180edt
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Prime factorization
22 × 32 × 5
Step size
10.5664¢
Octave
114\180edt (1204.57¢) (→19\30edt)
Consistency limit
2
Distinct consistency limit
2
Special properties
 |
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| ← 179edt | 180edt | 181edt → |
180 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 180edt or 180ed3), is a nonoctave tuning system that divides the interval of 3/1 into 180 equal parts of about 10.6 ¢ each. Each step represents a frequency ratio of 31/180, or the 180th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.57 | +0.00 | -1.42 | +3.22 | +4.57 | +1.86 | +3.15 | +0.00 | -2.77 | +1.28 | -1.42 |
| Relative (%) | +43.3 | +0.0 | -13.5 | +30.5 | +43.3 | +17.6 | +29.8 | +0.0 | -26.3 | +12.1 | -13.5 | |
| Steps (reduced) |
114 (114) |
180 (0) |
227 (47) |
264 (84) |
294 (114) |
319 (139) |
341 (161) |
360 (0) |
377 (17) |
393 (33) |
407 (47) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -4.13 | +3.22 | -2.85 | -2.14 | +4.57 | -4.50 | +1.80 | +1.86 | -4.71 | +2.86 |
| Relative (%) | -24.9 | -39.1 | +30.5 | -26.9 | -20.2 | +43.3 | -42.6 | +17.0 | +17.6 | -44.6 | +27.1 | |
| Steps (reduced) |
420 (60) |
432 (72) |
444 (84) |
454 (94) |
464 (104) |
474 (114) |
482 (122) |
491 (131) |
499 (139) |
506 (146) |
514 (154) | |