.11
|  45.11
|  34.22
|  34.22
Line 349: Line 315:
|-
|-
| 31
| 31
|  0.00
| -13.38
| -13.38
|  2.02
|  2.02
Line 360: Line 325:
|-
|-
| 32
| 32
|  0.00
|  28.12
|  28.12
| -30.17
| -30.17
Line 371: Line 335:
|-
|-
| 33
| 33
|  0.00
| -30.38
| -30.38
|  37.64
|  37.64
Line 382: Line 345:
|-
|-
| 34
| 34
|  0.00
|  11.13
|  11.13
|  5.44
|  5.44
Line 393: Line 355:
|-
|-
| 35
| 35
|  0.00
| -47.37
| -47.37
| -26.75
| -26.75
Line 404: Line 365:
|-
|-
| 36
| 36
|  0.00
|  -5.87
|  -5.87
|  41.06
|  41.06
Line 415: Line 375:
|-
|-
| 37
| 37
|  0.00
|  35.64
|  35.64
|  8.87
|  8.87
Line 426: Line 385:
|-
|-
| 38
| 38
|  0.00
| -22.86
| -22.86
| -23.33
| -23.33
Line 437: Line 395:
|-
|-
| 39
| 39
|  0.00
|  18.65
|  18.65
|  44.48
|  44.48
Line 448: Line 405:
|-
|-
| 40
| 40
|  0.00
| -39.85
| -39.85
|  12.29
|  12.29
Line 459: Line 415:
|-
|-
| 41
| 41
|  0.00
|  1.65
|  1.65
| -19.91
| -19.91
Line 470: Line 425:
|-
|-
| 42
| 42
|  0.00
|  43.16
|  43.16
|  47.90
|  47.90
Line 481: Line 435:
|-
|-
| 43
| 43
|  0.00
| -15.34
| -15.34
|  15.71
|  15.71
Line 492: Line 445:
|-
|-
| 44
| 44
|  0.00
|  26.16
|  26.16
| -16.48
| -16.48
Line 503: Line 455:
|-
|-
| 45
| 45
|  0.00
| -32.33
| -32.33
| -48.68
| -48.68
Line 514: Line 465:
|-
|-
| 46
| 46
|  0.00
|  9.17
|  9.17
|  19.13
|  19.13
Line 525: Line 475:
|-
|-
| 47
| 47
|  0.00
| -49.32
| -49.32
| -13.06
| -13.06
Line 536: Line 485:
|-
|-
| 48
| 48
|  0.00
|  -7.82
|  -7.82
| -45.25
| -45.25
Line 547: Line 495:
|-
|-
| 49
| 49
|  0.00
|  33.68
|  33.68
|  22.55
|  22.55
Line 558: Line 505:
|-
|-
| 50
| 50
|  0.00
| -24.81
| -24.81
|  -9.64
|  -9.64
Line 569: Line 515:
|-
|-
| 51
| 51
|  0.00
|  16.69
|  16.69
| -41.83
| -41.83
Line 580: Line 525:
|-
|-
| 52
| 52
|  0.00
| -41.81
| -41.81
|  25.97
|  25.97
Line 591: Line 535:
|-
|-
| 53
| 53
|  0.00
|  -0.30
|  -0.30
|  -6.22
|  -6.22
Line 602: Line 545:
|-
|-
| 54
| 54
|  0.00
|  41.20
|  41.20
| -38.41
| -38.41
Line 613: Line 555:
|-
|-
| 55
| 55
|  0.00
| -17.29
| -17.29
|  29.40
|  29.40
Line 624: Line 565:
|-
|-
| 56
| 56
|  0.00
|  24.21
|  24.21
|  -2.80
|  -2.80
Line 635: Line 575:
|-
|-
| 57
| 57
|  0.00
| -34.29
| -34.29
| -34.99
| -34.99
Line 646: Line 585:
|-
|-
| 58
| 58
|  0.00
|  7.22
|  7.22
|  32.82
|  32.82
