177edt
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Prime factorization
3 × 59
Step size
10.7455¢
Octave
112\177edt (1203.5¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 176edt | 177edt | 178edt → |
177 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 177edt or 177ed3), is a nonoctave tuning system that divides the interval of 3/1 into 177 equal parts of about 10.7 ¢ each. Each step represents a frequency ratio of 31/177, or the 177th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.50 | +0.00 | -3.75 | -3.23 | +3.50 | +5.26 | -0.25 | +0.00 | +0.27 | -3.55 | -3.75 |
| Relative (%) | +32.5 | +0.0 | -34.9 | -30.0 | +32.5 | +49.0 | -2.4 | +0.0 | +2.5 | -33.1 | -34.9 | |
| Steps (reduced) |
112 (112) |
177 (0) |
223 (46) |
259 (82) |
289 (112) |
314 (137) |
335 (158) |
354 (0) |
371 (17) |
386 (32) |
400 (46) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -1.98 | -3.23 | +3.24 | -5.00 | +3.50 | -4.14 | +3.77 | +5.26 | -0.05 | -1.79 |
| Relative (%) | -24.5 | -18.5 | -30.0 | +30.2 | -46.6 | +32.5 | -38.5 | +35.1 | +49.0 | -0.5 | -16.7 | |
| Steps (reduced) |
413 (59) |
425 (71) |
436 (82) |
447 (93) |
456 (102) |
466 (112) |
474 (120) |
483 (129) |
491 (137) |
498 (144) |
505 (151) | |