12ed7/4
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Prime factorization
22 × 3
Step size
80.7355¢
Octave
15\12ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth
24\12ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit
5
Distinct consistency limit
2
Special properties
 |
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| ← 11ed7/4 | 12ed7/4 | 13ed7/4 → |
12 equal divisions of 7/4 (abbreviated 12ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 12 equal parts of about 80.7 ¢ each. Each step represents a frequency ratio of (7/4)1/12, or the 12th root of 7/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 80.735 | 17/16, 21/20, 23/22 |
| 2 | 161.471 | 10/9 |
| 3 | 242.206 | 7/6, 8/7, 22/19 |
| 4 | 322.942 | 6/5, 17/14, 23/19 |
| 5 | 403.677 | 5/4 |
| 6 | 484.413 | 4/3, 17/13, 21/16 |
| 7 | 565.148 | 7/5 |
| 8 | 645.884 | 10/7, 19/13 |
| 9 | 726.619 | 3/2 |
| 10 | 807.355 | 8/5 |
| 11 | 888.09 | 5/3, 22/13 |
| 12 | 968.826 | 7/4, 16/9, 19/11, 23/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.0 | +35.7 | +22.1 | +39.4 | -34.0 | +22.1 | +33.1 | -9.3 | -30.3 | -33.8 | -23.0 |
| Relative (%) | +13.7 | +44.2 | +27.3 | +48.8 | -42.1 | +27.3 | +41.0 | -11.6 | -37.5 | -41.9 | -28.5 | |
| Steps (reduced) |
15 (3) |
24 (0) |
30 (6) |
35 (11) |
38 (2) |
42 (6) |
45 (9) |
47 (11) |
49 (1) |
51 (3) |
53 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.1 | +33.1 | -5.6 | -36.6 | +19.9 | +1.7 | -11.2 | -19.2 | -23.0 | -22.8 | -19.0 |
| Relative (%) | -0.1 | +41.0 | -6.9 | -45.3 | +24.7 | +2.1 | -13.8 | -23.8 | -28.5 | -28.2 | -23.5 | |
| Steps (reduced) |
55 (7) |
57 (9) |
58 (10) |
59 (11) |
61 (1) |
62 (2) |
63 (3) |
64 (4) |
65 (5) |
66 (6) |
67 (7) | |