83edo
The 83 equal temperament (83edo) divides the octave into 83 equal parts of 14.458 cents each. The 3/1 is 6.5 cents sharp and the 5/1 is 4 cents sharp, with 7, 11, and 13 more accurate but a little flat. It tempers out 15625/15552 in the 5-limit and 686/675, 4000/3969 and 6144/6125 in the 7-limit, and provides the optimal patent val for the 7-limit 27&56 temperament with wedgie <<5 18 17 17 13 -11||. In the 11-limit it tempers out 121/120, 176/175 and 385/384, and in the 13-limit 91/90, 169/168 and 196/195, and it provides the optimal patent val for the 11-limit 22&61 temperament and the 13-limit 15&83 temperament. 83 is the 23rd prime number.
| Prime number | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +6.48 | +4.05 | -0.15 | -1.92 | -1.97 | -3.75 | +6.10 | -6.59 |
| relative (%) | +44.8 | +28.0 | -1.0 | -13.3 | -13.6 | -25.9 | +42.2 | -45.6 | |
| Degree (reduced) | 132 (49) | 193 (27) | 233 (67) | 287 (38) | 307 (58) | 339 (7) | 353 (21) | 375 (43) | |