Relative errors of small EDOs
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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 |