233edt
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Prime factorization
233 (prime)
Step size
8.1629¢
Octave
147\233edt (1199.95¢)
(semiconvergent)
Consistency limit
5
Distinct consistency limit
5
 |
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| ← 232edt | 233edt | 234edt → |
(semiconvergent)
233 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 233edt or 233ed3), is a nonoctave tuning system that divides the interval of 3/1 into 233 equal parts of about 8.16 ¢ each. Each step represents a frequency ratio of 31/233, or the 233rd root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.05 | +0.00 | -0.11 | -2.77 | -0.05 | +2.45 | -0.16 | +0.00 | -2.82 | +3.60 | -0.11 |
| Relative (%) | -0.7 | +0.0 | -1.3 | -33.9 | -0.7 | +30.0 | -2.0 | +0.0 | -34.5 | +44.1 | -1.3 | |
| Steps (reduced) |
147 (147) |
233 (0) |
294 (61) |
341 (108) |
380 (147) |
413 (180) |
441 (208) |
466 (0) |
488 (22) |
509 (43) |
527 (61) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.09 | +2.40 | -2.77 | -0.22 | +0.95 | -0.05 | -3.87 | -2.87 | +2.45 | +3.54 | +0.05 |
| Relative (%) | +1.1 | +29.4 | -33.9 | -2.7 | +11.6 | -0.7 | -47.4 | -35.2 | +30.0 | +43.4 | +0.6 | |
| Steps (reduced) |
544 (78) |
560 (94) |
574 (108) |
588 (122) |
601 (135) |
613 (147) |
624 (158) |
635 (169) |
646 (180) |
656 (190) |
665 (199) | |