9ed5
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Prime factorization
32
Step size
309.59¢
Octave
4\9ed5 (1238.36¢)
(semiconvergent)
Twelfth
6\9ed5 (1857.54¢) (→2\3ed5)
Consistency limit
7
Distinct consistency limit
3
 |
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| ← 8ed5 | 9ed5 | 10ed5 → |
(semiconvergent)
9 equal divisions of the 5th harmonic (abbreviated 9ed5) is a nonoctave tuning system that divides the interval of 5/1 into 9 equal parts of about 310 ¢ each. Each step represents a frequency ratio of 51/9, or the 9th root of 5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 309.59 | 6/5, 11/9, 13/11, 17/14, 20/17 |
| 2 | 619.181 | 7/5, 10/7, 13/9, 17/12, 19/13 |
| 3 | 928.771 | 12/7, 17/10, 19/11, 22/13 |
| 4 | 1238.362 | 2/1 |
| 5 | 1547.952 | 5/2, 12/5, 17/7, 22/9 |
| 6 | 1857.542 | |
| 7 | 2167.133 | 7/2 |
| 8 | 2476.723 | 17/4, 21/5 |
| 9 | 2786.314 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +38 | -44 | +77 | +0 | -6 | +37 | +115 | -89 | +38 | -127 | +32 |
| Relative (%) | +12.4 | -14.3 | +24.8 | +0.0 | -2.0 | +11.8 | +37.2 | -28.7 | +12.4 | -40.9 | +10.4 | |
| Steps (reduced) |
4 (4) |
6 (6) |
8 (8) |
9 (0) |
10 (1) |
11 (2) |
12 (3) |
12 (3) |
13 (4) |
13 (4) |
14 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -106 | +75 | -44 | +153 | +48 | -50 | -144 | +77 | -8 | -88 | +144 |
| Relative (%) | -34.3 | +24.2 | -14.3 | +49.6 | +15.7 | -16.3 | -46.5 | +24.8 | -2.5 | -28.5 | +46.6 | |
| Steps (reduced) |
14 (5) |
15 (6) |
15 (6) |
16 (7) |
16 (7) |
16 (7) |
16 (7) |
17 (8) |
17 (8) |
17 (8) |
18 (0) | |