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]]. | |||
{| class="wikitable sortable mw-collapsible" style="text-align:right" | {| class="wikitable sortable mw-collapsible" style="text-align:right" | ||
! rowspan="2" | | ! rowspan="2" | EDO | ||
! colspan=" | ! colspan="8" | Relative Errors (Percent) | ||
|- | |- | ||
! 3/1 | ! 3/1 | ||
! 5/1 | ! 5/1 | ||
| Line 21: | Line 15: | ||
|- | |- | ||
| 1 | | 1 | ||
| 41.50 | | 41.50 | ||
| -32.19 | | -32.19 | ||
| Line 32: | Line 25: | ||
|- | |- | ||
| 2 | | 2 | ||
| -16.99 | | -16.99 | ||
| 35.61 | | 35.61 | ||
| Line 43: | Line 35: | ||
|- | |- | ||
| 3 | | 3 | ||
| 24.51 | | 24.51 | ||
| 3.42 | | 3.42 | ||
| Line 54: | Line 45: | ||
|- | |- | ||
| 4 | | 4 | ||
| -33.99 | | -33.99 | ||
| -28.77 | | -28.77 | ||
| Line 65: | Line 55: | ||
|- | |- | ||
| 5 | | 5 | ||
| 7.52 | | 7.52 | ||
| 39.04 | | 39.04 | ||
| Line 76: | Line 65: | ||
|- | |- | ||
| 6 | | 6 | ||
| 49.02 | | 49.02 | ||
| 6.84 | | 6.84 | ||
| Line 87: | Line 75: | ||
|- | |- | ||
| 7 | | 7 | ||
| -9.47 | | -9.47 | ||
| -25.35 | | -25.35 | ||
| Line 98: | Line 85: | ||
|- | |- | ||
| 8 | | 8 | ||
| 32.03 | | 32.03 | ||
| 42.46 | | 42.46 | ||
| Line 109: | Line 95: | ||
|- | |- | ||
| 9 | | 9 | ||
| -26.47 | | -26.47 | ||
| 10.26 | | 10.26 | ||
| Line 120: | Line 105: | ||
|- | |- | ||
| 10 | | 10 | ||
| 15.04 | | 15.04 | ||
| -21.93 | | -21.93 | ||
| Line 131: | Line 115: | ||
|- | |- | ||
| 11 | | 11 | ||
| -43.46 | | -43.46 | ||
| 45.88 | | 45.88 | ||
| Line 142: | Line 125: | ||
|- | |- | ||
| 12 | | 12 | ||
| -1.96 | | -1.96 | ||
| 13.69 | | 13.69 | ||
| Line 153: | Line 135: | ||
|- | |- | ||
| 13 | | 13 | ||
| 39.55 | | 39.55 | ||
| -18.51 | | -18.51 | ||
| Line 164: | Line 145: | ||
|- | |- | ||
| 14 | | 14 | ||
| -18.95 | | -18.95 | ||
| 49.30 | | 49.30 | ||
| Line 175: | Line 155: | ||
|- | |- | ||
| 15 | | 15 | ||
| 22.56 | | 22.56 | ||
| 17.11 | | 17.11 | ||
| Line 186: | Line 165: | ||
|- | |- | ||
| 16 | | 16 | ||
| -35.94 | | -35.94 | ||
| -15.08 | | -15.08 | ||
| Line 197: | Line 175: | ||
|- | |- | ||
| 17 | | 17 | ||
| 5.56 | | 5.56 | ||
| -47.28 | | -47.28 | ||
| Line 208: | Line 185: | ||
|- | |- | ||
| 18 | | 18 | ||
| 47.07 | | 47.07 | ||
| 20.53 | | 20.53 | ||
| Line 219: | Line 195: | ||
|- | |- | ||
| 19 | | 19 | ||
| -11.43 | | -11.43 | ||
| -11.66 | | -11.66 | ||
| Line 230: | Line 205: | ||
|- | |- | ||
| 20 | | 20 | ||
| 30.07 | | 30.07 | ||
| -43.86 | | -43.86 | ||
| Line 241: | Line 215: | ||
|- | |- | ||
| 21 | | 21 | ||
| -28.42 | | -28.42 | ||
| 23.95 | | 23.95 | ||
| Line 252: | Line 225: | ||
|- | |- | ||
| 22 | | 22 | ||
| 13.08 | | 13.08 | ||
| -8.24 | | -8.24 | ||
| Line 263: | Line 235: | ||
|- | |- | ||
| 23 | | 23 | ||
| -45.41 | | -45.41 | ||
| -40.43 | | -40.43 | ||
| Line 274: | Line 245: | ||
|- | |- | ||
| 24 | | 24 | ||
