1578edo
The 1578 equal division divides the octave into 1578 equal parts of 0.7605 cents each. It is a very strong higher limit system, and is a zeta peak, peak integer, integral and gap edo. It is distinctly consistent through the 29 limit, and is the first edo past 311 with a lower 29-limit relative error. It is also the lowest past 311 in the 31 limit, the lowest past 581 in the 23 limit, and the lowest past 1178 in the 19 limit. It is also quite strong taken just as an 11-limit system; the only smaller edo with a lower 11-limit relative error is 342.
It is also the most accurate EDO below 10000 for approximating quarter comma meantone, specifically in its m-chromatic 7L5s MOS scale.
Some 31 limit or lower superparticular commas it tempers out are 3249/3248, 3510/3509, 3876/3875, 3969/3968, 4186/4185, 4225/4224, 4641/4640, 4693/4692, 4761/4760, 4901/4900, 4914/4913, 4992/4991, 5083/5082, 5643/5642, 5776/5775, 5832/5831, 5888/5887, 5985/5984, 6175/6174, 6325/6324, 6480/6479, 6656/6655, 6728/6727, 7106/7105, 7425/7424, 7657/7656, 7866/7865, 7889/7888, 8092/8091, 8281/8280, 8464/8463, 8526/8525, 8625/8624, 8671/8670, 8960/8959, 9425/9424, 9801/9800, 9802/9801, 10241/10240, 10557/10556, 10626/10625, 10830/10829, 10881/10880, 11271/11270, 11340/11339, 11781/11780, 12006/12005, 12122/12121, 12168/12167, 12376/12375, 12636/12635, 12673/12672, 13225/13224, 13300/13299, 13311/13310, 13312/13311, 13377/13376, 14365/14364, 14400/14399, 15625/15624, 16929/16928, 19228/19227, 19251/19250, 19344/19343, 19551/19550, 19965/19964, 20736/20735, 21505/21504, 21736/21735, 23276/23275, 23375/23374, 23409/23408, 23716/23715, 23751/23750, 24795/24794, 25025/25024, 25840/25839, 25921/25920, 27000/26999... .
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.054 | -0.002 | -0.005 | +0.013 | -0.223 | -0.012 | -0.175 | -0.137 | +0.081 | +0.212 |
| Relative (%) | +0.0 | -7.1 | -0.3 | -0.6 | +1.7 | -29.4 | -1.6 | -23.0 | -18.1 | +10.6 | +27.8 | |
| Steps (reduced) |
1578 (0) |
2501 (923) |
3664 (508) |
4430 (1274) |
5459 (725) |
5839 (1105) |
6450 (138) |
6703 (391) |
7138 (826) |
7666 (1354) |
7818 (1506) | |