165edt
Jump to navigation
Jump to search
Prime factorization
3 × 5 × 11
Step size
11.527¢
Octave
104\165edt (1198.81¢)
Consistency limit
5
Distinct consistency limit
5
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 164edt | 165edt | 166edt → |
165 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 165edt or 165ed3), is a nonoctave tuning system that divides the interval of 3/1 into 165 equal parts of about 11.5 ¢ each. Each step represents a frequency ratio of 31/165, or the 165th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.19 | +0.00 | -2.38 | +3.22 | -1.19 | -2.94 | -3.58 | +0.00 | +2.03 | -1.60 | -2.38 |
| Relative (%) | -10.3 | +0.0 | -20.7 | +27.9 | -10.3 | -25.5 | -31.0 | +0.0 | +17.6 | -13.9 | -20.7 | |
| Steps (reduced) |
104 (104) |
165 (0) |
208 (43) |
242 (77) |
269 (104) |
292 (127) |
312 (147) |
330 (0) |
346 (16) |
360 (30) |
373 (43) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -4.13 | +3.22 | -4.77 | +5.55 | -1.19 | -2.58 | +0.84 | -2.94 | -2.79 | +0.94 |
| Relative (%) | -22.8 | -35.9 | +27.9 | -41.4 | +48.1 | -10.3 | -22.4 | +7.3 | -25.5 | -24.2 | +8.2 | |
| Steps (reduced) |
385 (55) |
396 (66) |
407 (77) |
416 (86) |
426 (96) |
434 (104) |
442 (112) |
450 (120) |
457 (127) |
464 (134) |
471 (141) | |