16ed5/4
Jump to navigation
Jump to search
Prime factorization
24
Step size
24.1446¢
Octave
50\16ed5/4 (1207.23¢) (→25\8ed5/4)
Twelfth
79\16ed5/4 (1907.42¢)
Consistency limit
3
Distinct consistency limit
3
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 15ed5/4 | 16ed5/4 | 17ed5/4 → |
16 equal divisions of 5/4 (abbreviated 16ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 16 equal parts of about 24.1 ¢ each. Each step represents a frequency ratio of (5/4)1/16, or the 16th root of 5/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 24.145 | |
| 2 | 48.289 | |
| 3 | 72.434 | 22/21, 23/22 |
| 4 | 96.578 | 20/19, 21/20 |
| 5 | 120.723 | 13/12 |
| 6 | 144.868 | 14/13, 23/21 |
| 7 | 169.012 | 10/9, 11/10, 12/11 |
| 8 | 193.157 | 9/8, 19/17, 21/19 |
| 9 | 217.301 | 17/15 |
| 10 | 241.446 | 8/7, 15/13, 23/20 |
| 11 | 265.591 | 7/6, 22/19 |
| 12 | 289.735 | 13/11, 20/17 |
| 13 | 313.88 | |
| 14 | 338.024 | 11/9, 23/19 |
| 15 | 362.169 | |
| 16 | 386.314 | 21/17 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.2 | +5.5 | -9.7 | -9.7 | -11.4 | +11.4 | -2.5 | +10.9 | -2.5 | +1.6 | -4.2 |
| Relative (%) | +29.9 | +22.7 | -40.1 | -40.1 | -47.4 | +47.3 | -10.2 | +45.3 | -10.2 | +6.4 | -17.5 | |
| Steps (reduced) |
50 (2) |
79 (15) |
99 (3) |
115 (3) |
128 (0) |
140 (12) |
149 (5) |
158 (14) |
165 (5) |
172 (12) |
178 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.1 | -5.5 | -4.2 | +4.8 | -3.6 | -6.0 | -3.0 | +4.8 | -7.3 | +8.8 | +4.3 |
| Relative (%) | +8.6 | -22.8 | -17.5 | +19.8 | -14.9 | -24.8 | -12.4 | +19.8 | -30.1 | +36.4 | +17.7 | |
| Steps (reduced) |
184 (8) |
189 (13) |
194 (2) |
199 (7) |
203 (11) |
207 (15) |
211 (3) |
215 (7) |
218 (10) |
222 (14) |
225 (1) | |