194edt: Difference between revisions
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== Harmonics == | |||
{{ | {{Harmonics in equal | ||
| steps = 194 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 194 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 09:54, 5 October 2024
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| ← 193edt | 194edt | 195edt → |
194 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 194edt or 194ed3), is a nonoctave tuning system that divides the interval of 3/1 into 194 equal parts of about 9.8 ¢ each. Each step represents a frequency ratio of 31/194, or the 194th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.93 | +0.00 | +1.95 | -2.01 | -3.93 | +3.71 | -1.97 | +0.00 | +3.87 | -4.27 | +1.95 |
| Relative (%) | -40.0 | +0.0 | +19.9 | -20.5 | -40.0 | +37.9 | -20.1 | +0.0 | +39.5 | -43.6 | +19.9 | |
| Steps (reduced) |
122 (122) |
194 (0) |
245 (51) |
284 (90) |
316 (122) |
344 (150) |
367 (173) |
388 (0) |
407 (19) |
423 (35) |
439 (51) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.64 | -0.21 | -2.01 | +3.91 | -3.01 | -3.93 | +0.51 | -0.05 | +3.71 | +1.61 | +3.08 |
| Relative (%) | +6.5 | -2.2 | -20.5 | +39.9 | -30.7 | -40.0 | +5.2 | -0.6 | +37.9 | +16.4 | +31.4 | |
| Steps (reduced) |
453 (65) |
466 (78) |
478 (90) |
490 (102) |
500 (112) |
510 (122) |
520 (132) |
529 (141) |
538 (150) |
546 (158) |
554 (166) | |