247edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
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== Harmonics == | == Harmonics == | ||
{{Harmonics in equal|247|3|1| | {{Harmonics in equal | ||
| steps = 247 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 247 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 10:30, 5 October 2024
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| ← 246edt | 247edt | 248edt → |
247 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 247edt or 247ed3), is a nonoctave tuning system that divides the interval of 3/1 into 247 equal parts of about 7.7 ¢ each. Each step represents a frequency ratio of 31/247, or the 247th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.00 | +2.47 | +1.17 | +1.23 | -3.83 | +3.70 | +0.00 | +2.40 | -0.90 | +2.47 |
| Relative (%) | +16.0 | +0.0 | +32.1 | +15.2 | +16.0 | -49.7 | +48.1 | +0.0 | +31.2 | -11.7 | +32.1 | |
| Steps (reduced) |
156 (156) |
247 (0) |
312 (65) |
362 (115) |
403 (156) |
437 (190) |
468 (221) |
494 (0) |
518 (24) |
539 (45) |
559 (65) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.50 | -2.59 | +1.17 | -2.76 | +0.09 | +1.23 | +0.03 | +3.64 | -3.83 | +0.34 | +0.38 |
| Relative (%) | +32.5 | -33.7 | +15.2 | -35.9 | +1.1 | +16.0 | +0.4 | +47.2 | -49.7 | +4.4 | +5.0 | |
| Steps (reduced) |
577 (83) |
593 (99) |
609 (115) |
623 (129) |
637 (143) |
650 (156) |
662 (168) |
674 (180) |
684 (190) |
695 (201) |
705 (211) | |