169edt
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Prime factorization
132
Step size
11.2542¢
Octave
107\169edt (1204.2¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 168edt | 169edt | 170edt → |
169 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 169edt or 169ed3), is a nonoctave tuning system that divides the interval of 3/1 into 169 equal parts of about 11.3 ¢ each. Each step represents a frequency ratio of 31/169, or the 169th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.20 | +0.00 | -2.86 | +4.72 | +4.20 | -3.83 | +1.33 | +0.00 | -2.34 | +1.47 | -2.86 |
| Relative (%) | +37.3 | +0.0 | -25.4 | +41.9 | +37.3 | -34.0 | +11.9 | +0.0 | -20.8 | +13.1 | -25.4 | |
| Steps (reduced) |
107 (107) |
169 (0) |
213 (44) |
248 (79) |
276 (107) |
299 (130) |
320 (151) |
338 (0) |
354 (16) |
369 (31) |
382 (44) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.87 | +0.37 | +4.72 | +5.53 | +1.86 | +4.20 | +0.63 | +1.86 | -3.83 | -5.59 | -3.76 |
| Relative (%) | +43.3 | +3.3 | +41.9 | +49.1 | +16.6 | +37.3 | +5.6 | +16.5 | -34.0 | -49.6 | -33.4 | |
| Steps (reduced) |
395 (57) |
406 (68) |
417 (79) |
427 (89) |
436 (98) |
445 (107) |
453 (115) |
461 (123) |
468 (130) |
475 (137) |
482 (144) | |