151edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{Harmonics in equal|151|3|1 | {{ED intro}} | ||
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== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 151 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 151 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 10:17, 5 October 2024
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| ← 150edt | 151edt | 152edt → |
151 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 151edt or 151ed3), is a nonoctave tuning system that divides the interval of 3/1 into 151 equal parts of about 12.6 ¢ each. Each step represents a frequency ratio of 31/151, or the 151st root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.41 | +0.00 | +5.78 | -2.66 | -3.41 | -5.77 | +2.38 | +0.00 | -6.06 | +5.27 | +5.78 |
| Relative (%) | -27.0 | +0.0 | +45.9 | -21.1 | -27.0 | -45.8 | +18.9 | +0.0 | -48.1 | +41.9 | +45.9 | |
| Steps (reduced) |
95 (95) |
151 (0) |
191 (40) |
221 (70) |
246 (95) |
267 (116) |
286 (135) |
302 (0) |
316 (14) |
330 (28) |
342 (40) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.76 | +3.42 | -2.66 | -1.03 | -5.22 | -3.41 | +3.76 | +3.13 | -5.77 | +1.87 | +0.48 |
| Relative (%) | +45.8 | +27.2 | -21.1 | -8.2 | -41.4 | -27.0 | +29.8 | +24.8 | -45.8 | +14.8 | +3.8 | |
| Steps (reduced) |
353 (51) |
363 (61) |
372 (70) |
381 (79) |
389 (87) |
397 (95) |
405 (103) |
412 (110) |
418 (116) |
425 (123) |
431 (129) | |