7ed8/5
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(semiconvergent)
7 equal divisions of 8/5 (abbreviated 7ed8/5) is a nonoctave tuning system that divides the interval of 8/5 into 7 equal parts of about 116 ¢ each. Each step represents a frequency ratio of (8/5)1/7, or the 7th root of 8/5.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37.6 | -42.1 | +41.1 | +3.5 | +36.5 | +2.2 | +3.5 | +32.0 | -34.1 | +33.4 | -1.0 |
| Relative (%) | -32.3 | -36.2 | +35.3 | +3.0 | +31.4 | +1.9 | +3.0 | +27.6 | -29.4 | +28.7 | -0.9 | |
| Steps (reduced) |
10 (3) |
16 (2) |
21 (0) |
24 (3) |
27 (6) |
29 (1) |
31 (3) |
33 (5) |
34 (6) |
36 (1) |
37 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -23.4 | -35.4 | -38.6 | -34.1 | -22.8 | -5.6 | +17.1 | +44.5 | -39.9 | -4.2 | +35.0 |
| Relative (%) | -20.1 | -30.5 | -33.2 | -29.4 | -19.6 | -4.8 | +14.7 | +38.3 | -34.4 | -3.6 | +30.2 | |
| Steps (reduced) |
38 (3) |
39 (4) |
40 (5) |
41 (6) |
42 (0) |
43 (1) |
44 (2) |
45 (3) |
45 (3) |
46 (4) |
47 (5) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 116.2 | 14/13, 15/14, 21/20 |
| 2 | 232.5 | 9/8, 10/9, 15/13, 17/15, 19/17, 20/17 |
| 3 | 348.7 | 17/14, 21/17 |
| 4 | 465 | 4/3, 13/10, 17/13 |
| 5 | 581.2 | 7/5, 10/7 |
| 6 | 697.4 | 3/2, 19/13, 20/13 |
| 7 | 813.7 | 11/7, 14/9, 21/13 |
Instruments
A Lumatone mapping for 7ed8/5 is available.
Music
- 7ed(8/5) improv (2025)