162edt: Difference between revisions
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== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 162 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 162 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 10:19, 5 October 2024
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| ← 161edt | 162edt | 163edt → |
162 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 162edt or 162ed3), is a nonoctave tuning system that divides the interval of 3/1 into 162 equal parts of about 11.7 ¢ each. Each step represents a frequency ratio of 31/162, or the 162nd root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.47 | +0.00 | -4.95 | -3.82 | -2.47 | +0.69 | +4.32 | +0.00 | +5.44 | +4.81 | -4.95 |
| Relative (%) | -21.1 | +0.0 | -42.1 | -32.6 | -21.1 | +5.9 | +36.8 | +0.0 | +46.4 | +40.9 | -42.1 | |
| Steps (reduced) |
102 (102) |
162 (0) |
204 (42) |
237 (75) |
264 (102) |
287 (125) |
307 (145) |
324 (0) |
340 (16) |
354 (30) |
366 (42) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -1.79 | -3.82 | +1.85 | +2.56 | -2.47 | -2.15 | +2.97 | +0.69 | +2.33 | -4.18 |
| Relative (%) | -22.4 | -15.2 | -32.6 | +15.8 | +21.8 | -21.1 | -18.3 | +25.3 | +5.9 | +19.9 | -35.6 | |
| Steps (reduced) |
378 (54) |
389 (65) |
399 (75) |
409 (85) |
418 (94) |
426 (102) |
434 (110) |
442 (118) |
449 (125) |
456 (132) |
462 (138) | |