平均律误差
各平均律在各限的误差:
其中n限误差指的是,对于所有小于等于n的奇数形成的有理数比例中(如5限包括3/1 5/1 5/3),最大的一组的误差是多少音分。
2.3.7限误差指的是,对于列举出来的数字互相之间形成的有理数误差中,最大的一组的误差是多少音分(如2.3.7包括3/2 7/2 7/3)。
| 平均律 | 3限 | 5限 | 2.3.7 | 7限 | 9限 | 2.3.9.11 | 2.3.5.9.11 | 11限 | 2.3.5.9.13 | 2.3.5.7.9.13 | 13限 | 15限 | 17限 | 19限 |
| 1 | 498.04 | 884.36 | 498.04 | 884.36 | 884.36 | 1049.36 | 1049.36 | 1049.36 | 884.36 | 884.36 | 1049.36 | 1049.36 | 1049.36 | 1049.36 |
| 2 | 101.96 | 315.64 | 333.13 | 333.13 | 435.08 | 252.59 | 417.60 | 435.08 | 454.21 | 471.70 | 471.70 | 471.70 | 471.70 | 528.69 |
| 3 | 98.04 | 98.04 | 266.87 | 266.87 | 364.92 | 347.41 | 347.41 | 364.92 | 236.62 | 364.92 | 364.92 | 364.92 | 364.92 | 364.92 |
| 4 | 101.96 | 101.96 | 101.96 | 101.96 | 198.04 | 198.04 | 198.04 | 198.04 | 198.04 | 198.04 | 198.04 | 213.69 | 216.69 | 216.69 |
| 5 | 18.04 | 93.69 | 26.87 | 102.51 | 102.51 | 107.41 | 165.00 | 165.00 | 119.47 | 128.30 | 190.79 | 190.79 | 224.43 | 224.43 |
| 6 | 98.04 | 98.04 | 98.04 | 98.04 | 101.96 | 101.96 | 101.96 | 101.96 | 138.57 | 138.57 | 138.57 | 186.31 | 186.31 | 195.56 |
| 7 | 16.24 | 43.46 | 75.99 | 103.20 | 103.20 | 37.03 | 43.46 | 103.20 | 60.07 | 103.20 | 103.20 | 119.44 | 126.17 | 126.17 |
| 9 | 35.29 | 48.97 | 35.49 | 49.18 | 98.25 | 98.04 | 98.04 | 98.25 | 103.28 | 103.28 | 103.28 | 103.28 | 103.28 | 103.28 |
| 10 | 18.04 | 44.36 | 26.87 | 44.36 | 62.40 | 48.68 | 75.00 | 75.00 | 62.40 | 62.40 | 75.00 | 75.00 | 75.00 | 106.20 |
| 11 | 47.41 | 97.46 | 60.40 | 97.46 | 97.46 | 61.68 | 97.46 | 97.46 | 97.46 | 97.46 | 97.46 | 97.46 | 97.46 | 97.46 |
| 12 | 1.96 | 15.64 | 33.13 | 33.13 | 35.08 | 52.59 | 52.59 | 52.59 | 54.21 | 71.70 | 89.21 | 89.21 | 89.21 | 89.21 |
| 13 | 36.51 | 53.59 | 82.26 | 82.26 | 82.26 | 55.80 | 55.80 | 82.26 | 55.80 | 82.26 | 82.26 | 82.26 | 82.26 | 82.26 |
| 14 | 16.24 | 58.50 | 25.97 | 68.23 | 74.74 | 37.03 | 79.29 | 79.29 | 74.74 | 74.74 | 79.29 | 79.29 | 79.29 | 82.63 |
| 15 | 18.04 | 18.04 | 26.87 | 26.87 | 44.92 | 36.09 | 36.09 | 44.92 | 39.47 | 48.30 | 48.30 | 48.30 | 64.43 | 64.43 |
| 16 | 26.96 | 26.96 | 33.13 | 33.13 | 48.04 | 48.04 | 48.04 | 48.04 | 48.04 | 48.04 | 48.04 | 63.69 | 66.69 | 66.69 |
| 17 | 3.93 | 37.30 | 19.41 | 52.78 | 52.78 | 13.39 | 46.76 | 52.78 | 41.23 | 52.78 | 52.78 | 52.78 | 53.78 | 53.78 |
| 18 | 31.38 | 31.38 | 31.38 | 31.38 | 35.29 | 49.36 | 49.36 | 49.36 | 35.29 | 35.29 | 49.36 | 52.98 | 52.98 | 62.22 |
| 19 | 7.22 | 7.37 | 21.46 | 21.46 | 21.46 | 31.54 | 31.54 | 38.56 | 19.48 | 21.46 | 38.56 | 38.56 | 42.82 | 42.82 |
| 21 | 16.24 | 29.93 | 18.84 | 29.93 | 40.90 | 40.90 | 40.90 | 40.90 | 40.90 | 40.90 | 40.90 | 40.90 | 40.90 | 40.90 |
