613edt
Jump to navigation
Jump to search
Prime factorization
613 (prime)
Step size
3.1027¢
Octave
387\613edt (1200.74¢)
Consistency limit
4
Distinct consistency limit
4
| ← 612edt | 613edt | 614edt → |
613 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 613edt or 613ed3), is a nonoctave tuning system that divides the interval of 3/1 into 613 equal parts of about 3.1 ¢ each. Each step represents a frequency ratio of 31/613, or the 613th root of 3. It corresponds to 386.75994edo.
Theory
613edt is strong in the 3.5.11.13.17.19.29.31 subgroup, tempering out 6175/6171, 27625/27621, 2873/2871, 9375/9367, 26195/26163, 767637/767125 and 265837/265625. Using the 3.5.7.11.13.17.19 subgroup, it tempers out 121125/121121.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.74 | +0.00 | +1.49 | -0.09 | +0.74 | +0.71 | -0.87 | +0.00 | +0.66 | +0.09 | +1.49 |
| Relative (%) | +24.0 | +0.0 | +48.0 | -2.9 | +24.0 | +22.8 | -28.0 | +0.0 | +21.1 | +3.0 | +48.0 | |
| Steps (reduced) |
387 (387) |
613 (0) |
774 (161) |
898 (285) |
1000 (387) |
1086 (473) |
1160 (547) |
1226 (0) |
1285 (59) |
1338 (112) |
1387 (161) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.56 | +1.45 | -0.09 | -0.12 | +0.41 | +0.74 | +0.22 | +1.40 | +0.71 | +0.84 | +1.45 | -0.87 | -0.18 | +0.18 | +0.00 |
| Relative (%) | -18.2 | +46.8 | -2.9 | -4.0 | +13.3 | +24.0 | +7.2 | +45.1 | +22.8 | +27.0 | +46.7 | -28.0 | -5.8 | +5.8 | +0.0 | |
| Steps (reduced) |
1431 (205) |
1473 (247) |
1511 (285) |
1547 (321) |
1581 (355) |
1613 (387) |
1643 (417) |
1672 (446) |
1699 (473) |
1725 (499) |
1750 (524) |
1773 (547) |
1796 (570) |
1818 (592) |
1839 (0) | |