Line 657: Line 595:
|-
|-
| 59
| 59
|  0.00
|  48.72
|  48.72
|  0.62
|  0.62
Line 668: Line 605:
|-
|-
| 60
| 60
|  0.00
|  -9.78
|  -9.78
| -31.57
| -31.57
Line 679: Line 615:
|-
|-
| 61
| 61
|  0.00
|  31.73
|  31.73
|  36.24
|  36.24
Line 690: Line 625:
|-
|-
| 62
| 62
|  0.00
| -26.77
| -26.77
|  4.05
|  4.05
Line 701: Line 635:
|-
|-
| 63
| 63
|  0.00
|  14.74
|  14.74
| -28.15
| -28.15
Line 712: Line 645:
|-
|-
| 64
| 64
|  0.00
| -43.76
| -43.76
|  39.66
|  39.66
Line 723: Line 655:
|-
|-
| 65
| 65
|  0.00
|  -2.26
|  -2.26
|  7.47
|  7.47
Line 734: Line 665:
|-
|-
| 66
| 66
|  0.00
|  39.25
|  39.25
| -24.73
| -24.73
Line 745: Line 675:
|-
|-
| 67
| 67
|  0.00
| -19.25
| -19.25
|  43.08
|  43.08
Line 756: Line 685:
|-
|-
| 68
| 68
|  0.00
|  22.25
|  22.25
|  10.89
|  10.89
Line 767: Line 695:
|-
|-
| 69
| 69
|  0.00
| -36.24
| -36.24
| -21.30
| -21.30
Line 778: Line 705:
|-
|-
| 70
| 70
|  0.00
|  5.26
|  5.26
|  46.50
|  46.50
Line 789: Line 715:
|-
|-
| 71
| 71
|  0.00
|  46.77
|  46.77
|  14.31
|  14.31
Line 800: Line 725:
|-
|-
| 72
| 72
|  0.00
| -11.73
| -11.73
| -17.88
| -17.88
Line 811: Line 735:
|-
|-
| 73
| 73
|  0.00
|  29.77
|  29.77
|  49.92
|  49.92
Line 822: Line 745:
|-
|-
| 74
| 74
|  0.00
| -28.72
| -28.72
|  17.73
|  17.73
Line 833: Line 755:
|-
|-
| 75
| 75
|  0.00
|  12.78
|  12.78
| -14.46
| -14.46
Line 844: Line 765:
|-
|-
| 76
| 76
|  0.00
| -45.72
| -45.72
| -46.65
| -46.65
Line 855: Line 775:
|-
|-
| 77
| 77
|  0.00
|  -4.21
|  -4.21
|  21.15
|  21.15
Line 866: Line 785:
|-
|-
| 78
| 78
|  0.00
|  37.29
|  37.29
| -11.04
| -11.04
Line 877: Line 795:
|-
|-
| 79
| 79
|  0.00
| -21.20
| -21.20
| -43.23
| -43.23
Line 888: Line 805:
|-
|-
| 80
| 80
|  0.00
|  20.30
|  20.30
|  24.58
|  24.58
Line 899: Line 815:
|-
|-
| 81
| 81
|  0.00
| -38.20
| -38.20
|  -7.62
|  -7.62
Line 910: Line 825:
|-
|-
| 82
| 82
|  0.00
|  3.31
|  3.31
| -39.81
| -39.81
Line 921: Line 835:
|-
|-
| 83
| 83
|  0.00
|  44.81
|  44.81
|  28.00
|  28.00
Line 932: Line 845:
|-
|-
| 84
| 84
|  0.00
| -13.69
| -13.69
|  -4.20
|  -4.20
Line 943: Line 855:
|-
|-
| 85
| 85
|  0.00
|  27.82
|  27.82
| -36.39
| -36.39
Line 954: Line 865:
|-
|-
| 86
| 86
|  0.00
| -30.68
| -30.68
|  31.42
|  31.42
Line 965: Line 875:
|-
|-
| 87
| 87
