8ed7/3
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Prime factorization
23
Step size
183.359¢
Octave
7\8ed7/3 (1283.51¢)
Twelfth
10\8ed7/3 (1833.59¢) (→5\4ed7/3)
Consistency limit
2
Distinct consistency limit
2
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| ← 7ed7/3 | 8ed7/3 | 9ed7/3 → |
8 equal divisions of 7/3 (abbreviated 8ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 8 equal parts of about 183 ¢ each. Each step represents a frequency ratio of (7/3)1/8, or the 8th root of 7/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 183.359 | 11/10, 12/11, 19/17 |
| 2 | 366.718 | 17/14 |
| 3 | 550.077 | 7/5, 18/13, 19/14 |
| 4 | 733.435 | 17/11 |
| 5 | 916.794 | 5/3, 17/10, 19/11 |
| 6 | 1100.153 | 13/7, 19/10 |
| 7 | 1283.512 | 15/7 |
| 8 | 1466.871 | 7/3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +83.5 | -68.4 | -16.3 | -35.9 | +15.1 | -68.4 | +67.2 | +46.6 | +47.6 | +65.9 | -84.7 |
| Relative (%) | +45.5 | -37.3 | -8.9 | -19.6 | +8.3 | -37.3 | +36.6 | +25.4 | +25.9 | +36.0 | -46.2 | |
| Steps (reduced) |
7 (7) |
10 (2) |
13 (5) |
15 (7) |
17 (1) |
18 (2) |
20 (4) |
21 (5) |
22 (6) |
23 (7) |
23 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -39.9 | +15.1 | +79.1 | -32.7 | +45.7 | -53.2 | +36.5 | -52.3 | +46.6 | -33.9 | +72.5 |
| Relative (%) | -21.8 | +8.3 | +43.1 | -17.8 | +24.9 | -29.0 | +19.9 | -28.5 | +25.4 | -18.5 | +39.5 | |
| Steps (reduced) |
24 (0) |
25 (1) |
26 (2) |
26 (2) |
27 (3) |
27 (3) |
28 (4) |
28 (4) |
29 (5) |
29 (5) |
30 (6) | |