| -3.91 | | -3.91 | ||
| 27.37 | | 27.37 | ||
| Line 285: | Line 255: | ||
|- | |- | ||
| 25 | | 25 | ||
| 37.59 | | 37.59 | ||
| -4.82 | | -4.82 | ||
| Line 296: | Line 265: | ||
|- | |- | ||
| 26 | | 26 | ||
| -20.90 | | -20.90 | ||
| -37.01 | | -37.01 | ||
| Line 307: | Line 275: | ||
|- | |- | ||
| 27 | | 27 | ||
| 20.60 | | 20.60 | ||
| 30.79 | | 30.79 | ||
| Line 318: | Line 285: | ||
|- | |- | ||
| 28 | | 28 | ||
| -37.90 | | -37.90 | ||
| -1.40 | | -1.40 | ||
| Line 329: | Line 295: | ||
|- | |- | ||
| 29 | | 29 | ||
| 3.61 | | 3.61 | ||
| -33.59 | | -33.59 | ||
| Line 340: | Line 305: | ||
|- | |- | ||
| 30 | | 30 | ||
| 45.11 | | 45.11 | ||
| 34.22 | | 34.22 | ||
| Line 351: | Line 315: | ||
|- | |- | ||
| 31 | | 31 | ||
| -13.38 | | -13.38 | ||
| 2.02 | | 2.02 | ||
| Line 362: | Line 325: | ||
|- | |- | ||
| 32 | | 32 | ||
| 28.12 | | 28.12 | ||
| -30.17 | | -30.17 | ||
| Line 373: | Line 335: | ||
|- | |- | ||
| 33 | | 33 | ||
| -30.38 | | -30.38 | ||
| 37.64 | | 37.64 | ||
| Line 384: | Line 345: | ||
|- | |- | ||
| 34 | | 34 | ||
| 11.13 | | 11.13 | ||
| 5.44 | | 5.44 | ||
| Line 395: | Line 355: | ||
|- | |- | ||
| 35 | | 35 | ||
| -47.37 | | -47.37 | ||
| -26.75 | | -26.75 | ||
| Line 406: | Line 365: | ||
|- | |- | ||
| 36 | | 36 | ||
| -5.87 | | -5.87 | ||
| 41.06 | | 41.06 | ||
| Line 417: | Line 375: | ||
|- | |- | ||
| 37 | | 37 | ||
| 35.64 | | 35.64 | ||
| 8.87 | | 8.87 | ||
| Line 428: | Line 385: | ||
|- | |- | ||
| 38 | | 38 | ||
| -22.86 | | -22.86 | ||
| -23.33 | | -23.33 | ||
| Line 439: | Line 395: | ||
|- | |- | ||
| 39 | | 39 | ||
| 18.65 | | 18.65 | ||
| 44.48 | | 44.48 | ||
| Line 450: | Line 405: | ||
|- | |- | ||
| 40 | | 40 | ||
| -39.85 | | -39.85 | ||
| 12.29 | | 12.29 | ||
| Line 461: | Line 415: | ||
|- | |- | ||
| 41 | | 41 | ||
| 1.65 | | 1.65 | ||
| -19.91 | | -19.91 | ||
| Line 472: | Line 425: | ||
|- | |- | ||
| 42 | | 42 | ||
| 43.16 | | 43.16 | ||
| 47.90 | | 47.90 | ||
| Line 483: | Line 435: | ||
|- | |- | ||
| 43 | | 43 | ||
| -15.34 | | -15.34 | ||
| 15.71 | | 15.71 | ||
| Line 494: | Line 445: | ||
|- | |- | ||
| 44 | | 44 | ||
| 26.16 | | 26.16 | ||
| -16.48 | | -16.48 | ||
| Line 505: | Line 455: | ||
|- | |- | ||
| 45 | | 45 | ||
| -32.33 | | -32.33 | ||
| -48.68 | | -48.68 | ||
| Line 516: | Line 465: | ||
|- | |- | ||
| 46 | | 46 | ||
| 9.17 | | 9.17 | ||
| 19.13 | | 19.13 | ||
| Line 527: | Line 475: | ||
|- | |- | ||
| 47 | | 47 | ||
| -49.32 | | -49.32 | ||
| -13.06 | | -13.06 | ||
| Line 538: | Line 485: | ||
|- | |- | ||
| 48 | | 48 | ||
| -7.82 | | -7.82 | ||
| -45.25 | | -45.25 | ||
| Line 549: | Line 495: | ||
|- | |- | ||
| 49 | | 49 | ||
| 33.68 | | 33.68 | ||
| 22.55 | | 22.55 | ||
| Line 560: | Line 505: | ||
|- | |- | ||
| 50 | | 50 | ||
| -24.81 | | -24.81 | ||
| -9.64 | | -9.64 | ||
| Line 571: | Line 515: | ||
|- | |- | ||