|  0.00
|  10.83
|  10.83
|  -0.77
|  -0.77
Line 976: Line 885:
|-
|-
| 88
| 88
|  0.00
| -47.67
| -47.67
| -32.97
| -32.97
Line 987: Line 895:
|-
|-
| 89
| 89
|  0.00
|  -6.17
|  -6.17
|  34.84
|  34.84
Line 998: Line 905:
|-
|-
| 90
| 90
|  0.00
|  35.34
|  35.34
|  2.65
|  2.65
Line 1,009: Line 915:
|-
|-
| 91
| 91
|  0.00
| -23.16
| -23.16
| -29.55
| -29.55
Line 1,020: Line 925:
|-
|-
| 92
| 92
|  0.00
|  18.34
|  18.34
|  38.26
|  38.26
Line 1,031: Line 935:
|-
|-
| 93
| 93
|  0.00
| -40.15
| -40.15
|  6.07
|  6.07
Line 1,042: Line 945:
|-
|-
| 94
| 94
|  0.00
|  1.35
|  1.35
| -26.12
| -26.12
Line 1,053: Line 955:
|-
|-
| 95
| 95
|  0.00
|  42.86
|  42.86
|  41.68
|  41.68
Line 1,064: Line 965:
|-
|-
| 96
| 96
|  0.00
| -15.64
| -15.64
|  9.49
|  9.49
Line 1,075: Line 975:
|-
|-
| 97
| 97
|  0.00
|  25.86
|  25.86
| -22.70
| -22.70
Line 1,086: Line 985:
|-
|-
| 98
| 98
|  0.00
| -32.63
| -32.63
|  45.10
|  45.10
Line 1,097: Line 995:
|-
|-
| 99
| 99
|  0.00
|  8.87
|  8.87
|  12.91
|  12.91
Line 1,108: Line 1,005:
|}
|}


== List of RMS Relative Errors of JI Subgroups 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]]
# 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. 
** [[Relative errors of small EDFs]]
# The weight of intervals is determined by the [[tonality diamond]]. For example, the [[9-odd-limit]] takes account of 3/1 twice.
** [[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="11" | Root Mean Squared Relative Errors (Percent)
|-
! 3 Odd Limit
! 5 Odd Limit
! 7 Odd Limit
! 9 Odd Limit
! 11 Odd Limit
! 13 Odd Limit
! 15 Odd Limit
! 17 Odd Limit
! 19 Odd Limit
! 21 Odd Limit
! 23 Odd Limit
|-
| 1
| 29.35
| 42.66
| 38.25
| 54.88
| 61.68
| 57.87
| 54.17
| 51.99
| 51.57
| 53.79
| 53.35
|-
| 2
| 12.02
| 31.00
| 33.35
| 40.44
| 36.97
| 40.91
| 39.38
| 38.05
| 41.60
| 41.18
| 39.43
|-
| 3
| 17.33
| 15.33
| 34.23
| 42.69
| 45.56
| 42.45
| 42.08
| 41.59
| 41.08
| 39.93
| 41.80
|-
| 4
| 24.03
| 21.13
| 18.34
| 31.02
| 37.61
| 40.74
| 43.75
| 41.62
| 40.86
| 41.54
| 40.21
|-
| 5
| 5.32
| 23.91
| 23.81
| 21.44
| 29.27
| 35.10
| 36.78
| 43.55
| 43.62
| 41.59
| 41.82
|-
| 6
| 34.66
| 30.66
| 26.61
| 51.22
| 47.03
| 50.72
| 49.62
| 47.53
| 56.32
| 56.32
| 56.23
|-
| 7
| 6.70
| 14.79
| 31.20
| 29.90
| 28.86
