10ed9/5
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Prime factorization
2 × 5
Step size
101.76¢
Octave
12\10ed9/5 (1221.12¢) (→6\5ed9/5)
Twelfth
19\10ed9/5 (1933.43¢)
Consistency limit
4
Distinct consistency limit
3
 |
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| ← 9ed9/5 | 10ed9/5 | 11ed9/5 → |
10 equal divisions of 9/5 (abbreviated 10ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 10 equal parts of about 102 ¢ each. Each step represents a frequency ratio of (9/5)1/10, or the 10th root of 9/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 101.76 | 14/13, 15/14, 20/19, 21/20, 22/21 |
| 2 | 203.519 | 9/8, 17/15, 19/17, 21/19 |
| 3 | 305.279 | 13/11, 17/14, 20/17 |
| 4 | 407.039 | 14/11, 19/15 |
| 5 | 508.798 | 4/3, 15/11, 19/14 |
| 6 | 610.558 | 7/5, 10/7, 13/9 |
| 7 | 712.317 | 3/2, 20/13 |
| 8 | 814.077 | 11/7, 13/8, 21/13 |
| 9 | 915.837 | 17/10, 19/11, 22/13 |
| 10 | 1017.596 | 11/6, 16/9, 20/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +21.1 | +31.5 | +42.2 | -38.8 | -49.2 | -10.8 | -38.4 | -38.8 | -17.7 | +20.8 | -28.1 |
| Relative (%) | +20.8 | +30.9 | +41.5 | -38.1 | -48.3 | -10.6 | -37.7 | -38.1 | -17.4 | +20.5 | -27.6 | |
| Steps (reduced) |
12 (2) |
19 (9) |
24 (4) |
27 (7) |
30 (0) |
33 (3) |
35 (5) |
37 (7) |
39 (9) |
41 (1) |
42 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +36.9 | +10.4 | -7.3 | -17.3 | -20.5 | -17.7 | -9.5 | +3.4 | +20.7 | +41.9 | -35.0 |
| Relative (%) | +36.3 | +10.2 | -7.2 | -17.0 | -20.1 | -17.4 | -9.4 | +3.4 | +20.4 | +41.2 | -34.4 | |
| Steps (reduced) |
44 (4) |
45 (5) |
46 (6) |
47 (7) |
48 (8) |
49 (9) |
50 (0) |
51 (1) |
52 (2) |
53 (3) |
53 (3) | |