90edo
The 90 equal temperament divides the octave into 90 equal parts of 13.333 cents each. It tempers out 2048/2025 in the 5-limit, 3125/3087 and 245/243 in the 7-limit, 121/120 and 176/175 in the 11-limit, and 275/273 and 169/168 in the 13-limit. It provides the optimal patent val for the 31&90 temperament in the 7-, 11- and 13-limits. Notably, it is the second lowest in a series of four consecutive EDOs to temper out 117440512/117406179.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.71 | +0.35 | +4.51 | -3.91 | -4.65 | -0.53 | +5.06 | +1.71 | -4.18 | -4.11 | -1.61 |
| Relative (%) | +35.3 | +2.6 | +33.8 | -29.3 | -34.9 | -4.0 | +38.0 | +12.8 | -31.3 | -30.9 | -12.1 | |
| Steps (reduced) |
143 (53) |
209 (29) |
253 (73) |
285 (15) |
311 (41) |
333 (63) |
352 (82) |
368 (8) |
382 (22) |
395 (35) |
407 (47) | |