| 51 | | 51 | ||
| 16.69 | | 16.69 | ||
| -41.83 | | -41.83 | ||
| Line 582: | Line 525: | ||
|- | |- | ||
| 52 | | 52 | ||
| -41.81 | | -41.81 | ||
| 25.97 | | 25.97 | ||
| Line 593: | Line 535: | ||
|- | |- | ||
| 53 | | 53 | ||
| -0.30 | | -0.30 | ||
| -6.22 | | -6.22 | ||
| Line 604: | Line 545: | ||
|- | |- | ||
| 54 | | 54 | ||
| 41.20 | | 41.20 | ||
| -38.41 | | -38.41 | ||
| Line 615: | Line 555: | ||
|- | |- | ||
| 55 | | 55 | ||
| -17.29 | | -17.29 | ||
| 29.40 | | 29.40 | ||
| Line 626: | Line 565: | ||
|- | |- | ||
| 56 | | 56 | ||
| 24.21 | | 24.21 | ||
| -2.80 | | -2.80 | ||
| Line 637: | Line 575: | ||
|- | |- | ||
| 57 | | 57 | ||
| -34.29 | | -34.29 | ||
| -34.99 | | -34.99 | ||
| Line 648: | Line 585: | ||
|- | |- | ||
| 58 | | 58 | ||
| 7.22 | | 7.22 | ||
| 32.82 | | 32.82 | ||
| Line 659: | Line 595: | ||
|- | |- | ||
| 59 | | 59 | ||
| 48.72 | | 48.72 | ||
| 0.62 | | 0.62 | ||
| Line 670: | Line 605: | ||
|- | |- | ||
| 60 | | 60 | ||
| -9.78 | | -9.78 | ||
| -31.57 | | -31.57 | ||
| Line 681: | Line 615: | ||
|- | |- | ||
| 61 | | 61 | ||
| 31.73 | | 31.73 | ||
| 36.24 | | 36.24 | ||
| Line 692: | Line 625: | ||
|- | |- | ||
| 62 | | 62 | ||
| -26.77 | | -26.77 | ||
| 4.05 | | 4.05 | ||
| Line 703: | Line 635: | ||
|- | |- | ||
| 63 | | 63 | ||
| 14.74 | | 14.74 | ||
| -28.15 | | -28.15 | ||
| Line 714: | Line 645: | ||
|- | |- | ||
| 64 | | 64 | ||
| -43.76 | | -43.76 | ||
| 39.66 | | 39.66 | ||
| Line 725: | Line 655: | ||
|- | |- | ||
| 65 | | 65 | ||
| -2.26 | | -2.26 | ||
| 7.47 | | 7.47 | ||
| Line 736: | Line 665: | ||
|- | |- | ||
| 66 | | 66 | ||
| 39.25 | | 39.25 | ||
| -24.73 | | -24.73 | ||
| Line 747: | Line 675: | ||
|- | |- | ||
| 67 | | 67 | ||
| -19.25 | | -19.25 | ||
| 43.08 | | 43.08 | ||
| Line 758: | Line 685: | ||
|- | |- | ||
| 68 | | 68 | ||
| 22.25 | | 22.25 | ||
| 10.89 | | 10.89 | ||
| Line 769: | Line 695: | ||
|- | |- | ||
| 69 | | 69 | ||
| -36.24 | | -36.24 | ||
| -21.30 | | -21.30 | ||
| Line 780: | Line 705: | ||
|- | |- | ||
| 70 | | 70 | ||
| 5.26 | | 5.26 | ||
| 46.50 | | 46.50 | ||
| Line 791: | Line 715: | ||
|- | |- | ||
| 71 | | 71 | ||
| 46.77 | | 46.77 | ||
| 14.31 | | 14.31 | ||
| Line 802: | Line 725: | ||
|- | |- | ||
| 72 | | 72 | ||
| -11.73 | | -11.73 | ||
| -17.88 | | -17.88 | ||
| Line 813: | Line 735: | ||
|- | |- | ||
| 73 | | 73 | ||
| 29.77 | | 29.77 | ||
| 49.92 | | 49.92 | ||
| Line 824: | Line 745: | ||
|- | |- | ||
| 74 | | 74 | ||
| -28.72 | | -28.72 | ||
| 17.73 | | 17.73 | ||
| Line 835: | Line 755: | ||
|- | |- | ||
| 75 | | 75 | ||
| 12.78 | | 12.78 | ||
| -14.46 | | -14.46 | ||
| Line 846: | Line 765: | ||
|- | |- | ||
| 76 | | 76 | ||
| -45.72 | | -45.72 | ||
| -46.65 | | -46.65 | ||
| Line 857: | Line 775: | ||
|- | |- | ||
| 77 | | 77 | ||
| -4.21 | | -4.21 | ||
| 21.15 | | 21.15 | ||
| Line 868: | Line 785: | ||
