Fifth
Interval of seven semitones.
What it means
The fifth spans five scale degrees; in its perfect form that is seven semitones, with the frequency ratio 3:2. After the octave it is the most stable interval and correspondingly appears low down in the harmonic series. Alongside it there is the diminished fifth with six semitones, corresponding to the tritone, and the augmented one with eight, which occurs in the augmented triad.
Musical use
The fifth is load-bearing in several respects. Together with the third it forms the triad and gives it its firmness; as the interval between tonic and dominant it determines the most important harmonic relation of all; and the stacking of fifths yields the circle of fifths, by which the keys are ordered and the accidentals counted.
In part-writing theory it counts as a perfect consonance, which is why parallel fifths are forbidden: two voices led in parallel fifths merge into one. Historically this was not always so — early organum rests precisely on parallel fifths, and in the power chord of popular music, the fifth without the third is the load-bearing element. There it tolerates heavy distortion and fits over major as well as minor, because it lacks the mode.
Acoustically the fifth is the starting point of the comma problem: twelve perfect fifths stacked do not yield the same note as seven octaves, and every tuning system is a way of handling this difference.
The fifth arises between the second and third partials of the harmonic series and counts, after the octave, as the most consonant interval. The circle of fifths orders the keys at fifth intervals. In strict writing, parallel fifths between independent voices are forbidden. The fifth is at the same time the tuning interval of the string instruments violin, viola, and cello.
Performance practice
Tune by fifths and listen for the disappearance of the beats; alongside the octaves they are the most reliable test. Note that the fifth in equal temperament is minimally narrow — in free ensemble playing it may be taken pure. And sing fifths in both directions, they belong among the most reliable reference intervals for the ear.