4ed11/5
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Prime factorization
22
Step size
341.251¢
Octave
4\4ed11/5 (1365¢) (→1\1ed11/5)
Twelfth
6\4ed11/5 (2047.51¢) (→3\2ed11/5)
Consistency limit
3
Distinct consistency limit
1
Special properties
| ← 3ed11/5 | 4ed11/5 | 5ed11/5 → |
4 equal divisions of 11/5 (abbreviated 4ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 4 equal parts of about 341 ¢ each. Each step represents a frequency ratio of (11/5)1/4, or the 4th root of 11/5.
A close approximation of 4ed11/5 is available by using every seventh note of the Triple Bohlen-Pierce scale (39edt).
Intervals
| # | Cents | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 341.3 | 17/14, 39/32, 11/9 |
| 2 | 682.5 | 3/2, 40/27 |
| 3 | 1023.8 | 9/5, 29/16, 20/11 |
| 4 | 1365.0 | 11/5 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +165 | +146 | -11 | -56 | -31 | +44 | +154 | -50 | +109 | -56 | +134 |
| Relative (%) | +48.4 | +42.7 | -3.3 | -16.5 | -9.0 | +12.8 | +45.1 | -14.7 | +31.9 | -16.5 | +39.4 | |
| Steps (reduced) |
4 (0) |
6 (2) |
7 (3) |
8 (0) |
9 (1) |
10 (2) |
11 (3) |
11 (3) |
12 (0) |
12 (0) |
13 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4 | -133 | +89 | -22 | -127 | +115 | +21 | -68 | -152 | +109 | +32 |
| Relative (%) | -1.2 | -38.8 | +26.2 | -6.6 | -37.3 | +33.7 | +6.2 | -19.8 | -44.5 | +31.9 | +9.3 | |
| Steps (reduced) |
13 (1) |
13 (1) |
14 (2) |
14 (2) |
14 (2) |
15 (3) |
15 (3) |
15 (3) |
15 (3) |
16 (0) |
16 (0) | |