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. 
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
! colspan="9" | Relative Errors (Percent)
! colspan="8" | Relative Errors (Percent)
|-
|-
!  2/1
!  3/1
!  3/1
!  5/1
!  5/1
Line 21: Line 15:
|-
|-
|  1
|  1
|  0.00
|  41.50
|  41.50
| -32.19
| -32.19
Line 32: Line 25:
|-
|-
|  2
|  2
|  0.00
| -16.99
| -16.99
|  35.61
|  35.61
Line 43: Line 35:
|-
|-
|  3
|  3
|  0.00
|  24.51
|  24.51
|  3.42
|  3.42
Line 54: Line 45:
|-
|-
|  4
|  4
|  0.00
| -33.99
| -33.99
| -28.77
| -28.77
Line 65: Line 55:
|-
|-
|  5
|  5
|  0.00
|  7.52
|  7.52
|  39.04
|  39.04
Line 76: Line 65:
|-
|-
|  6
|  6
|  0.00
|  49.02
|  49.02
|  6.84
|  6.84
Line 87: Line 75:
|-
|-
|  7
|  7
|  0.00
|  -9.47
|  -9.47
| -25.35
| -25.35
Line 98: Line 85:
|-
|-
|  8
|  8
|  0.00
|  32.03
|  32.03
|  42.46
|  42.46
Line 109: Line 95:
|-
|-
|  9
|  9
|  0.00
| -26.47
| -26.47
|  10.26
|  10.26
Line 120: Line 105:
|-
|-
| 10
| 10
|  0.00
|  15.04
|  15.04
| -21.93
| -21.93
Line 131: Line 115:
|-
|-
| 11
| 11
|  0.00
| -43.46
| -43.46
|  45.88
|  45.88
Line 142: Line 125:
|-
|-
| 12
| 12
|  0.00
|  -1.96
|  -1.96
|  13.69
|  13.69
Line 153: Line 135:
|-
|-
| 13
| 13
|  0.00
|  39.55
|  39.55
| -18.51
| -18.51
Line 164: Line 145:
|-
|-
| 14
| 14
|  0.00
| -18.95
| -18.95
|  49.30
|  49.30
Line 175: Line 155:
|-
|-
| 15
| 15
|  0.00
|  22.56
|  22.56
|  17.11
|  17.11
Line 186: Line 165:
|-
|-
| 16
| 16
|  0.00
| -35.94
| -35.94
| -15.08
| -15.08
Line 197: Line 175:
|-
|-
| 17
| 17
|  0.00
|  5.56
|  5.56
| -47.28
| -47.28
Line 208: Line 185:
|-
|-
| 18
| 18
|  0.00
|  47.07
|  47.07
|  20.53
|  20.53
Line 219: Line 195:
|-
|-
| 19
| 19
|  0.00
| -11.43
| -11.43
| -11.66
| -11.66
Line 230: Line 205:
|-
|-
| 20
| 20
|  0.00
|  30.07
|  30.07
| -43.86
| -43.86
Line 241: Line 215:
|-
|-
| 21
| 21
|  0.00
| -28.42
| -28.42
|  23.95
|  23.95
Line 252: Line 225:
|-
|-
| 22
| 22
|  0.00
|  13.08
|  13.08
|  -8.24
|  -8.24
Line 263: Line 235:
|-
|-
| 23
| 23
|  0.00
| -45.41
| -45.41
| -40.43
| -40.43
Line 274: Line 245:
|-
|-
| 24
| 24
|  0.00
|  -3.91
|  -3.91
|  27.37
|  27.37
Line 285: Line 255:
|-
|-
| 25
| 25
|  0.00
|  37.59
|  37.59
|  -4.82
|  -4.82
Line 296: Line 265:
|-
|-
| 26
| 26
|  0.00
| -20.90
| -20.90
| -37.01
| -37.01
Line 307: Line 275:
|-
|-
| 27
| 27
|  0.00
|  20.60
|  20.60
|  30.79
|  30.79
Line 318: Line 285:
|-
|-
| 28
| 28
|  0.00
| -37.90
| -37.90
|  -1.40
|  -1.40
Line 329: Line 295:
|-
|-
| 29
| 29
|  0.00
|  3.61
|  3.61
| -33.59
| -33.59
Line 340: Line 305:
|-
|-
| 30
| 30
|  0.00
|  45.11
|  45.11
|  34.22
|  34.22
Line 351: Line 315:
|-
|-
| 31
| 31
|  0.00
| -13.38
| -13.38
|  2.02
|  2.02
Line 362: Line 325:
|-
|-
| 32
| 32
|  0.00
|  28.12
|  28.12
| -30.17
| -30.17
Line 373: Line 335:
|-
|-
| 33
| 33
|  0.00
