143edt: Difference between revisions
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== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 143 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 143 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Revision as of 10:13, 2 October 2024
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| ← 142edt | 143edt | 144edt → |
143 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 143edt or 143ed3), is a nonoctave tuning system that divides the interval of 3/1 into 143 equal parts of about 13.3 ¢ each. Each step represents a frequency ratio of 31/143, or the 143rd root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.97 | +0.00 | -5.93 | -6.53 | -2.97 | -3.83 | +4.40 | +0.00 | +3.80 | -1.60 | -5.93 |
| Relative (%) | -22.3 | +0.0 | -44.6 | -49.1 | -22.3 | -28.8 | +33.1 | +0.0 | +28.6 | -12.0 | -44.6 | |
| Steps (reduced) |
90 (90) |
143 (0) |
180 (37) |
209 (66) |
233 (90) |
253 (110) |
271 (128) |
286 (0) |
300 (14) |
312 (26) |
323 (37) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.80 | +6.51 | -6.53 | +1.44 | +2.89 | -2.97 | -3.47 | +0.84 | -3.83 | -4.56 | -1.72 |
| Relative (%) | +13.5 | +48.9 | -49.1 | +10.8 | +21.7 | -22.3 | -26.1 | +6.3 | -28.8 | -34.3 | -12.9 | |
| Steps (reduced) |
334 (48) |
344 (58) |
352 (66) |
361 (75) |
369 (83) |
376 (90) |
383 (97) |
390 (104) |
396 (110) |
402 (116) |
408 (122) | |