| 27.93
| 29.75
| 34.97
| 35.45
| 35.34
| 35.97
|-
| 8
| 22.65
| 25.55
| 48.63
| 54.11
| 49.94
| 47.16
| 50.14
| 47.27
| 46.42
| 47.29
| 48.19
|-
| 9
| 18.71
| 21.88
| 22.98
| 31.51
| 28.92
| 27.45
| 25.73
| 30.28
| 28.94
| 31.48
| 35.50
|-
| 10
| 10.63
| 21.47
| 18.85
| 25.42
| 30.45
| 28.61
| 27.65
| 26.22
| 34.04
| 32.56
| 32.73
|-
| 11
| 30.73
| 51.59
| 45.19
| 65.23
| 59.74
| 59.17
| 55.52
| 52.52
| 51.64
| 50.73
| 49.81
|-
| 12
| 1.38
| 9.84
| 18.74
| 18.70
| 27.49
| 37.31
| 34.98
| 33.43
| 31.75
| 31.76
| 33.51
|-
| 13
| 27.97
| 34.24
| 45.60
| 63.59
| 58.18
| 54.71
| 51.65
| 49.64
| 48.56
| 46.59
| 45.14
|-
| 14
| 13.40
| 40.68
| 43.05
| 44.08
| 44.41
| 44.22
| 45.23
| 43.44
| 44.75
| 45.54
| 44.25
|-
| 15
| 15.95
| 13.59
| 18.95
| 27.35
| 25.06
| 29.02
| 28.80
| 35.91
| 34.47
| 32.94
| 31.54
|-
| 16
| 25.41
| 20.84
| 23.76
| 40.61
| 37.62
| 34.90
| 34.95
| 33.39
| 34.53
| 32.93
| 31.86
|-
| 17
| 3.93
| 33.53
| 38.55
| 35.46
| 33.98
| 31.63
| 36.39
| 40.08
| 38.50
| 40.44
| 39.15
|-
| 18
| 33.28
| 27.25
| 27.87
| 44.68
| 54.53
| 50.68
| 50.32
| 47.53
| 57.22
| 60.69
| 65.40
|-
| 19
| 8.08
| 7.70
| 17.42
| 16.32
| 27.15
| 27.40
| 26.15
| 32.36
| 34.49
| 36.87
| 35.68
|-
| 20
| 21.27
| 42.93
| 37.69
| 50.84
| 48.27
| 44.72
| 42.45
| 41.57
| 39.45
| 37.96
| 41.45
|-
| 21
| 20.10
| 30.27
| 26.48
| 39.94
| 43.95
| 43.78
| 41.04
| 39.33
| 38.55
| 38.00
| 36.40
|-
| 22
| 9.25
| 12.42
| 17.34
| 18.87
| 20.68
| 30.63
| 28.72
| 27.24
| 32.68
| 35.13
| 38.42
|-
| 23
| 32.11
| 28.76
| 50.48
| 63.98
| 69.09
| 64.00
| 68.54
| 65.37
| 65.64
| 62.83
| 60.29
|-
| 24
| 2.76
| 19.68
| 32.65
| 29.30
| 26.76
| 27.28
| 27.93
| 26.88
| 25.56
| 29.95
| 33.86
|-
| 25
| 26.58
| 26.81
| 29.35
| 48.26
| 56.30
| 56.12
| 53.32
| 52.49
| 51.55
| 49.34
| 47.78
|-
| 26
| 14.78
| 21.43
| 22.30
| 25.31
| 26.66
| 24.84
| 30.29
| 28.68
| 28.82
| 27.54
| 36.02
|-
| 27
| 14.57
| 18.11
| 15.80
| 19.33
| 37.61
| 34.85
| 37.55
| 42.45
| 41.14
| 40.85
| 40.71
|-
| 28
| 26.80
| 24.81
| 38.67
| 55.10
| 52.53
| 54.37
| 53.56
| 53.12
| 50.95
| 48.81
| 49.68
|-
| 29
| 2.55
| 23.69
| 28.09
| 28.84
| 28.27
| 27.23
| 26.06
| 38.29
| 36.43
| 36.16
| 34.64
|-
| 30
| 31.90
| 27.18
| 37.90
| 54.71
| 50.11
| 48.64
| 52.35
| 49.44
| 56.78
| 54.14
| 51.88
|-
| 31
| 9.46
| 9.67
