4ed6
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Prime factorization
22
Step size
775.489¢
Octave
2\4ed6 (1550.98¢) (→1\2ed6)
Twelfth
2\4ed6 (1550.98¢) (→1\2ed6)
Consistency limit
2
Distinct consistency limit
1
Special properties
| ← 3ed6 | 4ed6 | 5ed6 → |
4 equal divisions of the 6th harmonic (abbreviated 4ed6) is a nonoctave tuning system that divides the interval of 6/1 into 4 equal parts of about 775 ¢ each. Each step represents a frequency ratio of 61/4, or the 4th root of 6.
Harmonics
4ed6, notably, approximates the 23rd harmonic with incredible accuracy, less than 0.15 cents off.
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +351.0 | -351.0 | -73.5 | +315.6 | +0.0 | -266.9 | +277.4 | +73.5 | -108.9 | -273.9 | +351.0 | +212.4 | +84.1 | -35.3 | -147.1 |
| Relative (%) | +45.3 | -45.3 | -9.5 | +40.7 | +0.0 | -34.4 | +35.8 | +9.5 | -14.0 | -35.3 | +45.3 | +27.4 | +10.8 | -4.6 | -19.0 | |
| Steps (reduced) |
2 (2) |
2 (2) |
3 (3) |
4 (0) |
4 (0) |
4 (0) |
5 (1) |
5 (1) |
5 (1) |
5 (1) |
6 (2) |
6 (2) |
6 (2) |
6 (2) |
6 (2) | |
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +351.0 | -351.0 | +315.6 | -266.9 | -273.9 | +212.4 | -252.0 | +330.9 | +0.1 | +374.3 | +258.9 |
| Relative (%) | +45.3 | -45.3 | +40.7 | -34.4 | -35.3 | +27.4 | -32.5 | +42.7 | +0.0 | +48.3 | +33.4 | |
| Steps (reduced) |
2 (2) |
2 (2) |
4 (0) |
4 (0) |
5 (1) |
6 (2) |
6 (2) |
7 (3) |
7 (3) |
8 (0) |
8 (0) | |
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