13ed4
Jump to navigation
Jump to search
Prime factorization
13 (prime)
Step size
184.615¢
Octave
7\13ed4 (1292.31¢)
Twelfth
10\13ed4 (1846.15¢)
Consistency limit
1
Distinct consistency limit
1
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 11ed4 | 13ed4 | 15ed4 → |
13 equal divisions of the 4th harmonic (abbreviated 13ed4) is a nonoctave tuning system that divides the interval of 4/1 into 13 equal parts of about 185 ¢ each. Each step represents a frequency ratio of 41/13, or the 13th root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 184.6 | 19/17 |
| 2 | 369.2 | 11/9 |
| 3 | 553.8 | 15/11, 18/13, 19/14 |
| 4 | 738.5 | 23/15 |
| 5 | 923.1 | 17/10, 22/13 |
| 6 | 1107.7 | 19/10, 21/11 |
| 7 | 1292.3 | 23/11 |
| 8 | 1476.9 | 7/3 |
| 9 | 1661.5 | 13/5 |
| 10 | 1846.2 | |
| 11 | 2030.8 | |
| 12 | 2215.4 | 18/5 |
| 13 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +92.3 | -55.8 | +0.0 | -17.1 | +36.5 | -45.7 | +92.3 | +73.0 | +75.2 | -89.8 | -55.8 |
| Relative (%) | +50.0 | -30.2 | +0.0 | -9.3 | +19.8 | -24.8 | +50.0 | +39.5 | +40.7 | -48.6 | -30.2 | |
| Steps (reduced) |
7 (7) |
10 (10) |
13 (0) |
15 (2) |
17 (4) |
18 (5) |
20 (7) |
21 (8) |
22 (9) |
22 (9) |
23 (10) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.8 | +46.6 | -72.9 | +0.0 | +79.7 | -19.3 | +71.7 | -17.1 | +83.1 | +2.5 | -74.4 |
| Relative (%) | -5.3 | +25.2 | -39.5 | +0.0 | +43.1 | -10.5 | +38.8 | -9.3 | +45.0 | +1.4 | -40.3 | |
| Steps (reduced) |
24 (11) |
25 (12) |
25 (12) |
26 (0) |
27 (1) |
27 (1) |
28 (2) |
28 (2) |
29 (3) |
29 (3) |
29 (3) | |