8ed5/2
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Prime factorization
23
Step size
198.289¢
Octave
6\8ed5/2 (1189.74¢) (→3\4ed5/2)
Twelfth
10\8ed5/2 (1982.89¢) (→5\4ed5/2)
Consistency limit
3
Distinct consistency limit
2
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| ← 7ed5/2 | 8ed5/2 | 9ed5/2 → |
8 equal divisions of 5/2 (abbreviated 8ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 8 equal parts of about 198 ¢ each. Each step represents a frequency ratio of (5/2)1/8, or the 8th root of 5/2.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 198.289 | 8/7, 11/10, 17/15, 19/17, 21/19 |
| 2 | 396.578 | 5/4, 14/11, 16/13, 19/15, 21/17 |
| 3 | 594.868 | 7/5, 10/7, 11/8, 17/12 |
| 4 | 793.157 | 8/5, 11/7, 17/11, 19/12 |
| 5 | 991.446 | 7/4, 20/11 |
| 6 | 1189.735 | 2/1 |
| 7 | 1388.024 | 11/5, 16/7 |
| 8 | 1586.314 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.3 | +80.9 | -20.5 | -10.3 | +70.7 | +2.1 | -30.8 | -36.4 | -20.5 | +12.8 | +60.4 |
| Relative (%) | -5.2 | +40.8 | -10.4 | -5.2 | +35.6 | +1.1 | -15.5 | -18.4 | -10.4 | +6.4 | +30.5 | |
| Steps (reduced) |
6 (6) |
10 (2) |
12 (4) |
14 (6) |
16 (0) |
17 (1) |
18 (2) |
19 (3) |
20 (4) |
21 (5) |
22 (6) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -78.2 | -8.2 | +70.7 | -41.1 | +52.3 | -46.7 | +58.0 | -30.8 | +83.0 | +2.5 | -74.5 |
| Relative (%) | -39.4 | -4.1 | +35.6 | -20.7 | +26.4 | -23.5 | +29.3 | -15.5 | +41.9 | +1.3 | -37.6 | |
| Steps (reduced) |
22 (6) |
23 (7) |
24 (0) |
24 (0) |
25 (1) |
25 (1) |
26 (2) |
26 (2) |
27 (3) |
27 (3) |
27 (3) | |