178edt
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Prime factorization
2 × 89
Step size
10.6851¢
Octave
112\178edt (1196.74¢) (→56\89edt)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 177edt | 178edt | 179edt → |
178 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 178edt or 178ed3), is a nonoctave tuning system that divides the interval of 3/1 into 178 equal parts of about 10.7 ¢ each. Each step represents a frequency ratio of 31/178, or the 178th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.26 | +0.00 | +4.16 | +2.51 | -3.26 | -3.01 | +0.89 | +0.00 | -0.76 | +5.20 | +4.16 |
| Relative (%) | -30.5 | +0.0 | +38.9 | +23.5 | -30.5 | -28.1 | +8.4 | +0.0 | -7.1 | +48.7 | +38.9 | |
| Steps (reduced) |
112 (112) |
178 (0) |
225 (47) |
261 (83) |
290 (112) |
315 (137) |
337 (159) |
356 (0) |
373 (17) |
389 (33) |
403 (47) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.49 | +4.41 | +2.51 | -2.37 | -0.48 | -3.26 | -0.70 | -4.02 | -3.01 | +1.94 | -0.22 |
| Relative (%) | +42.0 | +41.3 | +23.5 | -22.2 | -4.5 | -30.5 | -6.6 | -37.6 | -28.1 | +18.1 | -2.1 | |
| Steps (reduced) |
416 (60) |
428 (72) |
439 (83) |
449 (93) |
459 (103) |
468 (112) |
477 (121) |
485 (129) |
493 (137) |
501 (145) |
508 (152) | |