2ed5
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Prime factorization
2 (prime)
Step size
1393.16¢
Octave
1\2ed5 (1393.16¢)
(convergent)
Twelfth
1\2ed5 (1393.16¢)
(semiconvergent)
Consistency limit
2
Distinct consistency limit
1
Special properties
| ← 1ed5 | 2ed5 | 3ed5 → |
(convergent)
(semiconvergent)
2 equal divisions of the 5th harmonic (abbreviated 2ed5) is a nonoctave tuning system that divides the interval of 5/1 into 2 equal parts of about 1390 ¢ each. Each step represents a frequency ratio of 51/2, or the 2nd root of 5.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 1393.157 | 9/4 |
| 2 | 2786.314 | 5/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +193 | -509 | +386 | +0 | -316 | -583 | +579 | +376 | +193 | +28 | -122 |
| Relative (%) | +13.9 | -36.5 | +27.7 | +0.0 | -22.7 | -41.8 | +41.6 | +27.0 | +13.9 | +2.0 | -8.8 | |
| Steps (reduced) |
1 (1) |
1 (1) |
2 (0) |
2 (0) |
2 (0) |
2 (0) |
3 (1) |
3 (1) |
3 (1) |
3 (1) |
3 (1) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -261 | -389 | -509 | -621 | +668 | +569 | +475 | +386 | +302 | +221 | +144 |
| Relative (%) | -18.7 | -27.9 | -36.5 | -44.5 | +47.9 | +40.8 | +34.1 | +27.7 | +21.7 | +15.9 | +10.4 | |
| Steps (reduced) |
3 (1) |
3 (1) |
3 (1) |
3 (1) |
4 (0) |
4 (0) |
4 (0) |
4 (0) |
4 (0) |
4 (0) |
4 (0) | |