16ed7/4
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Prime factorization
24
Step size
60.5516¢
Octave
20\16ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth
31\16ed7/4 (1877.1¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 15ed7/4 | 16ed7/4 | 17ed7/4 → |
(semiconvergent)
16 equal divisions of 7/4 (abbreviated 16ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 16 equal parts of about 60.6 ¢ each. Each step represents a frequency ratio of (7/4)1/16, or the 16th root of 7/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 60.6 | 23/22, 24/23 |
| 2 | 121.1 | 13/12 |
| 3 | 181.7 | 11/10, 19/17, 21/19 |
| 4 | 242.2 | 8/7, 15/13, 23/20 |
| 5 | 302.8 | 6/5 |
| 6 | 363.3 | 21/17 |
| 7 | 423.9 | 14/11, 19/15, 24/19 |
| 8 | 484.4 | 17/13 |
| 9 | 545 | 11/8, 18/13 |
| 10 | 605.5 | 10/7, 17/12, 24/17 |
| 11 | 666.1 | 16/11, 19/13 |
| 12 | 726.6 | |
| 13 | 787.2 | 11/7, 19/12 |
| 14 | 847.7 | 21/13, 23/14 |
| 15 | 908.3 | 17/10 |
| 16 | 968.8 | 7/4 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.0 | -24.9 | +22.1 | -0.9 | -13.8 | +22.1 | -27.5 | +10.8 | +10.1 | +26.7 | -2.8 |
| Relative (%) | +18.2 | -41.0 | +36.4 | -1.6 | -22.8 | +36.4 | -45.3 | +17.9 | +16.7 | +44.2 | -4.6 | |
| Steps (reduced) |
20 (4) |
31 (15) |
40 (8) |
46 (14) |
51 (3) |
56 (8) |
59 (11) |
63 (15) |
66 (2) |
69 (5) |
71 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.3 | -27.5 | -25.8 | -16.4 | -0.3 | +21.9 | -11.2 | +21.1 | -2.8 | -22.8 | +21.4 |
| Relative (%) | -33.5 | -45.3 | -42.6 | -27.1 | -0.5 | +36.1 | -18.5 | +34.9 | -4.6 | -37.6 | +35.3 | |
| Steps (reduced) |
73 (9) |
75 (11) |
77 (13) |
79 (15) |
81 (1) |
83 (3) |
84 (4) |
86 (6) |
87 (7) |
88 (8) |
90 (10) | |