1edf
1 equal division of the perfect fifth (abbreviated 1edf or 1ed3/2) is a nonoctave tuning system that uses equal steps of 3/2 (one perfect fifth), or about 702 ¢.
Theory
One note repeated in just perfect fifths is an example of a trivial temperament. 1edf can be viewed as the circle of fifths or Pythagorean tuning without octave reduction.
The adjacent open strings of a violin, viola or cello are traditionally tuned in perfect fifths. These instruments are hence tuned in 1edf.
In terms of harmonic approximations, the 5th harmonic is roughly represented at 4 steps (just 81/16), being sharp by exactly 81/80 = 21.5 ¢, the syntonic comma.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +204 | +204 | -294 | +22 | -294 | +141 | -90 | -294 | +225 | +60 | -90 |
| Relative (%) | +29.0 | +29.0 | -41.9 | +3.1 | -41.9 | +20.1 | -12.9 | -41.9 | +32.1 | +8.6 | -12.9 | |
| Step | 2 | 3 | 3 | 4 | 4 | 5 | 5 | 5 | 6 | 6 | 6 | |
Music
In whole
In part
- Violin Concertino, violin part