16ed11/5
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Prime factorization
24
Step size
85.3128¢
Octave
14\16ed11/5 (1194.38¢) (→7\8ed11/5)
Twelfth
22\16ed11/5 (1876.88¢) (→11\8ed11/5)
Consistency limit
4
Distinct consistency limit
2
 |
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| ← 15ed11/5 | 16ed11/5 | 17ed11/5 → |
16 equal divisions of 11/5 (abbreviated 16ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 16 equal parts of about 85.3 ¢ each. Each step represents a frequency ratio of (11/5)1/16, or the 16th root of 11/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 85.3 | 17/16, 18/17, 20/19, 23/22 |
| 2 | 170.6 | 11/10 |
| 3 | 255.9 | 7/6, 15/13, 22/19, 23/20 |
| 4 | 341.3 | 16/13, 17/14, 23/19 |
| 5 | 426.6 | 9/7, 19/15 |
| 6 | 511.9 | 4/3 |
| 7 | 597.2 | 17/12, 24/17 |
| 8 | 682.5 | 3/2, 22/15 |
| 9 | 767.8 | 14/9 |
| 10 | 853.1 | 13/8 |
| 11 | 938.4 | 12/7, 19/11 |
| 12 | 1023.8 | 20/11 |
| 13 | 1109.1 | 17/9, 19/10 |
| 14 | 1194.4 | 2/1 |
| 15 | 1279.7 | 23/11 |
| 16 | 1365 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.6 | -25.1 | -11.2 | +29.0 | -30.7 | -41.6 | -16.9 | +35.2 | +23.4 | +29.0 | -36.3 |
| Relative (%) | -6.6 | -29.4 | -13.2 | +34.0 | -36.0 | -48.8 | -19.8 | +41.2 | +27.4 | +34.0 | -42.6 | |
| Steps (reduced) |
14 (14) |
22 (6) |
28 (12) |
33 (1) |
36 (4) |
39 (7) |
42 (10) |
45 (13) |
47 (15) |
49 (1) |
50 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.3 | +38.1 | +3.9 | -22.5 | -42.1 | +29.5 | +21.3 | +17.8 | +18.6 | +23.4 | +31.7 |
| Relative (%) | -5.0 | +44.6 | +4.6 | -26.4 | -49.4 | +34.6 | +24.9 | +20.8 | +21.8 | +27.4 | +37.2 | |
| Steps (reduced) |
52 (4) |
54 (6) |
55 (7) |
56 (8) |
57 (9) |
59 (11) |
60 (12) |
61 (13) |
62 (14) |
63 (15) |
64 (0) | |