197edt
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Prime factorization
197 (prime)
Step size
9.65459¢
Octave
124\197edt (1197.17¢)
Consistency limit
2
Distinct consistency limit
2
| ← 196edt | 197edt | 198edt → |
197 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 197edt or 197ed3), is a nonoctave tuning system that divides the interval of 3/1 into 197 equal parts of about 9.65 ¢ each. Each step represents a frequency ratio of 31/197, or the 197th root of 3.
197edt can be described as approximately 124.293edo. This implies that each step of 197edt can be approximated by 7 steps of 870edo.
It is a very strong no-twos, no-fives 19-limit system, though it additionally represents the interval of 5/4 very well, and the 8th harmonic decently.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.83 | +0.00 | +3.86 | +0.63 | +0.16 | +0.59 | -0.42 | +0.11 | -2.39 |
| Relative (%) | -29.3 | +0.0 | +40.0 | +6.5 | +1.6 | +6.1 | -4.4 | +1.2 | -24.8 | |
| Steps (reduced) |
124 (124) |
197 (0) |
289 (92) |
349 (152) |
430 (36) |
460 (66) |
508 (114) |
528 (134) |
562 (168) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.93 | +0.00 | +1.80 | +2.19 | +0.16 | +4.49 | -4.82 | +0.59 | +0.90 | -4.32 | +3.86 |
| Relative (%) | -20.0 | +0.0 | +18.6 | +22.7 | +1.6 | +46.5 | -49.9 | +6.1 | +9.3 | -44.8 | +40.0 | |
| Steps (reduced) |
577 (183) |
591 (0) |
604 (13) |
616 (25) |
627 (36) |
638 (47) |
647 (56) |
657 (66) |
666 (75) |
674 (83) |
683 (92) | |
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