241edt
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Prime factorization
241 (prime)
Step size
7.89193¢
Octave
152\241edt (1199.57¢)
Consistency limit
14
Distinct consistency limit
14
| ← 240edt | 241edt | 242edt → |
241 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 241edt or 241ed3), is a nonoctave tuning system that divides the interval of 3/1 into 241 equal parts of about 7.89 ¢ each. Each step represents a frequency ratio of 31/241, or the 241st root of 3.
241edt is related to 152edo, but with the 3/1 rather than the 2/1 being just. The octave is about 0.4267 cents compressed and the step size is about 7.8919 cents. It is consistent to the 15-integer-limit, but not to the 16-integer-limit. In comparison, 152edo is only consistent up to the 12-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.43 | +0.00 | -0.85 | -0.46 | -0.43 | +1.03 | -1.28 | +0.00 | -0.89 | -0.16 | -0.85 |
| Relative (%) | -5.4 | +0.0 | -10.8 | -5.9 | -5.4 | +13.0 | -16.2 | +0.0 | -11.3 | -2.1 | -10.8 | |
| Steps (reduced) |
152 (152) |
241 (0) |
304 (63) |
353 (112) |
393 (152) |
427 (186) |
456 (215) |
482 (0) |
505 (23) |
526 (44) |
545 (63) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.63 | +0.60 | -0.46 | -1.71 | +3.82 | -0.43 | +0.67 | -1.32 | +1.03 | -0.59 | +1.37 |
| Relative (%) | +33.3 | +7.6 | -5.9 | -21.6 | +48.5 | -5.4 | +8.5 | -16.7 | +13.0 | -7.5 | +17.4 | |
| Steps (reduced) |
563 (81) |
579 (97) |
594 (112) |
608 (126) |
622 (140) |
634 (152) |
646 (164) |
657 (175) |
668 (186) |
678 (196) |
688 (206) | |