336edt: Difference between revisions
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Created page with "{{Infobox ET}} {{ED intro}} == 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 === {{Harmonics in equal|336|3|1|int..." |
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=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|336|3|1|intervals=integer|columns=11}} | {{Harmonics in equal|336|3|1|intervals=integer|columns=11}} | ||
{{Harmonics in equal|336|3|1|intervals=integer|columns=12|start=12|collapsed=1|title=Approximation of harmonics in | {{Harmonics in equal|336|3|1|intervals=integer|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 336edt (continued)}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since | Since 336 factors into primes as {{nowrap| 2<sup>4</sup> × 3 × 7 }}, 336edt contains subset edts {{EDs|equave=t| 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, and 168 }}. | ||
== See also == | == See also == | ||
* [[124edf]] – relative edf | * [[124edf]] – relative edf | ||
* [[212edo]] – relative edo | * [[212edo]] – relative edo | ||
Latest revision as of 14:51, 18 April 2025
| ← 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.