9ed5/4
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Prime factorization
32
Step size
42.9237¢
Octave
28\9ed5/4 (1201.86¢)
(convergent)
Twelfth
44\9ed5/4 (1888.64¢)
(semiconvergent)
Consistency limit
6
Distinct consistency limit
2
 |
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| ← 8ed5/4 | 9ed5/4 | 10ed5/4 → |
(convergent)
(semiconvergent)
9 equal divisions of 5/4 (abbreviated 9ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 9 equal parts of about 42.9 ¢ each. Each step represents a frequency ratio of (5/4)1/9, or the 9th root of 5/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 42.9 | |
| 2 | 85.8 | 17/16, 18/17, 20/19 |
| 3 | 128.8 | 12/11, 13/12, 14/13, 15/14, 16/15, 19/18 |
| 4 | 171.7 | 9/8, 11/10 |
| 5 | 214.6 | 10/9, 17/15, 19/17 |
| 6 | 257.5 | 7/6, 8/7, 13/11, 15/13, 22/19 |
| 7 | 300.5 | 6/5, 19/16, 20/17 |
| 8 | 343.4 | 17/14, 21/17 |
| 9 | 386.3 | 5/4, 11/9, 14/11, 16/13 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.9 | -13.3 | +3.7 | +3.7 | -11.4 | -20.8 | +5.6 | +16.3 | +5.6 | +12.3 | -9.6 |
| Relative (%) | +4.3 | -31.0 | +8.7 | +8.7 | -26.7 | -48.4 | +13.0 | +38.0 | +13.0 | +28.6 | -22.3 | |
| Steps (reduced) |
28 (1) |
44 (8) |
56 (2) |
65 (2) |
72 (0) |
78 (6) |
84 (3) |
89 (8) |
93 (3) |
97 (7) |
100 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -19.4 | -18.9 | -9.6 | +7.5 | -11.6 | +18.2 | +10.4 | +7.5 | +8.8 | +14.2 | -19.9 |
| Relative (%) | -45.2 | -44.1 | -22.3 | +17.4 | -27.1 | +42.3 | +24.3 | +17.4 | +20.6 | +33.0 | -46.3 | |
| Steps (reduced) |
103 (4) |
106 (7) |
109 (1) |
112 (4) |
114 (6) |
117 (0) |
119 (2) |
121 (4) |
123 (6) |
125 (8) |
126 (0) | |