336edt
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| ← 335edt | 336edt | 337edt → |
336 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 336edt or 336ed3), is a nonoctave tuning system that divides the interval of 3/1 into 336 equal parts of about 5.66 ¢ each. Each step represents a frequency ratio of 31/336, or the 336th root of 3.
Theory
336edt is nearly identical to 212edo, but with the perfect twelfth instead of the octave tuned just. The octave is stretched by about 0.0430 cents. Like 212edo, 336edt is consistent to the 16-integer-limit. The stretch is so subtle that most of the prime harmonics tuned flat in 212edo remain flat.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.04 | +0.00 | +0.09 | -1.31 | +0.04 | -0.78 | +0.13 | +0.00 | -1.27 | -2.11 | +0.09 |
| Relative (%) | +0.8 | +0.0 | +1.5 | -23.1 | +0.8 | -13.8 | +2.3 | +0.0 | -22.4 | -37.3 | +1.5 | |
| Steps (reduced) |
212 (212) |
336 (0) |
424 (88) |
492 (156) |
548 (212) |
595 (259) |
636 (300) |
672 (0) |
704 (32) |
733 (61) |
760 (88) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -0.74 | -1.31 | +0.17 | +2.77 | +0.04 | +2.67 | -1.22 | -0.78 | -2.07 | +0.22 | +0.13 |
| Relative (%) | -46.5 | -13.0 | -23.1 | +3.0 | +48.9 | +0.8 | +47.2 | -21.6 | -13.8 | -36.6 | +3.9 | +2.3 | |
| Steps (reduced) |
784 (112) |
807 (135) |
828 (156) |
848 (176) |
867 (195) |
884 (212) |
901 (229) |
916 (244) |
931 (259) |
945 (273) |
959 (287) |
972 (300) | |
Subsets and supersets
Since 336 factors into primes as 24 × 3 × 7, 336edt contains subset edts 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, and 168.