179edt
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179 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 179edt or 179ed3), is a nonoctave tuning system that divides the interval of 3/1 into 179 equal parts of about 10.6 ¢ each. Each step represents a frequency ratio of 31/179, or the 179th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.68 | +0.00 | +1.35 | -2.45 | +0.68 | -0.56 | +2.03 | +0.00 | -1.77 | +3.23 | +1.35 |
| Relative (%) | +6.4 | +0.0 | +12.7 | -23.0 | +6.4 | -5.3 | +19.1 | +0.0 | -16.7 | +30.4 | +12.7 | |
| Steps (reduced) |
113 (113) |
179 (0) |
226 (47) |
262 (83) |
292 (113) |
317 (138) |
339 (160) |
358 (0) |
375 (17) |
391 (33) |
405 (47) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.91 | +0.12 | -2.45 | +2.70 | +4.00 | +0.68 | +2.70 | -1.10 | -0.56 | +3.91 | +1.33 |
| Relative (%) | +8.6 | +1.1 | -23.0 | +25.4 | +37.7 | +6.4 | +25.4 | -10.3 | -5.3 | +36.8 | +12.5 | |
| Steps (reduced) |
418 (60) |
430 (72) |
441 (83) |
452 (94) |
462 (104) |
471 (113) |
480 (122) |
488 (130) |
496 (138) |
504 (146) |
511 (153) | |