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) | |