5ed9/5
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Prime factorization
5 (prime)
Step size
203.519¢
Octave
6\5ed9/5 (1221.12¢)
(convergent)
Twelfth
9\5ed9/5 (1831.67¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
2
 |
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| ← 4ed9/5 | 5ed9/5 | 6ed9/5 → |
(convergent)
(semiconvergent)
5 equal divisions of 9/5 (abbreviated 5ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 5 equal parts of about 204 ¢ each. Each step represents a frequency ratio of (9/5)1/5, or the 5th root of 9/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 203.519 | 8/7, 12/11, 13/12, 15/13, 17/15, 19/17, 21/19 |
| 2 | 407.039 | 5/4, 11/9, 13/10, 16/13, 17/13, 19/15, 21/16, 21/17 |
| 3 | 610.558 | 7/5, 10/7, 15/11, 17/12, 19/13 |
| 4 | 814.077 | 8/5, 13/8, 17/11, 18/11, 19/12, 20/13, 21/13 |
| 5 | 1017.596 | 7/4, 11/6, 13/7, 15/8, 19/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +21.1 | -70.3 | +42.2 | +63.0 | -49.2 | +91.0 | +63.3 | +63.0 | +84.1 | -80.9 | -28.1 |
| Relative (%) | +10.4 | -34.5 | +20.8 | +30.9 | -24.2 | +44.7 | +31.1 | +30.9 | +41.3 | -39.8 | -13.8 | |
| Steps (reduced) |
6 (1) |
9 (4) |
12 (2) |
14 (4) |
15 (0) |
17 (2) |
18 (3) |
19 (4) |
20 (0) |
20 (0) |
21 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +36.9 | -91.4 | -7.3 | +84.5 | -20.5 | +84.1 | -9.5 | -98.3 | +20.7 | -59.8 | +66.7 |
| Relative (%) | +18.1 | -44.9 | -3.6 | +41.5 | -10.1 | +41.3 | -4.7 | -48.3 | +10.2 | -29.4 | +32.8 | |
| Steps (reduced) |
22 (2) |
22 (2) |
23 (3) |
24 (4) |
24 (4) |
25 (0) |
25 (0) |
25 (0) |
26 (1) |
26 (1) |
27 (2) | |