174edt
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Prime factorization
2 × 3 × 29
Step size
10.9308¢
Octave
110\174edt (1202.39¢) (→55\87edt)
Consistency limit
5
Distinct consistency limit
5
 |
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| ← 173edt | 174edt | 175edt → |
174 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 174edt or 174ed3), is a nonoctave tuning system that divides the interval of 3/1 into 174 equal parts of about 10.9 ¢ each. Each step represents a frequency ratio of 31/174, or the 174th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.39 | +0.00 | +4.77 | +1.03 | +2.39 | -2.15 | -3.77 | +0.00 | +3.42 | +2.38 | +4.77 |
| Relative (%) | +21.8 | +0.0 | +43.6 | +9.5 | +21.8 | -19.6 | -34.5 | +0.0 | +31.3 | +21.7 | +43.6 | |
| Steps (reduced) |
110 (110) |
174 (0) |
220 (46) |
255 (81) |
284 (110) |
308 (134) |
329 (155) |
348 (0) |
365 (17) |
380 (32) |
394 (46) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +0.24 | +1.03 | -1.39 | +2.96 | +2.39 | -3.77 | -5.13 | -2.15 | +4.76 | +4.32 |
| Relative (%) | -24.1 | +2.2 | +9.5 | -12.7 | +27.1 | +21.8 | -34.5 | -46.9 | -19.6 | +43.6 | +39.5 | |
| Steps (reduced) |
406 (58) |
418 (70) |
429 (81) |
439 (91) |
449 (101) |
458 (110) |
466 (118) |
474 (126) |
482 (134) |
490 (142) |
497 (149) | |