| 8.39
| 15.13
| 16.20
| 24.64
| 23.22
| 26.82
| 29.15
| 28.68
| 28.86
|-
| 32
| 19.88
| 33.66
| 30.98
| 40.68
| 38.04
| 45.48
| 42.83
| 40.79
| 38.70
| 39.73
| 38.37
|-
| 33
| 21.48
| 39.34
| 39.71
| 53.83
| 49.58
| 45.99
| 43.50
| 41.64
| 40.02
| 38.37
| 37.93
|-
| 34
| 7.87
| 6.42
| 31.44
| 32.66
| 36.26
| 34.20
| 32.30
| 30.55
| 36.09
| 37.48
| 36.77
|-
| 35
| 33.49
| 27.42
| 23.76
| 44.83
| 44.04
| 57.61
| 59.14
| 56.64
| 59.15
| 60.36
| 57.86
|-
| 36
| 4.15
| 29.52
| 27.89
| 27.14
| 33.46
| 34.81
| 35.32
| 35.03
| 33.23
| 32.64
| 31.49
|-
| 37
| 25.20
| 21.42
| 18.60
| 36.26
| 35.75
| 33.72
| 33.63
| 37.80
| 38.79
| 39.54
| 43.41
|-
| 38
| 16.16
| 15.40
| 31.97
| 37.24
| 38.40
| 45.06
| 45.49
| 43.64
| 42.83
| 42.40
| 41.91
|-
| 39
| 13.18
| 25.79
| 48.19
| 47.12
| 43.03
| 44.87
| 50.25
| 52.82
| 51.45
| 51.48
| 52.56
|-
| 40
| 28.18
| 31.47
| 29.94
| 45.70
| 42.07
| 41.23
| 38.58
| 37.96
| 39.19
| 41.56
| 41.99
|-
| 41
| 1.17
| 13.85
| 12.25
| 12.44
| 15.99
| 20.85
| 21.84
| 27.57
| 27.66
| 26.76
| 31.80
|-
| 42
| 30.52
| 30.48
| 29.43
| 43.52
| 53.12
| 59.59
| 65.77
| 62.08
| 65.55
| 63.88
| 61.75
|-
| 43
| 10.85
| 17.93
| 23.24
| 29.85
| 30.23
| 29.04
| 27.17
| 27.50
| 29.04
| 27.80
| 31.12
|-
| 44
| 18.50
| 24.83
| 34.67
| 37.73
| 41.36
| 38.33
| 35.94
| 33.89
| 32.23
| 39.18
| 38.59
|-
| 45
| 22.86
| 28.60
| 25.05
| 30.33
| 45.42
| 55.24
| 60.43
| 58.39
| 55.42
| 56.13
| 59.79
|-
| 46
| 6.49
| 11.05
| 17.16
| 17.47
| 19.10
| 21.65
| 24.29
| 23.04
| 28.49
| 27.19
| 26.15
|-
| 47
| 34.88
| 29.51
| 30.18
| 54.85
| 62.76
| 59.63
| 59.97
| 56.72
| 58.62
| 57.15
| 59.00
|-
| 48
| 5.53
| 27.93
| 35.48
| 32.10
| 29.36
| 35.49
| 41.00
| 39.01
| 37.90
| 37.47
| 36.00
|-
| 49
| 23.82
| 19.82
| 23.09
| 31.61
| 29.96
| 43.69
| 43.20
| 48.35
| 48.67
| 52.04
| 49.97
|-
| 50
| 17.55
| 14.44
| 19.91
| 25.32
| 27.15
| 26.58
| 26.14
| 25.91
| 25.78
| 29.12
| 28.10
|-
| 51
| 11.80
| 34.81
| 30.66
| 37.05
| 40.21
| 41.37
| 40.00
| 41.66
| 44.12
| 42.12
| 42.63
|-
| 52
| 29.56
| 39.49
| 34.47
| 54.80
| 52.54
| 50.56
| 47.31
| 52.73
| 50.88
| 50.14
| 48.19
|-
| 53
| 0.21
| 4.05
| 14.63
| 13.30
| 23.32
| 22.02
| 20.62
| 26.78
| 26.05
| 26.47
| 27.14
|-
| 54
| 29.13
| 45.97
| 46.54
| 58.09
| 53.13
| 49.29
| 47.08
| 44.50
| 49.35
| 54.18
