5ed4
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Prime factorization
5 (prime)
Step size
480¢
Octave
3\5ed4 (1440¢)
Twelfth
4\5ed4 (1920¢)
(convergent)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 3ed4 | 5ed4 | 7ed4 → |
(convergent)
5 equal divisions of the 4th harmonic (abbreviated 5ed4) is a nonoctave tuning system that divides the interval of 4/1 into 5 equal parts of exactly 480 ¢ each. Each step represents a frequency ratio of 41/5, or the 5th root of 4.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 480 | 9/7, 14/11, 15/11, 17/13, 19/14, 19/15 |
| 2 | 960 | 9/5, 19/11 |
| 3 | 1440 | 7/3 |
| 4 | 1920 | 3/1 |
| 5 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +240 | +18 | +0 | +94 | -222 | -9 | +240 | +36 | -146 | +169 | +18 |
| Relative (%) | +50.0 | +3.8 | +0.0 | +19.5 | -46.2 | -1.8 | +50.0 | +7.5 | -30.5 | +35.1 | +3.8 | |
| Steps (reduced) |
3 (3) |
4 (4) |
5 (0) |
6 (1) |
6 (1) |
7 (2) |
8 (3) |
8 (3) |
8 (3) |
9 (4) |
9 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -121 | +231 | +112 | +0 | -105 | -204 | +182 | +94 | +9 | -71 | -148 |
| Relative (%) | -25.1 | +48.2 | +23.3 | +0.0 | -21.9 | -42.5 | +38.0 | +19.5 | +1.9 | -14.9 | -30.9 | |
| Steps (reduced) |
9 (4) |
10 (0) |
10 (0) |
10 (0) |
10 (0) |
10 (0) |
11 (1) |
11 (1) |
11 (1) |
11 (1) |
11 (1) | |