499edt
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Prime factorization
499 (prime)
Step size
3.81153¢
Octave
315\499edt (1200.63¢)
Consistency limit
7
Distinct consistency limit
7
| ← 498edt | 499edt | 500edt → |
499 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 499edt or 499ed3), is a nonoctave tuning system that divides the interval of 3/1 into 499 equal parts of about 3.81 ¢ each. Each step represents a frequency ratio of 31/499, or the 499th root of 3. It correspondes to 314.8342edo.
Theory
499edt is a strong 3.5.7.11.13.17.23 subgroup, tempering out 2277/2275, 21879/21875, 104247/104125, 12397/12393, 9317/9315 and 584375/583443. Using the 3.5.11.13.17.23 subgroup, it tempers out 73125/73117.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.63 | +0.00 | +1.27 | -0.08 | +0.63 | +0.57 | +1.90 | +0.00 | +0.55 | -0.56 | +1.27 |
| Relative (%) | +16.6 | +0.0 | +33.2 | -2.2 | +16.6 | +14.9 | +49.8 | +0.0 | +14.4 | -14.7 | +33.2 | |
| Steps (reduced) |
315 (315) |
499 (0) |
630 (131) |
731 (232) |
814 (315) |
884 (385) |
945 (446) |
998 (0) |
1046 (48) |
1089 (91) |
1129 (131) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.09 | +1.20 | -0.08 | -1.28 | +0.49 | +0.63 | -1.49 | +1.18 | +0.57 | +0.07 | -0.65 | +1.90 | -0.17 | +0.54 | +0.00 |
| Relative (%) | -2.4 | +31.5 | -2.2 | -33.6 | +12.8 | +16.6 | -39.2 | +31.0 | +14.9 | +2.0 | -17.1 | +49.8 | -4.4 | +14.2 | +0.0 | |
| Steps (reduced) |
1165 (167) |
1199 (201) |
1230 (232) |
1259 (261) |
1287 (289) |
1313 (315) |
1337 (339) |
1361 (363) |
1383 (385) |
1404 (406) |
1424 (426) |
1444 (446) |
1462 (464) |
1480 (482) |
1497 (0) | |