| 55.25
|-
| 55
| 12.23
| 27.26
| 36.05
| 35.80
| 33.53
| 43.84
| 41.88
| 40.75
| 41.83
| 46.81
| 45.74
|-
| 56
| 17.12
| 17.15
| 22.83
| 34.14
| 32.50
| 34.74
| 33.13
| 31.24
| 29.65
| 28.40
| 31.56
|-
| 57
| 24.24
| 23.10
| 23.84
| 35.77
| 33.01
| 34.87
| 39.51
| 39.42
| 37.70
| 36.33
| 38.15
|-
| 58
| 5.10
| 19.91
| 17.42
| 15.58
| 18.00
| 19.28
| 20.19
| 23.33
| 33.00
| 31.76
| 36.48
|-
| 59
| 34.45
| 32.27
| 30.56
| 50.92
| 52.75
| 57.52
| 55.52
| 55.24
| 52.96
| 56.85
| 54.79
|-
| 60
| 6.91
| 18.66
| 24.63
| 22.05
| 39.47
| 36.74
| 37.51
| 35.74
| 35.78
| 38.17
| 37.90
|-
| 61
| 22.44
| 22.80
| 35.17
| 43.33
| 41.50
| 38.74
| 42.93
| 48.09
| 47.45
| 45.38
| 43.57
|-
| 62
| 18.93
| 19.34
| 16.79
| 30.27
| 32.40
| 31.75
| 29.71
| 29.11
| 27.98
| 26.75
| 26.58
|-
| 63
| 10.42
| 25.16
| 24.46
| 27.48
| 25.09
| 24.99
| 24.64
| 31.49
| 32.75
| 32.14
| 31.01
|-
| 64
| 30.94
| 48.18
| 46.71
| 67.95
| 63.84
| 61.41
| 57.55
| 58.80
| 56.33
| 53.79
| 55.53
|-
| 65
| 1.60
| 5.88
| 30.76
| 27.73
| 28.10
| 36.84
| 34.49
| 35.00
| 33.99
| 39.13
| 37.48
|-
| 66
| 27.75
| 37.25
| 38.19
| 57.61
| 57.72
| 55.24
| 52.04
| 49.84
| 50.46
| 48.27
| 49.12
|-
| 67
| 13.61
| 36.85
| 33.61
| 38.37
| 37.73
| 35.12
| 34.59
| 32.93
| 34.44
| 36.06
| 34.88
|-
| 68
| 15.74
| 12.85
| 11.15
| 21.53
| 29.47
| 30.25
| 29.63
| 28.40
| 26.95
| 26.60
| 27.00
|-
| 69
| 25.63
| 21.03
| 34.80
| 48.35
| 51.43
| 48.76
| 49.79
| 47.53
| 45.20
| 43.31
| 41.50
|-
| 70
| 3.72
| 29.41
| 31.86
| 29.66
| 33.73
| 32.60
| 35.45
| 36.02
| 40.23
| 42.36
| 41.42
|-
| 71
| 33.07
| 27.67
| 40.14
| 60.61
| 55.78
| 51.65
| 50.91
| 53.28
| 50.91
| 48.80
| 49.64
|-
| 72
| 8.29
| 10.49
| 9.28
| 11.02
| 10.44
| 18.07
| 17.94
| 17.66
| 22.25
| 21.50
| 27.66
|-
| 73
| 21.05
| 29.00
| 28.01
| 33.03
| 31.46
| 36.71
| 42.68
| 51.07
| 50.59
| 48.62
| 49.68
|-
| 74
| 20.31
| 27.07
| 29.50
| 43.48
| 39.96
| 38.83
| 36.48
| 39.27
| 38.77
| 37.14
| 38.34
|-
| 75
| 9.04
| 15.74
| 30.96
| 28.93
| 40.99
| 43.48
| 41.03
| 41.78
| 41.39
| 43.06
| 44.95
|-
| 76
| 32.33
| 30.79
| 26.85
| 41.29
| 46.68
| 43.62
| 49.21
| 57.43
| 58.19
| 59.67
| 60.83
|-
| 77
| 2.98
| 15.70
| 19.26
| 17.88
| 25.03
| 24.22
| 24.99
| 26.92
| 25.86
| 26.01
| 27.38
|-
| 78
| 26.37
| 29.24
| 25.60
| 44.46
| 40.65
| 38.52
