Relative errors of small EDOs
(WIP) Relative Errors of Small Edos
The relative error of an interval in an edo is the error approximating JI divided by the size of a single step. The formula: error(r) = round (n log2r) - n log2r, where n is the edo number and r is the frequency ratio. By definition, the relative error ranges from -0.5 to +0.5.
This article lists relative errors of the first 9 prime harmonies for edos up to 99. For other intervals, the relative error follows the additive rule (on condition of consistency), that is, if r3 = r1r2, then error (r3) = error (r1) + error (r2), so they can be derived easily.
Bolded are relative errors lower than 0.2.
| Edo | Relative Errors (Permille) | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| 2/1 | 3/1 | 5/1 | 7/1 | 11/1 | 13/1 | 17/1 | 19/1 | 23/1 | |
| 1 | 0.0 | 415.0 | -321.9 | 192.6 | -459.4 | 299.6 | -87.5 | -247.9 | 476.4 |
| 2 | 0.0 | -169.9 | 356.1 | 385.3 | 81.1 | -400.9 | -174.9 | -495.9 | 47.1 |
| 3 | 0.0 | 245.1 | 34.2 | -422.1 | -378.3 | -101.3 | -262.4 | 256.2 | 429.3 |
| 4 | 0.0 | -339.9 | -287.7 | -229.4 | 162.3 | 198.2 | -349.9 | 8.3 | 94.2 |
| 5 | 0.0 | 75.2 | 390.4 | -36.8 | -297.2 | 497.8 | -437.3 | -239.6 | 382.2 |
| 6 | 0.0 | 490.2 | 68.4 | 155.9 | 243.4 | -202.6 | 475.2 | -487.6 | -141.4 |
| 7 | 0.0 | -94.7 | -253.5 | 348.5 | -216.0 | 96.9 | 387.8 | 264.5 | 335.1 |
| 8 | 0.0 | 320.3 | 424.6 | -458.8 | 324.5 | 396.5 | 300.3 | 16.6 | -188.5 |
| 9 | 0.0 | -264.7 | 102.6 | -266.2 | -134.9 | -304.0 | 212.8 | -231.3 | 287.9 |
| 10 | 0.0 | 150.4 | -219.3 | -73.5 | 405.7 | -4.4 | 125.4 | -479.3 | -235.6 |
| 11 | 0.0 | -434.6 | 458.8 | 119.1 | -53.7 | 295.2 | 37.9 | 272.8 | 240.8 |
| 12 | 0.0 | -19.6 | 136.9 | 311.7 | 486.8 | -405.3 | -49.6 | 24.9 | 282.7 |
| 13 | 0.0 | 395.5 | -185.1 | -495.6 | 27.4 | -105.7 | -137.0 | -223.1 | 193.7 |
| 14 | 0.0 | -189.5 | 493.0 | -303.0 | -432.0 | 193.8 | -224.5 | -471.0 | -329.9 |
| 15 | 0.0 | 225.6 | 171.1 | -110.3 | 108.5 | 493.4 | -311.9 | 281.1 | 146.6 |
| 16 | 0.0 | -359.4 | -150.8 | 82.3 | -350.9 | -207.0 | -399.4 | 33.2 | -377.0 |
| 17 | 0.0 | 55.6 | -472.8 | 275.0 | 189.7 | 92.5 | -486.9 | -214.8 | 99.4 |
| 18 | 0.0 | 470.7 | 205.3 | 467.6 | -269.8 | 392.1 | 425.7 | -462.7 | -424.1 |
| 19 | 0.0 | -114.3 | -116.6 | -339.7 | 270.8 | -308.4 | 338.2 | 289.4 | 52.3 |
| 20 | 0.0 | 300.7 | -438.6 | -147.1 | -188.6 | -8.8 | 250.7 | 41.4 | 471.2 |
| 21 | 0.0 | -284.2 | 239.5 | 45.5 | 351.9 | 290.8 | 163.3 | -206.5 | 5.2 |
| 22 | 0.0 | 130.8 | -82.4 | 238.2 | -107.5 | -409.7 | 75.8 | -454.4 | 481.6 |
| 23 | 0.0 | -454.1 | -404.3 | 430.8 | 433.1 | -110.1 | -11.6 | 297.7 | -41.9 |
| 24 | 0.0 | -39.1 | 273.7 | -376.5 | -26.4 | 189.4 | -99.1 | 49.7 | 434.5 |