9ed4
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Prime factorization
32
Step size
266.667¢
Octave
5\9ed4 (1333.33¢)
Twelfth
7\9ed4 (1866.67¢)
(semiconvergent)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 7ed4 | 9ed4 | 11ed4 → |
(semiconvergent)
9 equal divisions of the 4th harmonic (abbreviated 9ed4) is a nonoctave tuning system that divides the interval of 4/1 into 9 equal parts of about 267 ¢ each. Each step represents a frequency ratio of 41/9, or the 9th root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 266.667 | 7/6, 13/11 |
| 2 | 533.333 | 18/13 |
| 3 | 800 | 11/7, 21/13 |
| 4 | 1066.667 | 11/6, 13/7, 17/9, 20/11 |
| 5 | 1333.333 | 13/6 |
| 6 | 1600 | 18/7 |
| 7 | 1866.667 | 3/1 |
| 8 | 2133.333 | 7/2, 17/5 |
| 9 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +133 | -35 | +0 | -120 | +98 | +98 | +133 | -71 | +14 | +115 | -35 |
| Relative (%) | +50.0 | -13.2 | +0.0 | -44.9 | +36.8 | +36.7 | +50.0 | -26.5 | +5.1 | +43.3 | -13.2 | |
| Steps (reduced) |
5 (5) |
7 (7) |
9 (0) |
10 (1) |
12 (3) |
13 (4) |
14 (5) |
14 (5) |
15 (6) |
16 (7) |
16 (7) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +93 | -35 | +112 | +0 | -105 | +63 | -31 | -120 | +63 | -18 | -95 |
| Relative (%) | +34.8 | -13.3 | +41.9 | +0.0 | -39.4 | +23.5 | -11.6 | -44.9 | +23.5 | -6.7 | -35.6 | |
| Steps (reduced) |
17 (8) |
17 (8) |
18 (0) |
18 (0) |
18 (0) |
19 (1) |
19 (1) |
19 (1) |
20 (2) |
20 (2) |
20 (2) | |