22ed5/4
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Prime factorization
2 × 11
Step size
17.5597¢
Octave
68\22ed5/4 (1194.06¢) (→34\11ed5/4)
Twelfth
108\22ed5/4 (1896.45¢) (→54\11ed5/4)
Consistency limit
3
Distinct consistency limit
2
 |
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| ← 21ed5/4 | 22ed5/4 | 23ed5/4 → |
22 equal divisions of 5/4 (abbreviated 22ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 22 equal parts of about 17.6 ¢ each. Each step represents a frequency ratio of (5/4)1/22, or the 22nd root of 5/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 17.56 | |
| 2 | 35.119 | |
| 3 | 52.679 | |
| 4 | 70.239 | 22/21 |
| 5 | 87.799 | 18/17, 20/19, 21/20, 23/22 |
| 6 | 105.358 | 19/18 |
| 7 | 122.918 | 14/13, 15/14 |
| 8 | 140.478 | 12/11 |
| 9 | 158.037 | 11/10, 23/21, 25/23 |
| 10 | 175.597 | 21/19 |
| 11 | 193.157 | 10/9, 19/17 |
| 12 | 210.717 | 9/8, 17/15 |
| 13 | 228.276 | |
| 14 | 245.836 | 15/13, 22/19, 23/20 |
| 15 | 263.396 | |
| 16 | 280.955 | 7/6, 20/17 |
| 17 | 298.515 | 13/11 |
| 18 | 316.075 | 25/21 |
| 19 | 333.635 | 17/14, 23/19 |
| 20 | 351.194 | 11/9 |
| 21 | 368.754 | 21/17 |
| 22 | 386.314 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.94 | -5.51 | +5.68 | +5.68 | +6.11 | +2.64 | -0.26 | +6.55 | -0.26 | -7.23 | +0.17 |
| Relative (%) | -33.8 | -31.4 | +32.4 | +32.4 | +34.8 | +15.0 | -1.5 | +37.3 | -1.5 | -41.1 | +1.0 | |
| Steps (reduced) |
68 (2) |
108 (20) |
137 (5) |
159 (5) |
177 (1) |
192 (16) |
205 (7) |
217 (19) |
227 (7) |
236 (16) |
245 (3) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.08 | -3.30 | +0.17 | -6.20 | -5.80 | +0.61 | -5.20 | -6.20 | -2.87 | +4.39 | -2.32 |
| Relative (%) | +11.8 | -18.8 | +1.0 | -35.3 | -33.0 | +3.5 | -29.6 | -35.3 | -16.3 | +25.0 | -13.2 | |
| Steps (reduced) |
253 (11) |
260 (18) |
267 (3) |
273 (9) |
279 (15) |
285 (21) |
290 (4) |
295 (9) |
300 (14) |
305 (19) |
309 (1) | |