10ed11/5
Jump to navigation
Jump to search
Prime factorization
2 × 5
Step size
136.5¢
Octave
9\10ed11/5 (1228.5¢)
Twelfth
14\10ed11/5 (1911.01¢) (→7\5ed11/5)
Consistency limit
4
Distinct consistency limit
2
 |
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |
| ← 9ed11/5 | 10ed11/5 | 11ed11/5 → |
10 equal divisions of 11/5 (abbreviated 10ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 10 equal parts of about 137 ¢ each. Each step represents a frequency ratio of (11/5)1/10, or the 10th root of 11/5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 136.5 | 11/10, 13/12, 14/13 |
| 2 | 273.001 | 7/6, 20/17, 22/19 |
| 3 | 409.501 | 9/7, 19/15 |
| 4 | 546.002 | 15/11, 18/13 |
| 5 | 682.502 | 3/2, 22/15 |
| 6 | 819.003 | 13/8, 21/13 |
| 7 | 955.503 | 7/4, 12/7, 19/11 |
| 8 | 1092.003 | 13/7, 17/9, 19/10 |
| 9 | 1228.504 | 2/1 |
| 10 | 1365.004 | 11/5, 13/6, 20/9 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +28.5 | +9.1 | +57.0 | -56.3 | +37.6 | +43.7 | -51.0 | +18.1 | -27.8 | -56.3 | +66.1 |
| Relative (%) | +20.9 | +6.6 | +41.8 | -41.2 | +27.5 | +32.0 | -37.4 | +13.3 | -20.4 | -41.2 | +48.4 | |
| Steps (reduced) |
9 (9) |
14 (4) |
18 (8) |
20 (0) |
23 (3) |
25 (5) |
26 (6) |
28 (8) |
29 (9) |
30 (0) |
32 (2) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +64.0 | -64.3 | -47.3 | -22.5 | +9.1 | +46.6 | -47.0 | +0.7 | +52.7 | -27.8 | +31.7 |
| Relative (%) | +46.9 | -47.1 | -34.6 | -16.5 | +6.6 | +34.1 | -34.4 | +0.5 | +38.6 | -20.4 | +23.3 | |
| Steps (reduced) |
33 (3) |
33 (3) |
34 (4) |
35 (5) |
36 (6) |
37 (7) |
37 (7) |
38 (8) |
39 (9) |
39 (9) |
40 (0) | |