156edt
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Prime factorization
22 × 3 × 13
Step size
12.192¢
Octave
98\156edt (1194.82¢) (→49\78edt)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 155edt | 156edt | 157edt → |
156 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 156edt or 156ed3), is a nonoctave tuning system that divides the interval of 3/1 into 156 equal parts of about 12.2 ¢ each. Each step represents a frequency ratio of 31/156, or the 156th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.18 | +0.00 | +1.83 | +5.66 | -5.18 | -3.83 | -3.35 | +0.00 | +0.48 | -6.03 | +1.83 |
| Relative (%) | -42.5 | +0.0 | +15.0 | +46.4 | -42.5 | -31.4 | -27.5 | +0.0 | +3.9 | -49.5 | +15.0 | |
| Steps (reduced) |
98 (98) |
156 (0) |
197 (41) |
229 (73) |
254 (98) |
276 (120) |
295 (139) |
312 (0) |
327 (15) |
340 (28) |
353 (41) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +3.18 | +5.66 | +3.66 | -3.76 | -5.18 | -1.25 | -4.71 | -3.83 | +0.98 | -2.83 |
| Relative (%) | -21.6 | +26.1 | +46.4 | +30.0 | -30.9 | -42.5 | -10.2 | -38.6 | -31.4 | +8.0 | -23.2 | |
| Steps (reduced) |
364 (52) |
375 (63) |
385 (73) |
394 (82) |
402 (90) |
410 (98) |
418 (106) |
425 (113) |
432 (120) |
439 (127) |
445 (133) | |