13ed5/4
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Prime factorization
13 (prime)
Step size
29.7164¢
Octave
40\13ed5/4 (1188.66¢)
Twelfth
64\13ed5/4 (1901.85¢)
(convergent)
Consistency limit
3
Distinct consistency limit
2
 |
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| ← 12ed5/4 | 13ed5/4 | 14ed5/4 → |
(convergent)
13 equal divisions of 5/4 (abbreviated 13ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 13 equal parts of about 29.7 ¢ each. Each step represents a frequency ratio of (5/4)1/13, or the 13th root of 5/4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 29.7 | |
| 2 | 59.4 | |
| 3 | 89.1 | 18/17, 21/20, 22/21, 23/22 |
| 4 | 118.9 | 14/13, 19/18 |
| 5 | 148.6 | 13/12, 21/19 |
| 6 | 178.3 | 10/9, 11/10, 23/21 |
| 7 | 208 | 8/7, 17/15, 19/17 |
| 8 | 237.7 | 22/19 |
| 9 | 267.4 | 7/6, 13/11, 15/13, 20/17, 23/20 |
| 10 | 297.2 | 6/5 |
| 11 | 326.9 | 23/19 |
| 12 | 356.6 | 11/9, 17/14, 21/17 |
| 13 | 386.3 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | -0.1 | +7.0 | +7.0 | -11.4 | -10.9 | -4.3 | -0.2 | -4.3 | +9.0 | +6.9 |
| Relative (%) | -38.2 | -0.3 | +23.7 | +23.7 | -38.5 | -36.6 | -14.5 | -0.7 | -14.5 | +30.2 | +23.3 | |
| Steps (reduced) |
40 (1) |
64 (12) |
81 (3) |
94 (3) |
104 (0) |
113 (9) |
121 (4) |
128 (11) |
134 (4) |
140 (10) |
145 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -12.8 | +7.5 | +6.9 | +14.1 | -1.7 | -11.5 | +13.7 | +14.1 | -11.0 | -2.4 | +9.8 |
| Relative (%) | -43.0 | +25.3 | +23.3 | +47.3 | -5.9 | -38.9 | +46.2 | +47.3 | -36.9 | -7.9 | +33.1 | |
| Steps (reduced) |
149 (6) |
154 (11) |
158 (2) |
162 (6) |
165 (9) |
168 (12) |
172 (3) |
175 (6) |
177 (8) |
180 (11) |
183 (1) | |