12ed7/3
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Prime factorization
22 × 3
Step size
122.239¢
Octave
10\12ed7/3 (1222.39¢) (→5\6ed7/3)
Twelfth
16\12ed7/3 (1955.83¢) (→4\3ed7/3)
Consistency limit
5
Distinct consistency limit
2
Special properties
 |
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| ← 11ed7/3 | 12ed7/3 | 13ed7/3 → |
12 equal divisions of 7/3 (abbreviated 12ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 12 equal parts of about 122 ¢ each. Each step represents a frequency ratio of (7/3)1/12, or the 12th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 122.239 | 15/14, 16/15 |
| 2 | 244.478 | 7/6, 8/7, 22/19 |
| 3 | 366.718 | 5/4 |
| 4 | 488.957 | 4/3, 17/13, 21/16 |
| 5 | 611.196 | 10/7 |
| 6 | 733.435 | 17/11 |
| 7 | 855.675 | |
| 8 | 977.914 | 7/4, 16/9, 23/13 |
| 9 | 1100.153 | 15/8, 19/10 |
| 10 | 1222.392 | 2/1 |
| 11 | 1344.632 | 11/5, 15/7 |
| 12 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +22.4 | +53.9 | +44.8 | +25.2 | -46.0 | +53.9 | -55.1 | -14.5 | +47.6 | +4.8 | -23.6 |
| Relative (%) | +18.3 | +44.1 | +36.6 | +20.6 | -37.6 | +44.1 | -45.0 | -11.9 | +38.9 | +3.9 | -19.3 | |
| Steps (reduced) |
10 (10) |
16 (4) |
20 (8) |
23 (11) |
25 (1) |
28 (4) |
29 (5) |
31 (7) |
33 (9) |
34 (10) |
35 (11) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | -46.0 | -43.2 | -32.7 | -15.4 | +7.9 | +36.5 | -52.3 | -14.5 | +27.2 | -49.7 |
| Relative (%) | -32.7 | -37.6 | -35.3 | -26.7 | -12.6 | +6.5 | +29.9 | -42.8 | -11.9 | +22.3 | -40.7 | |
| Steps (reduced) |
36 (0) |
37 (1) |
38 (2) |
39 (3) |
40 (4) |
41 (5) |
42 (6) |
42 (6) |
43 (7) |
44 (8) |
44 (8) | |