234edt: Difference between revisions
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== Harmonics == | |||
{{ | {{Harmonics in equal | ||
| steps = 234 | |||
| num = 3 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 234 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
Latest revision as of 10:11, 5 October 2024
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234 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 234edt or 234ed3), is a nonoctave tuning system that divides the interval of 3/1 into 234 equal parts of about 8.13 ¢ each. Each step represents a frequency ratio of 31/234, or the 234th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.95 | +0.00 | -2.24 | +1.59 | +2.95 | -3.83 | +0.71 | +0.00 | -3.59 | +2.10 | -2.24 |
| Relative (%) | +36.2 | +0.0 | -27.5 | +19.6 | +36.2 | -47.1 | +8.7 | +0.0 | -44.1 | +25.8 | -27.5 | |
| Steps (reduced) |
148 (148) |
234 (0) |
295 (61) |
343 (109) |
382 (148) |
414 (180) |
443 (209) |
468 (0) |
490 (22) |
511 (43) |
529 (61) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -0.88 | +1.59 | +3.66 | -3.76 | +2.95 | -1.25 | -0.64 | -3.83 | -3.09 | +1.24 |
| Relative (%) | -32.4 | -10.9 | +19.6 | +45.0 | -46.3 | +36.2 | -15.4 | -7.9 | -47.1 | -38.0 | +15.2 | |
| Steps (reduced) |
546 (78) |
562 (94) |
577 (109) |
591 (123) |
603 (135) |
616 (148) |
627 (159) |
638 (170) |
648 (180) |
658 (190) |
668 (200) | |