4190edo
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Prime factorization
2 × 5 × 419
Step size
0.286396¢
Fifth
2451\4190 (701.957¢)
Semitones (A1:m2)
397:315 (113.7¢ : 90.21¢)
Consistency limit
15
Distinct consistency limit
15
Special properties
| ← 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.
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 | +1 | +12 | +18 | -2 | +16 | -47 | +18 | +28 | +6 | -8 | |
| Steps (reduced) |
4190 (0) |
6641 (2451) |
9729 (1349) |
11763 (3383) |
14495 (1925) |
15505 (2935) |
17126 (366) |
17799 (1039) |
18954 (2194) |
20355 (3595) |
20758 (3998) | |
Divisors
Since 4190 factors into 2 × 5 × 419, 4190edo has subset edos 2, 5, 10, 419, 838, and 2095.