5ed7/4
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Prime factorization
5 (prime)
Step size
193.765¢
Octave
6\5ed7/4 (1162.59¢)
(semiconvergent)
Twelfth
10\5ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit
3
Distinct consistency limit
2
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| ← 4ed7/4 | 5ed7/4 | 6ed7/4 → |
(semiconvergent)
5 equal divisions of 7/4 (abbreviated 5ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 5 equal parts of about 194 ¢ each. Each step represents a frequency ratio of (7/4)1/5, or the 5th root of 7/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 193.765 | 7/6, 8/7, 11/10, 12/11, 13/12, 15/13, 15/14, 17/15, 19/17, 21/19 |
| 2 | 387.53 | 5/4, 6/5, 14/11, 17/14, 19/15, 21/17 |
| 3 | 581.296 | 7/5, 10/7, 11/8, 13/9, 15/11, 16/11, 17/12, 18/13, 19/14 |
| 4 | 775.061 | 3/2, 8/5, 11/7, 17/11, 19/12, 21/13 |
| 5 | 968.826 | 7/4, 12/7, 17/10, 19/11, 20/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37.4 | +35.7 | -74.8 | -73.6 | -1.7 | -74.8 | +81.5 | +71.4 | +82.8 | -82.2 | -39.1 |
| Relative (%) | -19.3 | +18.4 | -38.6 | -38.0 | -0.9 | -38.6 | +42.1 | +36.8 | +42.7 | -42.4 | -20.2 | |
| Steps (reduced) |
6 (1) |
10 (0) |
12 (2) |
14 (4) |
16 (1) |
17 (2) |
19 (4) |
20 (0) |
21 (1) |
21 (1) |
22 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.1 | +81.5 | -37.9 | +44.1 | -60.8 | +34.0 | -59.6 | +45.3 | -39.1 | +74.1 | -2.8 |
| Relative (%) | +8.3 | +42.1 | -19.6 | +22.8 | -31.4 | +17.5 | -30.8 | +23.4 | -20.2 | +38.2 | -1.5 | |
| Steps (reduced) |
23 (3) |
24 (4) |
24 (4) |
25 (0) |
25 (0) |
26 (1) |
26 (1) |
27 (2) |
27 (2) |
28 (3) |
28 (3) | |