518edo
| ← 517edo | 518edo | 519edo → |
518 equal divisions of the octave (abbreviated 518edo or 518ed2), also called 518-tone equal temperament (518tet) or 518 equal temperament (518et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 518 equal parts of about 2.32 ¢ each. Each step represents a frequency ratio of 21/518, or the 518th root of 2.
518edo is consistent in the 15-odd-limit and is an exceptionally strong 2.3.11-subgroup tuning, where it tempers out the frameshift comma as well as the 37-11-comma.
In the 5-limit, it tempers out the counterschisma ([-69 45 -1⟩), and is a strong tuning for the counterschismic temperament hence. In the 7-limit, it tempers out 235298/234375, 420175/419904, 1959552/1953125, and 5250987/5242880 (mitonisma). In the 11-limit, it tempers out 5632/5625, 9801/9800, as well as being a tuning for loki.
In the 13-limit, 518edo tempers out 1001/1000, 4096/4095, and it is a strong tuning for the 14th-octave silicon temperament.
The 518c val, ⟨518 821 1202 1454 1792], though less accurate, is of theoretical interest as well because it tunes quintilipyth and compass.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.02 | +0.56 | -0.49 | +0.03 | +0.40 | -0.71 | -0.99 | -0.48 | -1.01 | -0.63 |
| Relative (%) | +0.0 | -1.1 | +24.1 | -21.0 | +1.4 | +17.2 | -30.6 | -42.6 | -20.5 | -43.4 | -27.4 | |
| Steps (reduced) |
518 (0) |
821 (303) |
1203 (167) |
1454 (418) |
1792 (238) |
1917 (363) |
2117 (45) |
2200 (128) |
2343 (271) |
2516 (444) |
2566 (494) | |
Subsets and supersets
Since 518 factors into primes as 2 × 7 × 37, 518edo has subsets edos 2, 7, 14, 37, 74, 259.