The perfect fifth: three vibrations against two, from Twinkle Twinkle to punk
Sing the opening of Twinkle, Twinkle, Little Star and the jump from the first twinkle to the second is a perfect fifth. The upper note vibrates three times for every two of the lower, a ratio so stable that only the unison and the octave sound smoother. That simple relationship underpins tuning systems, chords and rock power chords.
On the staff, a fifth spans five positions, and on a piano it covers seven semitones, such as C up to G. It appears naturally in the harmonic series as the gap between the second and third harmonics, and in a major scale the dominant note sits a fifth above the tonic. The Greeks called it diapente, a name still used until the late nineteenth century. Turn it upside down and it becomes a perfect fourth.
The ideal ratio of 3:2 is what violinists listen for when tuning neighbouring strings. Pianos cannot keep it pure in every key, so equal temperament shaves the interval to exactly 700 cents, about two cents narrower than the just version of roughly 702. Tuning a twelve-note keyboard with pure fifths instead, as in Pythagorean tuning, leaves one badly sour interval nicknamed the wolf fifth, though strictly speaking that clash is a diminished sixth. Kepler catalogued even rougher fifths, and Helmholtz used a sharp 301:200 version to discuss the beating that mistuning produces.
Every major and minor triad contains a perfect fifth above its root, and it can soften harsher intervals, as in the major seventh chord. Since many instruments already sound a fifth among their overtones, arrangers often leave it out of chords. Stacking fifths produces quintal harmony, heard in Hindemith and in a five-note chord from brass in The Rite of Spring.
A chord of just root and fifth, with no third, is called open or bare. It closes Machaut's Messe de Nostre Dame and the Kyrie of Mozart's Requiem, runs through Sacred Harp singing and Andean sikuri music, and leaves a cadence ambiguous between major and minor. In distorted rock guitar, thirds turn muddy while fifths stay crisp, which is why hard rock, metal and punk lean so heavily on the two-note power chord.
Source: Perfect fifth