| -30.38
| -30.38
|  37.64
|  37.64
Line 384: Line 345:
|-
|-
| 34
| 34
|  0.00
|  11.13
|  11.13
|  5.44
|  5.44
Line 395: Line 355:
|-
|-
| 35
| 35
|  0.00
| -47.37
| -47.37
| -26.75
| -26.75
Line 406: Line 365:
|-
|-
| 36
| 36
|  0.00
|  -5.87
|  -5.87
|  41.06
|  41.06
Line 417: Line 375:
|-
|-
| 37
| 37
|  0.00
|  35.64
|  35.64
|  8.87
|  8.87
Line 428: Line 385:
|-
|-
| 38
| 38
|  0.00
| -22.86
| -22.86
| -23.33
| -23.33
Line 439: Line 395:
|-
|-
| 39
| 39
|  0.00
|  18.65
|  18.65
|  44.48
|  44.48
Line 450: Line 405:
|-
|-
| 40
| 40
|  0.00
| -39.85
| -39.85
|  12.29
|  12.29
Line 461: Line 415:
|-
|-
| 41
| 41
|  0.00
|  1.65
|  1.65
| -19.91
| -19.91
Line 472: Line 425:
|-
|-
| 42
| 42
|  0.00
|  43.16
|  43.16
|  47.90
|  47.90
Line 483: Line 435:
|-
|-
| 43
| 43
|  0.00
| -15.34
| -15.34
|  15.71
|  15.71
Line 494: Line 445:
|-
|-
| 44
| 44
|  0.00
|  26.16
|  26.16
| -16.48
| -16.48
Line 505: Line 455:
|-
|-
| 45
| 45
|  0.00
| -32.33
| -32.33
| -48.68
| -48.68
Line 516: Line 465:
|-
|-
| 46
| 46
|  0.00
|  9.17
|  9.17
|  19.13
|  19.13
Line 527: Line 475:
|-
|-
| 47
| 47
|  0.00
| -49.32
| -49.32
| -13.06
| -13.06
Line 538: Line 485:
|-
|-
| 48
| 48
|  0.00
|  -7.82
|  -7.82
| -45.25
| -45.25
Line 549: Line 495:
|-
|-
| 49
| 49
|  0.00
|  33.68
|  33.68
|  22.55
|  22.55
Line 560: Line 505:
|-
|-
| 50
| 50
|  0.00
| -24.81
| -24.81
|  -9.64
|  -9.64
Line 571: Line 515:
|-
|-
| 51
| 51
|  0.00
|  16.69
|  16.69
| -41.83
| -41.83
Line 582: Line 525:
|-
|-
| 52
| 52
|  0.00
| -41.81
| -41.81
|  25.97
|  25.97
Line 593: Line 535:
|-
|-
| 53
| 53
|  0.00
|  -0.30
|  -0.30
|  -6.22
|  -6.22
Line 604: Line 545:
|-
|-
| 54
| 54
|  0.00
|  41.20
|  41.20
| -38.41
| -38.41
Line 615: Line 555:
|-
|-
| 55
| 55
|  0.00
| -17.29
| -17.29
|  29.40
|  29.40
Line 626: Line 565:
|-
|-
| 56
| 56
|  0.00
|  24.21
|  24.21
|  -2.80
|  -2.80
Line 637: Line 575:
|-
|-
| 57
| 57
|  0.00
| -34.29
| -34.29
| -34.99
| -34.99
Line 648: Line 585:
|-
|-
| 58
| 58
|  0.00
|  7.22
|  7.22
|  32.82
|  32.82
Line 659: Line 595:
|-
|-
| 59
| 59
|  0.00
|  48.72
|  48.72
|  0.62
|  0.62
Line 670: Line 605:
|-
|-
| 60
| 60
|  0.00
|  -9.78
|  -9.78
| -31.57
| -31.57
Line 681: Line 615:
|-
|-
| 61
| 61
|  0.00
|  31.73
|  31.73
|  36.24
|  36.24
Line 692: Line 625:
|-
|-
| 62
| 62
|  0.00
| -26.77
| -26.77
|  4.05
|  4.05
Line 703: Line 635:
|-
|-
| 63
| 63
|  0.00
|  14.74
|  14.74
| -28.15
| -28.15
Line 714: Line 645:
|-
|-
| 64
| 64
|  0.00
| -43.76
| -43.76
|  39.66
|  39.66
Line 725: Line 655:
|-
|-
| 65
| 65
|  0.00
|  -2.26
|  -2.26
|  7.47
|  7.47
Line 736: Line 665:
|-
|-
| 66
| 66
|  0.00
|  39.25
|  39.25
| -24.73
| -24.73
Line 747: Line 675:
|-
|-
| 67
| 67
|  0.00
| -19.25
| -19.25
|  43.08
|  43.08
Line 758: Line 685:
|-
|-
| 68
| 68
|  0.00
|  22.25
|  22.25
