197edt
| ← 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.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.83 | +0.00 | +3.99 | +3.86 | -2.83 | +0.63 | +1.16 | +0.00 | +1.03 | +0.16 | +3.99 |
| Relative (%) | -29.3 | +0.0 | +41.4 | +40.0 | -29.3 | +6.5 | +12.1 | +0.0 | +10.7 | +1.6 | +41.4 | |
| Steps (reduced) |
124 (124) |
197 (0) |
249 (52) |
289 (92) |
321 (124) |
349 (152) |
373 (176) |
394 (0) |
413 (19) |
430 (36) |
446 (52) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.59 | -2.20 | +3.86 | -1.67 | -0.42 | -2.83 | +0.11 | -1.80 | +0.63 | -2.67 | -2.39 |
| Relative (%) | +6.1 | -22.8 | +40.0 | -17.3 | -4.4 | -29.3 | +1.2 | -18.6 | +6.5 | -27.7 | -24.8 | |
| Steps (reduced) |
460 (66) |
473 (79) |
486 (92) |
497 (103) |
508 (114) |
518 (124) |
528 (134) |
537 (143) |
546 (152) |
554 (160) |
562 (168) | |
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