6ed9/5
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Prime factorization
2 × 3
Step size
169.599¢
Octave
7\6ed9/5 (1187.2¢)
(convergent)
Twelfth
11\6ed9/5 (1865.59¢)
(semiconvergent)
Consistency limit
6
Distinct consistency limit
2
Special properties
 |
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| ← 5ed9/5 | 6ed9/5 | 7ed9/5 → |
(convergent)
(semiconvergent)
6 equal divisions of 9/5 (abbreviated 6ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 6 equal parts of about 170 ¢ each. Each step represents a frequency ratio of (9/5)1/6, or the 6th root of 9/5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 169.6 | 9/8, 10/9, 11/10, 12/11, 13/12, 14/13, 16/15, 19/17, 21/19 |
| 2 | 339.2 | 5/4, 6/5, 11/9, 13/11, 16/13, 17/14, 19/16, 21/17 |
| 3 | 508.8 | 4/3, 11/8, 13/10, 15/11, 17/13, 18/13, 19/14, 21/16 |
| 4 | 678.4 | 3/2, 13/9, 16/11, 19/13 |
| 5 | 848 | 5/3, 8/5, 13/8, 18/11, 19/12, 21/13 |
| 6 | 1017.6 | 7/4, 9/5, 11/6, 13/7, 16/9, 20/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.8 | -36.4 | -25.6 | -72.7 | -49.2 | +23.2 | -38.4 | -72.7 | +84.1 | -80.9 | -62.0 |
| Relative (%) | -7.5 | -21.4 | -15.1 | -42.9 | -29.0 | +13.7 | -22.6 | -42.9 | +49.6 | -47.7 | -36.5 | |
| Steps (reduced) |
7 (1) |
11 (5) |
14 (2) |
16 (4) |
18 (0) |
20 (2) |
21 (3) |
22 (4) |
24 (0) |
24 (0) |
25 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -30.9 | +10.4 | +60.5 | -51.2 | +13.4 | +84.1 | -9.5 | +71.3 | -13.2 | +75.9 | -1.1 |
| Relative (%) | -18.2 | +6.1 | +35.7 | -30.2 | +7.9 | +49.6 | -5.6 | +42.0 | -7.8 | +44.7 | -0.6 | |
| Steps (reduced) |
26 (2) |
27 (3) |
28 (4) |
28 (4) |
29 (5) |
30 (0) |
30 (0) |
31 (1) |
31 (1) |
32 (2) |
32 (2) | |