199edt: Difference between revisions
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== Harmonics == | |||
{{ | {{Harmonics in equal | ||
| steps = 199 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 199 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 09:56, 5 October 2024
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| ← 198edt | 199edt | 200edt → |
199 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 199edt or 199ed3), is a nonoctave tuning system that divides the interval of 3/1 into 199 equal parts of about 9.56 ¢ each. Each step represents a frequency ratio of 31/199, or the 199th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.25 | +0.00 | -1.05 | +4.49 | +4.25 | -4.56 | +3.20 | +0.00 | -0.81 | -3.34 | -1.05 |
| Relative (%) | +44.5 | +0.0 | -11.0 | +47.0 | +44.5 | -47.8 | +33.5 | +0.0 | -8.5 | -34.9 | -11.0 | |
| Steps (reduced) |
126 (126) |
199 (0) |
251 (52) |
292 (93) |
325 (126) |
352 (153) |
377 (178) |
398 (0) |
417 (19) |
434 (36) |
450 (52) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.74 | -0.31 | +4.49 | -2.10 | -1.93 | +4.25 | -3.33 | +3.44 | -4.56 | +0.92 | +0.42 |
| Relative (%) | +39.1 | -3.3 | +47.0 | -22.0 | -20.1 | +44.5 | -34.9 | +36.0 | -47.8 | +9.6 | +4.4 | |
| Steps (reduced) |
465 (67) |
478 (80) |
491 (93) |
502 (104) |
513 (115) |
524 (126) |
533 (135) |
543 (145) |
551 (153) |
560 (162) |
568 (170) | |