176edt
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Prime factorization
24 × 11
Step size
10.8066¢
Octave
111\176edt (1199.53¢)
Consistency limit
22
Distinct consistency limit
16
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| ← 175edt | 176edt | 177edt → |
176 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 176edt or 176ed3), is a nonoctave tuning system that divides the interval of 3/1 into 176 equal parts of about 10.8 ¢ each. Each step represents a frequency ratio of 31/176, or the 176th root of 3. It is related to 111edo, but with the 3/1 tuned just instead of the 2/1.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.47 | +0.00 | -0.94 | +1.78 | -0.47 | +2.82 | -1.41 | +0.00 | +1.31 | -1.60 | -0.94 |
| Relative (%) | -4.4 | +0.0 | -8.7 | +16.5 | -4.4 | +26.1 | -13.1 | +0.0 | +12.1 | -14.8 | -8.7 | |
| Steps (reduced) |
111 (111) |
176 (0) |
222 (46) |
258 (82) |
287 (111) |
312 (136) |
333 (157) |
352 (0) |
369 (17) |
384 (32) |
398 (46) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.97 | +2.35 | +1.78 | -1.89 | +1.22 | -0.47 | +3.18 | +0.84 | +2.82 | -2.07 | -3.38 |
| Relative (%) | +9.0 | +21.7 | +16.5 | -17.5 | +11.3 | -4.4 | +29.5 | +7.7 | +26.1 | -19.2 | -31.3 | |
| Steps (reduced) |
411 (59) |
423 (71) |
434 (82) |
444 (92) |
454 (102) |
463 (111) |
472 (120) |
480 (128) |
488 (136) |
495 (143) |
502 (150) | |