Perfect consonance
A perfect consonance is one of the most consonant intervals; they are usually extremely easy to sing and recognize by ear. The set of perfect consonances is equivalent in most systems of theory to the 3-odd-limit, which is the set of intervals wherein the highest allowable odd in the numerator and denominator is 3. It is the smallest odd-limit containing intervals of the 3-limit.
Table of 3-odd-limit intervals
Reduced to an octave, the intervals of the 3-odd-limit are:
| Interval | Cents | Name |
|---|---|---|
| 1/1 | 0.0 | Unison |
| 4/3 | 498.0 | Perfect 4th |
| 3/2 | 702.0 | Perfect 5th |
| 2/1 | 1200.0 | Octave |
Approximation by edos
All edos are consistent to the 3-odd-limit, because the requirement is simply to map 3/1 somewhere between 1800c and 2400c, which is a property of all edos. The first edo that is distinctly consistent to the 3-odd-limit is 3edo. However, the first edos that tune all its intervals reasonably accurately are 5edo and 7edo, outlining the basic structures of equipentatonic and equiheptatonic scales.
Intervals of the 3-odd-limit
More info at 5-odd-limit#Perfect consonances.