| 36.07
| 34.09
| 40.15
| 39.44
| 37.77
|-
| 79
| 14.99
| 24.96
| 34.25
| 35.51
| 33.09
| 31.45
| 35.72
| 37.20
| 44.52
| 43.00
| 42.02
|-
| 80
| 14.35
| 15.16
| 20.73
| 21.46
| 19.59
| 23.04
| 24.26
| 25.19
| 23.99
| 28.19
| 27.47
|-
| 81
| 27.01
| 23.34
| 25.10
| 38.39
| 35.52
| 43.31
| 41.97
| 40.27
| 38.75
| 43.37
| 41.87
|-
| 82
| 2.34
| 27.71
| 24.51
| 24.88
| 31.98
| 35.80
| 35.92
| 33.94
| 33.32
| 31.78
| 31.60
|-
| 83
| 31.69
| 26.14
| 27.44
| 47.40
| 49.48
| 49.59
| 52.72
| 54.79
| 52.81
| 51.10
| 56.03
|-
| 84
| 9.68
| 8.10
| 16.38
| 21.35
| 31.18
| 29.69
| 29.65
| 32.25
| 31.74
| 30.33
| 29.05
|-
| 85
| 19.67
| 37.18
| 40.58
| 45.47
| 43.11
| 43.13
| 42.21
| 47.43
| 45.48
| 49.49
| 49.63
|-
| 86
| 21.69
| 35.85
| 40.91
| 46.50
| 56.12
| 52.46
| 49.39
| 53.13
| 51.87
| 56.60
| 54.32
|-
| 87
| 7.66
| 7.49
| 17.95
| 21.45
| 19.59
| 18.27
| 17.46
| 22.87
| 26.46
| 27.06
| 29.54
|-
| 88
| 33.71
| 28.19
| 27.93
| 48.75
| 44.65
| 55.03
| 57.31
| 61.03
| 60.92
| 59.39
| 57.26
|-
| 89
| 4.36
| 25.53
| 22.32
| 23.87
| 21.94
| 28.68
| 29.76
| 29.05
| 28.11
| 26.83
| 29.08
|-
| 90
| 24.99
| 22.73
| 23.56
| 36.52
| 47.19
| 45.01
| 43.48
| 41.05
| 44.05
| 47.93
| 47.32
|-
| 91
| 16.38
| 17.95
| 23.77
| 24.47
| 33.89
| 39.10
| 40.72
| 39.76
| 45.62
| 49.78
| 51.74
|-
| 92
| 12.97
| 22.10
| 34.33
| 34.93
| 38.20
| 43.31
| 48.59
| 46.07
| 44.10
| 42.54
| 41.62
|-
| 93
| 28.39
| 29.00
| 25.18
| 45.40
| 49.64
| 45.97
| 43.85
| 41.39
| 39.58
| 39.96
| 42.98
|-
| 94
| 0.96
| 17.88
| 19.42
| 17.71
| 18.34
| 19.87
| 21.42
| 21.61
| 22.84
| 23.45
| 23.13
|-
| 95
| 30.30
| 28.19
| 24.44
| 38.98
| 35.67
| 33.18
| 37.32
| 48.98
| 46.57
| 46.63
| 45.03
|-
| 96
| 11.06
| 14.65
| 33.96
| 38.60
| 35.89
| 35.36
| 33.10
| 35.08
| 35.27
| 37.11
| 36.83
|-
| 97
| 18.29
| 28.06
| 31.37
| 43.50
| 44.67
| 41.44
| 38.92
| 44.81
| 42.64
| 40.78
| 39.81
|-
| 98
| 23.07
| 45.07
| 40.28
| 51.63
| 47.45
| 49.69
| 47.15
| 48.80
| 48.28
| 49.40
| 48.41
|-
| 99
| 6.27
| 7.63
| 6.60
| 8.38
| 31.37
| 33.58
| 33.84
| 35.67
| 38.51
| 36.92
| 35.54
|}
 
== See Also ==
 
* [[EDO]]
* [[Relative error]]
* [[Relative Errors of Small EDTs]]
* [[Relative Errors of Small EDFs]]
* [[Relative Errors of Small ED6s]]


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