|  10.89
|  10.89
Line 769: Line 695:
|-
|-
| 69
| 69
|  0.00
| -36.24
| -36.24
| -21.30
| -21.30
Line 780: Line 705:
|-
|-
| 70
| 70
|  0.00
|  5.26
|  5.26
|  46.50
|  46.50
Line 791: Line 715:
|-
|-
| 71
| 71
|  0.00
|  46.77
|  46.77
|  14.31
|  14.31
Line 802: Line 725:
|-
|-
| 72
| 72
|  0.00
| -11.73
| -11.73
| -17.88
| -17.88
Line 813: Line 735:
|-
|-
| 73
| 73
|  0.00
|  29.77
|  29.77
|  49.92
|  49.92
Line 824: Line 745:
|-
|-
| 74
| 74
|  0.00
| -28.72
| -28.72
|  17.73
|  17.73
Line 835: Line 755:
|-
|-
| 75
| 75
|  0.00
|  12.78
|  12.78
| -14.46
| -14.46
Line 846: Line 765:
|-
|-
| 76
| 76
|  0.00
| -45.72
| -45.72
| -46.65
| -46.65
Line 857: Line 775:
|-
|-
| 77
| 77
|  0.00
|  -4.21
|  -4.21
|  21.15
|  21.15
Line 868: Line 785:
|-
|-
| 78
| 78
|  0.00
|  37.29
|  37.29
| -11.04
| -11.04
Line 879: Line 795:
|-
|-
| 79
| 79
|  0.00
| -21.20
| -21.20
| -43.23
| -43.23
Line 890: Line 805:
|-
|-
| 80
| 80
|  0.00
|  20.30
|  20.30
|  24.58
|  24.58
Line 901: Line 815:
|-
|-
| 81
| 81
|  0.00
| -38.20
| -38.20
|  -7.62
|  -7.62
Line 912: Line 825:
|-
|-
| 82
| 82
|  0.00
|  3.31
|  3.31
| -39.81
| -39.81
Line 923: Line 835:
|-
|-
| 83
| 83
|  0.00
|  44.81
|  44.81
|  28.00
|  28.00
Line 934: Line 845:
|-
|-
| 84
| 84
|  0.00
| -13.69
| -13.69
|  -4.20
|  -4.20
Line 945: Line 855:
|-
|-
| 85
| 85
|  0.00
|  27.82
|  27.82
| -36.39
| -36.39
Line 956: Line 865:
|-
|-
| 86
| 86
|  0.00
| -30.68
| -30.68
|  31.42
|  31.42
Line 967: Line 875:
|-
|-
| 87
| 87
|  0.00
|  10.83
|  10.83
|  -0.77
|  -0.77
Line 978: Line 885:
|-
|-
| 88
| 88
|  0.00
| -47.67
| -47.67
| -32.97
| -32.97
Line 989: Line 895:
|-
|-
| 89
| 89
|  0.00
|  -6.17
|  -6.17
|  34.84
|  34.84
Line 1,000: Line 905:
|-
|-
| 90
| 90
|  0.00
|  35.34
|  35.34
|  2.65
|  2.65
Line 1,011: Line 915:
|-
|-
| 91
| 91
|  0.00
| -23.16
| -23.16
| -29.55
| -29.55
Line 1,022: Line 925:
|-
|-
| 92
| 92
|  0.00
|  18.34
|  18.34
|  38.26
|  38.26
Line 1,033: Line 935:
|-
|-
| 93
| 93
|  0.00
| -40.15
| -40.15
|  6.07
|  6.07
Line 1,044: Line 945:
|-
|-
| 94
| 94
|  0.00
|  1.35
|  1.35
| -26.12
| -26.12
Line 1,055: Line 955:
|-
|-
| 95
| 95
|  0.00
|  42.86
|  42.86
|  41.68
|  41.68
Line 1,066: Line 965:
|-
|-
| 96
| 96
|  0.00
| -15.64
| -15.64
|  9.49
|  9.49
Line 1,077: Line 975:
|-
|-
| 97
| 97
|  0.00
|  25.86
|  25.86
| -22.70
| -22.70
Line 1,088: Line 985:
|-
|-
| 98
| 98
|  0.00
| -32.63
| -32.63
|  45.10
|  45.10
Line 1,099: Line 995:
|-
|-
| 99
| 99
|  0.00
|  8.87
|  8.87
|  12.91
|  12.91
Line 1,110: 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]]
[[Category:EDO theory pages]]
[[category:list]]
[[Category:Tables]]
[[category:table]]

Latest revision as of 09:46, 19 May 2024

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

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