7ed4/3
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Prime factorization
7 (prime)
Step size
71.1493¢
Octave
17\7ed4/3 (1209.54¢)
(semiconvergent)
Twelfth
27\7ed4/3 (1921.03¢)
Consistency limit
5
Distinct consistency limit
3
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| ← 6ed4/3 | 7ed4/3 | 8ed4/3 → |
(semiconvergent)
7 equal divisions of 4/3 (abbreviated 7ed4/3) is a nonoctave tuning system that divides the interval of 4/3 into 7 equal parts of about 71.1 ¢ each. Each step represents a frequency ratio of (4/3)1/7, or the 7th root of 4/3. This tuning system is related to vishnu temperament.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 71.149 | 17/16, 19/18, 20/19, 21/20 |
| 2 | 142.299 | 10/9, 11/10, 14/13, 15/14, 16/15, 18/17, 21/19 |
| 3 | 213.448 | 9/8, 17/15, 19/17 |
| 4 | 284.597 | 13/11, 15/13, 19/16, 20/17 |
| 5 | 355.746 | 5/4, 6/5, 17/14, 21/17 |
| 6 | 426.896 | 13/10, 14/11, 19/15, 21/16 |
| 7 | 498.045 | 4/3, 17/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +9.5 | +19.1 | +19.1 | -11.5 | +28.6 | -24.8 | +28.6 | -33.0 | -2.0 | -24.7 | -33.0 |
| Relative (%) | +13.4 | +26.8 | +26.8 | -16.2 | +40.2 | -34.9 | +40.2 | -46.4 | -2.7 | -34.7 | -46.4 | |
| Steps (reduced) |
17 (3) |
27 (6) |
34 (6) |
39 (4) |
44 (2) |
47 (5) |
51 (2) |
53 (4) |
56 (0) |
58 (2) |
60 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -29.3 | -15.3 | +7.6 | -33.0 | +4.3 | -23.5 | +25.2 | +7.6 | -5.7 | -15.1 | -20.9 |
| Relative (%) | -41.1 | -21.5 | +10.7 | -46.4 | +6.1 | -33.0 | +35.5 | +10.7 | -8.1 | -21.3 | -29.4 | |
| Steps (reduced) |
62 (6) |
64 (1) |
66 (3) |
67 (4) |
69 (6) |
70 (0) |
72 (2) |
73 (3) |
74 (4) |
75 (5) |
76 (6) | |