82edo
82edo, or 82 equal temperament, divides the octave into 82 equal parts of 14.634 cents each. The patent val is contorted in the 11-limit, from 82 = 2*41, and in the 13-limit the patent val tempers out 169/168 and 676/675, and in the 17-limit tempers out 273/272. It provides the optimal patent val for soothsaying temperament and supports baladic temperament.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +0.48 | -5.83 | -2.97 | +4.78 | -6.38 | -2.52 | -4.83 | +0.99 | -5.19 | -3.57 |
| Relative (%) | +0.0 | +3.3 | -39.8 | -20.3 | +32.7 | -43.6 | -17.2 | -33.0 | +6.8 | -35.4 | -24.4 | |
| Steps (reduced) |
82 (0) |
130 (48) |
190 (26) |
230 (66) |
284 (38) |
303 (57) |
335 (7) |
348 (20) |
371 (43) |
398 (70) |
406 (78) | |
Interval table
| Degree | Cents |
|---|---|
| 0 | 0.000 |
| 1 | 14.634 |
| 2 | 29.268 |
| 3 | 43.902 |
| 4 | 58.537 |
| 5 | 73.171 |
| 6 | 87.805 |
| 7 | 102.439 |
| 8 | 117.073 |
| 9 | 131.707 |
| 10 | 146.341 |
| 11 | 160.976 |
| 12 | 175.610 |
| 13 | 190.244 |
| 14 | 204.878 |
| 15 | 219.512 |
| 16 | 234.146 |
| 17 | 248.780 |
| 18 | 263.415 |
| 19 | 278.049 |
| 20 | 292.683 |
| 21 | 307.317 |
| 22 | 321.951 |
| 23 | 336.585 |
| 24 | 351.220 |
| 25 | 365.854 |
| 26 | 380.488 |
| 27 | 395.122 |
| 28 | 409.756 |
| 29 | 424.390 |
| 30 | 439.024 |
| 31 | 453.659 |
| 32 | 468.293 |
| 33 | 482.927 |
| 34 | 497.561 |
| 35 | 512.195 |
| 36 | 526.829 |
| 37 | 541.463 |
| 38 | 556.098 |
| 39 | 570.732 |
| 40 | 585.366 |
| 41 | 600.000 |
| ... | ... |