6ed5/3
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Prime factorization
2 × 3
Step size
147.393¢
Octave
8\6ed5/3 (1179.14¢) (→4\3ed5/3)
Twelfth
13\6ed5/3 (1916.11¢)
(convergent)
Consistency limit
7
Distinct consistency limit
2
Special properties
 |
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| ← 5ed5/3 | 6ed5/3 | 7ed5/3 → |
(convergent)
6 equal divisions of 5/3 (abbreviated 6ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 6 equal parts of about 147 ¢ each. Each step represents a frequency ratio of (5/3)1/6, or the 6th root of 5/3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 147.393 | 10/9, 11/10, 12/11, 13/12, 14/13, 15/14, 17/16, 18/17, 19/18, 21/19 |
| 2 | 294.786 | 6/5, 7/6, 11/9, 13/11, 15/13, 17/14, 20/17 |
| 3 | 442.179 | 4/3, 5/4, 9/7, 13/10, 14/11, 17/13, 19/15 |
| 4 | 589.572 | 7/5, 10/7, 11/8, 13/9, 15/11, 16/11, 17/12, 18/13 |
| 5 | 736.966 | 3/2, 11/7, 14/9, 17/11, 20/13 |
| 6 | 884.359 | 5/3, 12/7, 13/8, 17/10, 18/11, 21/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -20.9 | +14.2 | -41.7 | +14.2 | -6.7 | +21.2 | -62.6 | +28.3 | -6.7 | -24.3 | -27.6 |
| Relative (%) | -14.1 | +9.6 | -28.3 | +9.6 | -4.5 | +14.4 | -42.4 | +19.2 | -4.5 | -16.5 | -18.7 | |
| Steps (reduced) |
8 (2) |
13 (1) |
16 (4) |
19 (1) |
21 (3) |
23 (5) |
24 (0) |
26 (2) |
27 (3) |
28 (4) |
29 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -18.7 | +0.4 | +28.3 | +64.0 | -41.0 | +7.5 | +61.2 | -27.6 | +35.4 | -45.2 | +25.3 |
| Relative (%) | -12.7 | +0.2 | +19.2 | +43.4 | -27.8 | +5.1 | +41.6 | -18.7 | +24.0 | -30.6 | +17.1 | |
| Steps (reduced) |
30 (0) |
31 (1) |
32 (2) |
33 (3) |
33 (3) |
34 (4) |
35 (5) |
35 (5) |
36 (0) |
36 (0) |
37 (1) | |