30ed5
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Prime factorization
2 × 3 × 5
Step size
92.8771¢
Octave
13\30ed5 (1207.4¢)
(semiconvergent)
Twelfth
20\30ed5 (1857.54¢) (→2\3ed5)
Consistency limit
2
Distinct consistency limit
2
| ← 29ed5 | 30ed5 | 31ed5 → |
(semiconvergent)
30 equal divisions of the 5th harmonic (abbreviated 30ed5) is a nonoctave tuning system that divides the interval of 5/1 into 30 equal parts of about 92.9 ¢ each. Each step represents a frequency ratio of 51/30, or the 30th root of 5.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 92.9 | 20/19 |
| 2 | 185.8 | 19/17 |
| 3 | 278.6 | 20/17 |
| 4 | 371.5 | |
| 5 | 464.4 | 17/13 |
| 6 | 557.3 | 11/8 |
| 7 | 650.1 | 16/11, 19/13 |
| 8 | 743 | 20/13, 23/15, 26/17 |
| 9 | 835.9 | 13/8 |
| 10 | 928.8 | 12/7 |
| 11 | 1021.6 | |
| 12 | 1114.5 | 19/10 |
| 13 | 1207.4 | 2/1 |
| 14 | 1300.3 | 17/8 |
| 15 | 1393.2 | |
| 16 | 1486 | 26/11 |
| 17 | 1578.9 | 5/2 |
| 18 | 1671.8 | |
| 19 | 1764.7 | |
| 20 | 1857.5 | |
| 21 | 1950.4 | |
| 22 | 2043.3 | 13/4 |
| 23 | 2136.2 | 24/7 |
| 24 | 2229.1 | |
| 25 | 2321.9 | 23/6 |
| 26 | 2414.8 | |
| 27 | 2507.7 | 17/4 |
| 28 | 2600.6 | |
| 29 | 2693.4 | 19/4 |
| 30 | 2786.3 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.4 | -44.4 | +14.8 | +0.0 | -37.0 | -25.2 | +22.2 | +4.1 | +7.4 | +28.2 | -29.6 |
| Relative (%) | +8.0 | -47.8 | +15.9 | +0.0 | -39.8 | -27.2 | +23.9 | +4.4 | +8.0 | +30.3 | -31.9 | |
| Steps (reduced) |
13 (13) |
20 (20) |
26 (26) |
30 (0) |
33 (3) |
36 (6) |
39 (9) |
41 (11) |
43 (13) |
45 (15) |
46 (16) | |
|
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