164edt
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Prime factorization
22 × 41
Step size
11.5973¢
Octave
103\164edt (1194.52¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 163edt | 164edt | 165edt → |
164 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 164edt or 164ed3), is a nonoctave tuning system that divides the interval of 3/1 into 164 equal parts of about 11.6 ¢ each. Each step represents a frequency ratio of 31/164, or the 164th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.48 | +0.00 | +0.64 | -2.96 | -5.48 | -5.61 | -4.84 | +0.00 | +3.15 | +0.51 | +0.64 |
| Relative (%) | -47.2 | +0.0 | +5.5 | -25.6 | -47.2 | -48.4 | -41.7 | +0.0 | +27.2 | +4.4 | +5.5 | |
| Steps (reduced) |
103 (103) |
164 (0) |
207 (43) |
240 (76) |
267 (103) |
290 (126) |
310 (146) |
328 (0) |
344 (16) |
358 (30) |
371 (43) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.51 | -2.96 | +1.28 | +0.70 | -5.48 | +5.29 | -2.33 | -5.61 | -4.97 | -0.74 |
| Relative (%) | +10.6 | +4.4 | -25.6 | +11.0 | +6.0 | -47.2 | +45.6 | -20.1 | -48.4 | -42.8 | -6.4 | |
| Steps (reduced) |
383 (55) |
394 (66) |
404 (76) |
414 (86) |
423 (95) |
431 (103) |
440 (112) |
447 (119) |
454 (126) |
461 (133) |
468 (140) | |