Perfect fifth
In classical music from Western culture, a fifth is the interval from the first to the last of the first five consecutive notes in a diatonic scale.
[4] When an instrument with only twelve notes to an octave (such as the piano) is tuned using Pythagorean tuning, one of the twelve fifths (the wolf fifth) sounds severely discordant and can hardly be qualified as "perfect", if this term is interpreted as "highly consonant".
In terms of semitones, these are equivalent to the tritone (or augmented fourth), and the minor sixth, respectively.
The justly tuned pitch ratio of a perfect fifth is 3:2 (also known, in early music theory, as a hemiola),[11][12] meaning that the upper note makes three vibrations in the same amount of time that the lower note makes two.
[15] Hermann von Helmholtz argues that some intervals, namely the perfect fourth, fifth, and octave, "are found in all the musical scales known", though the editor of the English translation of his book notes the fourth and fifth may be interchangeable or indeterminate.
[16] The perfect fifth is a basic element in the construction of major and minor triads, and their extensions.
The presence of a perfect fifth can in fact soften the dissonant intervals of these chords, as in the major seventh chord in which the dissonance of a major seventh is softened by the presence of two perfect fifths.
The closing chords of Pérotin's Viderunt omnes and Sederunt Principes, Guillaume de Machaut's Messe de Nostre Dame, the Kyrie in Mozart's Requiem, and the first movement of Bruckner's Ninth Symphony are all examples of pieces ending on an open fifth.
In hard rock, metal, and punk music, overdriven or distorted electric guitar can make thirds sound muddy while the bare fifths remain crisp.
In addition, fast chord-based passages are made easier to play by combining the four most common guitar hand shapes into one.
The just perfect fifth, together with the octave, forms the basis of Pythagorean tuning.
