193edt: Difference between revisions
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== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 193 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 193 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 09:54, 5 October 2024
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| ← 192edt | 193edt | 194edt → |
193 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 193edt or 193ed3), is a nonoctave tuning system that divides the interval of 3/1 into 193 equal parts of about 9.85 ¢ each. Each step represents a frequency ratio of 31/193, or the 193rd root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.27 | +0.00 | +4.54 | +2.56 | +2.27 | +1.48 | -3.04 | +0.00 | +4.84 | -2.49 | +4.54 |
| Relative (%) | +23.1 | +0.0 | +46.1 | +26.0 | +23.1 | +15.0 | -30.8 | +0.0 | +49.1 | -25.3 | +46.1 | |
| Steps (reduced) |
122 (122) |
193 (0) |
244 (51) |
283 (90) |
315 (122) |
342 (149) |
365 (172) |
386 (0) |
405 (19) |
421 (35) |
437 (51) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.94 | +3.75 | +2.56 | -0.77 | +2.68 | +2.27 | -2.64 | -2.75 | +1.48 | -0.22 | +1.66 |
| Relative (%) | +40.0 | +38.1 | +26.0 | -7.8 | +27.2 | +23.1 | -26.8 | -27.9 | +15.0 | -2.3 | +16.8 | |
| Steps (reduced) |
451 (65) |
464 (78) |
476 (90) |
487 (101) |
498 (112) |
508 (122) |
517 (131) |
526 (140) |
535 (149) |
543 (157) |
551 (165) | |