Perfect fifth
Seven semitones, ratio 3:2. The most stable interval after the octave.
What it means
The perfect fifth spans seven semitones, its frequency ratio is 3:2. After the octave it is the simplest and most stable interval; in the harmonic series it appears immediately after the first octave. Its sound is firm and open but without a mode, because the third is absent.
Musical use
Its significance reaches far beyond the single interval. From the root, third, and fifth the triad arises, whose firmness rests on it. Between tonic and dominant there is a fifth's distance — the most important harmonic relation of major-minor tonality. And the stacking of perfect fifths yields the circle of fifths, by which the keys are ordered and the accidentals increase.
At the same time the fifth is the starting point of the tuning problem: twelve perfect fifths stacked do not meet the same note as seven octaves; the difference is called the Pythagorean comma, and every tuning system distributes it differently. In equal temperament, every fifth is therefore minimally narrower than pure.
In part-writing theory it counts as a perfect consonance, from which the prohibition of parallel fifths follows. Outside this tradition, by contrast, it is a load-bearing tonal device: as a drone in many folk-music traditions, as the fifth-sonority of early polyphony, as the power chord of popular music, where the absence of the third is precisely the advantage.
The perfect fifth is the basic building block of the circle of fifths and of Pythagorean tuning, which derives all notes from perfect fifths. When tuning string instruments, the strings are tuned in perfect fifths, recognizable by the absence of beats. In equal temperament the fifth is barely two cents smaller than pure, which is hardly audible.
Performance practice
Tune by fifths and listen for the sound becoming calm; together with the octaves they are the most reliable test. Take them without vibrato when checking. In an ensemble without a keyboard instrument, fifths may be taken pure, even if that departs from the piano. And give open fifth sonorities room — they work through openness, not through force.