5ed5/3
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Prime factorization
5 (prime)
Step size
176.872¢
Octave
7\5ed5/3 (1238.1¢)
(semiconvergent)
Twelfth
11\5ed5/3 (1945.59¢)
Consistency limit
6
Distinct consistency limit
2
 |
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| ← 4ed5/3 | 5ed5/3 | 6ed5/3 → |
(semiconvergent)
5 equal divisions of 5/3 (abbreviated 5ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 5 equal parts of about 177 ¢ each. Each step represents a frequency ratio of (5/3)1/5, or the 5th root of 5/3.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 176.9 | 9/8, 10/9, 14/13, 15/14, 16/15, 17/15, 19/17, 21/19 |
| 2 | 353.7 | 5/4, 6/5, 13/11, 17/14, 19/15, 20/17, 21/17 |
| 3 | 530.6 | 4/3, 7/5, 17/12, 17/13, 19/14 |
| 4 | 707.5 | 3/2, 14/9, 19/13 |
| 5 | 884.4 | 5/3, 8/5, 17/10, 21/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +38.1 | +43.6 | +76.2 | +43.6 | +81.7 | -8.3 | -62.6 | +87.3 | +81.7 | -83.3 | -57.0 |
| Relative (%) | +21.5 | +24.7 | +43.1 | +24.7 | +46.2 | -4.7 | -35.4 | +49.3 | +46.2 | -47.1 | -32.2 | |
| Steps (reduced) |
7 (2) |
11 (1) |
14 (4) |
16 (1) |
18 (3) |
19 (4) |
20 (0) |
22 (2) |
23 (3) |
23 (3) |
24 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | +29.8 | +87.3 | -24.5 | +47.5 | -51.5 | +31.8 | -57.0 | +35.4 | -45.2 | +54.7 |
| Relative (%) | -10.6 | +16.9 | +49.3 | -13.8 | +26.8 | -29.1 | +18.0 | -32.2 | +20.0 | -25.5 | +31.0 | |
| Steps (reduced) |
25 (0) |
26 (1) |
27 (2) |
27 (2) |
28 (3) |
28 (3) |
29 (4) |
29 (4) |
30 (0) |
30 (0) |
31 (1) | |