11ed7/4
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Prime factorization
11 (prime)
Step size
88.0751¢
Octave
14\11ed7/4 (1233.05¢)
Twelfth
22\11ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit
3
Distinct consistency limit
2
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| ← 10ed7/4 | 11ed7/4 | 12ed7/4 → |
11 equal divisions of 7/4 (abbreviated 11ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 11 equal parts of about 88.1 ¢ each. Each step represents a frequency ratio of (7/4)1/11, or the 11th root of 7/4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 88.075 | 22/21 |
| 2 | 176.15 | 9/8, 10/9, 19/17, 21/19 |
| 3 | 264.225 | 13/11, 22/19 |
| 4 | 352.3 | 17/14, 21/17 |
| 5 | 440.375 | 14/11, 22/17 |
| 6 | 528.45 | 4/3, 19/14 |
| 7 | 616.526 | |
| 8 | 704.601 | 3/2 |
| 9 | 792.676 | 11/7 |
| 10 | 880.751 | 5/3 |
| 11 | 968.826 | 19/11 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +33.1 | +35.7 | -22.0 | +32.1 | -19.3 | -22.0 | +11.1 | -16.7 | -22.9 | -11.8 | +13.7 |
| Relative (%) | +37.5 | +40.5 | -24.9 | +36.4 | -21.9 | -24.9 | +12.6 | -18.9 | -26.0 | -13.4 | +15.6 | |
| Steps (reduced) |
14 (3) |
22 (0) |
27 (5) |
32 (10) |
35 (2) |
38 (5) |
41 (8) |
43 (10) |
45 (1) |
47 (3) |
49 (5) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -36.8 | +11.1 | -20.3 | -43.9 | +27.2 | +16.4 | +10.8 | +10.1 | +13.7 | +21.3 | +32.4 |
| Relative (%) | -41.8 | +12.6 | -23.0 | -49.9 | +30.9 | +18.6 | +12.3 | +11.5 | +15.6 | +24.1 | +36.8 | |
| Steps (reduced) |
50 (6) |
52 (8) |
53 (9) |
54 (10) |
56 (1) |
57 (2) |
58 (3) |
59 (4) |
60 (5) |
61 (6) |
62 (7) | |