188edt: Difference between revisions
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== Harmonics == | == Harmonics == | ||
Latest revision as of 10:17, 5 October 2024
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| ← 187edt | 188edt | 189edt → |
188 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 188edt or 188ed3), is a nonoctave tuning system that divides the interval of 3/1 into 188 equal parts of about 10.1 ¢ each. Each step represents a frequency ratio of 31/188, or the 188th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.90 | +0.00 | -2.32 | -4.20 | +3.90 | +0.06 | +1.57 | +0.00 | -0.30 | -3.44 | -2.32 |
| Relative (%) | +38.5 | +0.0 | -23.0 | -41.5 | +38.5 | +0.6 | +15.6 | +0.0 | -3.0 | -34.0 | -23.0 | |
| Steps (reduced) |
119 (119) |
188 (0) |
237 (49) |
275 (87) |
307 (119) |
333 (145) |
356 (168) |
376 (0) |
394 (18) |
410 (34) |
425 (49) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.74 | +3.96 | -4.20 | -4.65 | +1.68 | +3.90 | +1.35 | +3.60 | +0.06 | +0.46 | +4.44 |
| Relative (%) | +7.3 | +39.1 | -41.5 | -45.9 | +16.6 | +38.5 | +13.3 | +35.5 | +0.6 | +4.5 | +43.9 | |
| Steps (reduced) |
439 (63) |
452 (76) |
463 (87) |
474 (98) |
485 (109) |
495 (119) |
504 (128) |
513 (137) |
521 (145) |
529 (153) |
537 (161) | |