| 22 | 7.14 | 11.63 | 12.99 | 17.49 | 18.77 | 20.14 | 20.14 | 20.14 | 36.62 | 36.62 | 36.62 | 36.62 | 36.62 | 39.06 |
| 24 | 1.96 | 15.64 | 18.83 | 32.51 | 32.51 | 3.91 | 17.60 | 32.51 | 17.60 | 32.51 | 32.51 | 32.51 | 32.51 | 32.51 |
| 26 | 9.65 | 17.08 | 10.05 | 17.49 | 19.70 | 21.82 | 21.82 | 21.82 | 19.29 | 19.70 | 21.82 | 38.72 | 38.72 | 40.01 |
| 27 | 9.16 | 13.69 | 9.16 | 13.69 | 18.31 | 36.30 | 36.30 | 36.30 | 18.31 | 18.31 | 36.30 | 39.91 | 39.91 | 39.91 |
| 29 | 1.49 | 15.39 | 18.60 | 18.60 | 20.09 | 16.37 | 16.89 | 20.09 | 16.89 | 20.09 | 20.09 | 20.09 | 36.28 | 36.28 |
| 30 | 18.04 | 18.04 | 26.87 | 26.87 | 26.87 | 21.96 | 21.96 | 26.87 | 21.96 | 26.87 | 26.87 | 26.87 | 26.87 | 35.56 |
| 31 | 5.18 | 5.96 | 5.18 | 5.96 | 11.14 | 10.36 | 11.14 | 11.14 | 21.45 | 21.45 | 21.45 | 21.45 | 21.54 | 22.53 |
| 34 | 3.93 | 3.93 | 19.81 | 19.81 | 23.74 | 13.39 | 13.39 | 29.27 | 7.85 | 23.74 | 29.27 | 29.27 | 29.27 | 29.27 |
| 36 | 1.96 | 15.64 | 2.16 | 15.85 | 17.60 | 19.26 | 19.26 | 19.26 | 20.88 | 20.88 | 22.54 | 22.54 | 22.54 | 22.54 |
| 40 | 11.96 | 15.64 | 11.96 | 15.64 | 18.04 | 18.04 | 18.04 | 18.04 | 18.04 | 18.04 | 18.04 | 18.04 | 21.05 | 21.05 |
| 41 | 0.48 | 6.31 | 3.46 | 6.31 | 6.79 | 4.78 | 10.61 | 10.61 | 14.08 | 14.08 | 14.08 | 14.08 | 17.94 | 17.94 |
| 43 | 4.28 | 8.66 | 12.20 | 12.20 | 16.48 | 15.38 | 15.38 | 16.48 | 12.95 | 16.48 | 16.48 | 16.48 | 16.48 | 18.02 |
| 46 | 2.39 | 4.99 | 6.00 | 8.60 | 8.60 | 8.28 | 8.48 | 8.60 | 10.74 | 10.74 | 10.74 | 13.13 | 13.13 | 17.94 |
| 50 | 5.96 | 5.96 | 8.83 | 8.83 | 11.91 | 12.59 | 12.59 | 12.59 | 11.91 | 11.91 | 12.59 | 12.59 | 12.59 | 12.59 |
| 53 | 0.07 | 1.41 | 4.83 | 6.17 | 6.17 | 7.92 | 7.92 | 12.68 | 2.79 | 7.55 | 12.68 | 12.68 | 16.17 | 16.17 |
| 58 | 1.49 | 6.79 | 3.59 | 6.79 | 6.79 | 7.30 | 7.30 | 7.30 | 7.75 | 7.75 | 7.75 | 8.28 | 9.79 | 16.14 |
| 65 | 0.42 | 1.80 | 8.83 | 10.20 | 10.20 | 3.36 | 3.36 | 11.35 | 9.54 | 17.53 | 17.53 | 17.53 | 17.53 | 17.53 |
| 68 | 3.93 | 3.93 | 3.93 | 3.93 | 7.85 | 12.11 | 12.11 | 12.11 | 7.85 | 7.85 | 12.11 | 12.11 | 12.11 | 12.11 |
| 72 | 1.96 | 2.98 | 2.16 | 2.98 | 3.91 | 3.91 | 3.91 | 3.91 | 7.19 | 7.19 | 7.19 | 7.19 | 7.19 | 9.68 |
| 77 | 0.66 | 3.95 | 2.59 | 5.89 | 5.89 | 5.86 | 9.16 | 9.16 | 4.61 | 5.89 | 9.16 | 9.16 | 10.00 | 10.00 |
| 80 | 3.04 | 3.69 | 6.17 | 6.17 | 6.17 | 6.09 | 6.09 | 6.17 | 6.62 | 6.70 | 6.70 | 7.26 | 7.26 | 7.26 |
| 87 | 1.49 | 1.60 | 4.80 | 4.80 | 6.30 | 2.99 | 3.09 | 6.30 | 3.09 | 6.30 | 6.30 | 6.30 | 8.70 | 9.24 |
| 94 | 0.17 | 3.51 | 1.39 | 4.72 | 4.72 | 2.73 | 3.68 | 4.72 | 5.36 | 5.36 | 5.36 | 5.36 | 5.36 | 5.92 |
| 99 | 1.08 | 1.57 | 1.08 | 1.57 | 2.15 | 8.01 | 8.01 | 8.01 | 6.31 | 6.31 | 8.01 | 8.50 | 10.00 | 11.38 |