525edo
Theory
525edo is distinctly consistent through the 25-odd-limit. It tempers out the schisma, 32805/32768, and [8 77 -5⟩ in the 5-limit; 250047/250000, 703125/702464 and [21 3 1 -10⟩ in the 7-limit; 3025/3024, 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; 729/728, 1716/1715, 2200/2197, 4096/4095 and 14641/14625 in the 13-limit.
It supports the 140 & 525 temperament, with period 35 which sets 7/5 and 10/7 to two "legs" of 35edo (17\35 and 18\35) opposing the tonic and tempers out [34 0 70 -70⟩, setting a circle of thirty-five 50/49's equal with the octave. In addition, it supports 21st-octave period called akjayland.
525's divisors are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.24 | -0.03 | +0.32 | -0.46 | +0.62 | +0.19 | -0.37 | +0.30 | -1.01 | +0.11 |
| Relative (%) | +0.0 | -10.5 | -1.2 | +13.9 | -20.2 | +26.9 | +8.2 | -16.2 | +13.0 | -44.0 | +4.7 | |
| Steps (reduced) |
525 (0) |
832 (307) |
1219 (169) |
1474 (424) |
1816 (241) |
1943 (368) |
2146 (46) |
2230 (130) |
2375 (275) |
2550 (450) |
2601 (501) | |