205edt: Difference between revisions
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== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 205 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 205 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 09:57, 5 October 2024
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| ← 204edt | 205edt | 206edt → |
205 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 205edt or 205ed3), is a nonoctave tuning system that divides the interval of 3/1 into 205 equal parts of about 9.28 ¢ each. Each step represents a frequency ratio of 31/205, or the 205th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.16 | +0.00 | +2.96 | -2.96 | -3.16 | -0.97 | -0.20 | +0.00 | +3.15 | -4.13 | +2.96 |
| Relative (%) | -34.1 | +0.0 | +31.9 | -32.0 | -34.1 | -10.5 | -2.2 | +0.0 | +34.0 | -44.5 | +31.9 | |
| Steps (reduced) |
129 (129) |
205 (0) |
259 (54) |
300 (95) |
334 (129) |
363 (158) |
388 (183) |
410 (0) |
430 (20) |
447 (37) |
464 (54) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.55 | -4.13 | -2.96 | -3.36 | +3.02 | -3.16 | -3.98 | -0.01 | -0.97 | +1.99 | -0.74 |
| Relative (%) | +38.3 | -44.6 | -32.0 | -36.2 | +32.5 | -34.1 | -42.9 | -0.1 | -10.5 | +21.4 | -8.0 | |
| Steps (reduced) |
479 (69) |
492 (82) |
505 (95) |
517 (107) |
529 (119) |
539 (129) |
549 (139) |
559 (149) |
568 (158) |
577 (167) |
585 (175) | |