4190edo
| ← 4189edo | 4190edo | 4191edo → |
4190 equal divisions of the octave (abbreviated 4190edo or 4190ed2), also called 4190-tone equal temperament (4190tet) or 4190 equal temperament (4190et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 4190 equal parts of about 0.286 ¢ each. Each step represents a frequency ratio of 21/4190, or the 4190th root of 2.
4190edo is notable for being a zeta gap edo. It is fairly strong in the 13-limit and the 4190g val does well if not outstandingly in a number of higher limits. Using this val, some of the simpler commas it tempers out include 9801/9800 in the 11-limit; 10648/10647 and 123201/123200 in the 13-limit; 4914/4913, 5832/5831, and 14400/14399 in the 17-limit; 10830/10829 and 12636/12635 in the 19-limit; 10626/10625 and 12168/12167 in the 23-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.002 | +0.035 | +0.052 | -0.005 | +0.045 | -0.134 | +0.053 | +0.079 | +0.017 | -0.024 |
| Relative (%) | +0.0 | +0.7 | +12.1 | +18.3 | -1.8 | +15.8 | -46.9 | +18.4 | +27.5 | +6.0 | -8.3 | |
| Steps (reduced) |
4190 (0) |
6641 (2451) |
9729 (1349) |
11763 (3383) |
14495 (1925) |
15505 (2935) |
17126 (366) |
17799 (1039) |
18954 (2194) |
20355 (3595) |
20758 (3998) | |
Subsets and supersets
Since 4190 factors into 2 × 5 × 419, 4190edo has subset edos 2, 5, 10, 419, 838, and 2095.