|- | |- | ||
| 78 | | 78 | ||
| 37.29 | | 37.29 | ||
| -11.04 | | -11.04 | ||
| Line 879: | Line 795: | ||
|- | |- | ||
| 79 | | 79 | ||
| -21.20 | | -21.20 | ||
| -43.23 | | -43.23 | ||
| Line 890: | Line 805: | ||
|- | |- | ||
| 80 | | 80 | ||
| 20.30 | | 20.30 | ||
| 24.58 | | 24.58 | ||
| Line 901: | Line 815: | ||
|- | |- | ||
| 81 | | 81 | ||
| -38.20 | | -38.20 | ||
| -7.62 | | -7.62 | ||
| Line 912: | Line 825: | ||
|- | |- | ||
| 82 | | 82 | ||
| 3.31 | | 3.31 | ||
| -39.81 | | -39.81 | ||
| Line 923: | Line 835: | ||
|- | |- | ||
| 83 | | 83 | ||
| 44.81 | | 44.81 | ||
| 28.00 | | 28.00 | ||
| Line 934: | Line 845: | ||
|- | |- | ||
| 84 | | 84 | ||
| -13.69 | | -13.69 | ||
| -4.20 | | -4.20 | ||
| Line 945: | Line 855: | ||
|- | |- | ||
| 85 | | 85 | ||
| 27.82 | | 27.82 | ||
| -36.39 | | -36.39 | ||
| Line 956: | Line 865: | ||
|- | |- | ||
| 86 | | 86 | ||
| -30.68 | | -30.68 | ||
| 31.42 | | 31.42 | ||
| Line 967: | Line 875: | ||
|- | |- | ||
| 87 | | 87 | ||
| 10.83 | | 10.83 | ||
| -0.77 | | -0.77 | ||
| Line 978: | Line 885: | ||
|- | |- | ||
| 88 | | 88 | ||
| -47.67 | | -47.67 | ||
| -32.97 | | -32.97 | ||
| Line 989: | Line 895: | ||
|- | |- | ||
| 89 | | 89 | ||
| -6.17 | | -6.17 | ||
| 34.84 | | 34.84 | ||
| Line 1,000: | Line 905: | ||
|- | |- | ||
| 90 | | 90 | ||
| 35.34 | | 35.34 | ||
| 2.65 | | 2.65 | ||
| Line 1,011: | Line 915: | ||
|- | |- | ||
| 91 | | 91 | ||
| -23.16 | | -23.16 | ||
| -29.55 | | -29.55 | ||
| Line 1,022: | Line 925: | ||
|- | |- | ||
| 92 | | 92 | ||
| 18.34 | | 18.34 | ||
| 38.26 | | 38.26 | ||
| Line 1,033: | Line 935: | ||
|- | |- | ||
| 93 | | 93 | ||
| -40.15 | | -40.15 | ||
| 6.07 | | 6.07 | ||
| Line 1,044: | Line 945: | ||
|- | |- | ||
| 94 | | 94 | ||
| 1.35 | | 1.35 | ||
| -26.12 | | -26.12 | ||
| Line 1,055: | Line 955: | ||
|- | |- | ||
| 95 | | 95 | ||
| 42.86 | | 42.86 | ||
| 41.68 | | 41.68 | ||
| Line 1,066: | Line 965: | ||
|- | |- | ||
| 96 | | 96 | ||
| -15.64 | | -15.64 | ||
| 9.49 | | 9.49 | ||
| Line 1,077: | Line 975: | ||
|- | |- | ||
| 97 | | 97 | ||
| 25.86 | | 25.86 | ||
| -22.70 | | -22.70 | ||
| Line 1,088: | Line 985: | ||
|- | |- | ||
| 98 | | 98 | ||
| -32.63 | | -32.63 | ||
| 45.10 | | 45.10 | ||
| Line 1,099: | Line 995: | ||
|- | |- | ||
| 99 | | 99 | ||
| 8.87 | | 8.87 | ||
| 12.91 | | 12.91 | ||
| Line 1,110: | Line 1,005: | ||
|} | |} | ||
== | == See also == | ||
* Relative errors of small ed-''p''<span/>'s: | |||
** [[Relative errors of small EDTs]] | |||
** [[Relative errors of small EDFs]] | |||
** [[Relative errors of small ED5s]] | |||
** [[Relative errors of small ED6s]] | |||
* [[Relative errors of small equal temperaments]] | |||
* [[ | |||
* [[Relative | |||
* [[Relative | |||
* [[Relative | |||
* [[Relative | |||
[[ | [[Category:EDO theory pages]] | ||
[[ | [[Category:Tables]] | ||