212edo
212 equal temperament divides the octave into 212 equal parts of 5.660 cents each.
212 = 4 × 53, and it shares the 3rd, 5th, and 13th harmonics with 53edo, but the mapping differs for 7 and 11. It tempers out the same commas (32805/32768, 15625/15552 and 1600000/1594323) as 53 in the 5-limit. In the 7-limit it tempers out 2401/2400, 390625/388962 and 4802000/4782969; in the 11-limit 385/384, 1375/1372, 6250/6237, 9801/9800 and 14641/14580; and in the 13-limit 325/324, 625/624, 676/675 and 1001/1000.
It is distinctly consistent in the 15-odd-limit with harmonics of 3 through 13 all tuned flat. It is the optimal patent val for 7 and 13 limit quadritikleismic temperament, and the 13-limit rank three agni temperament. 212gh val shows some potential beyond 15-odd-limit. Also, using 212bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning almost identical to the POTE tuning for 5-limit meantone.
Just approximation
| prime 2 | prime 3 | prime 5 | prime 7 | prime 11 | prime 13 | prime 17 | prime 19 | prime 23 | prime 29 | prime 31 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | 0.00 | -0.07 | -1.41 | -0.90 | -2.26 | -2.79 | +2.59 | +2.49 | +0.03 | +0.61 | -1.64 |
| relative (%) | 0.0 | -1.2 | -24.9 | -15.9 | -40.0 | -49.3 | +45.8 | +43.9 | +0.5 | +10.8 | -29.0 | |