Wiktionary
n. A musical interval of the Western twelve-semitone system consisting of five semitones and spanning four degrees of the diatonic scale. It is enharmonically equivalent to an augmented third.
Wikipedia
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions (see Interval number for more details), and the perfect fourth is a fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there are four staff positions from C to F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones (four and six).
The perfect fourth may be derived from the harmonic series as the interval between the third and fourth harmonics. The term perfect identifies this interval as belonging to the group of perfect intervals, so called because they are neither major nor minor (unlike thirds, which are either minor or major) but perfect.
Up until the late 19th century, the perfect fourth was often called by its Greek name, diatessaron. Its most common occurrence is between the fifth and upper root of all major and minor triads and their extensions.
A perfect fourth in just intonation corresponds to a pitch ratio of 4:3, or about 498 cents , while in equal temperament a perfect fourth is equal to five semitones, or 500 cents.
A helpful way to recognize a perfect fourth is to hum the starting of the "Bridal Chorus" from Wagner's Lohengrin ("Treulich geführt", the colloquially-titled " Here Comes the Bride"). Other examples are the first two notes of the Christmas carol " Hark! The Herald Angels Sing" or " El Cóndor Pasa", and, for a descending perfect fourth, the second and third notes of " O Come All Ye Faithful".
The perfect fourth is a perfect interval like the unison, octave, and perfect fifth, and it is a sensory consonance. In common practice harmony, however, it is considered a stylistic dissonance in certain contexts, namely in two-voice textures and whenever it appears above the bass. If the bass note also happens to be the chord's root, the interval's upper note almost always temporarily displaces the third of any chord, and, in the terminology used in popular music, is then called a suspended fourth.
Conventionally, adjacent strings of the double bass and of the bass guitar are a perfect fourth apart when unstopped, as are all pairs but one of adjacent guitar strings under standard guitar tuning. Sets of tom-tom drums are also commonly tuned in perfect fourths. The 4:3 just perfect fourth arises in the C major scale between G and C.
Usage examples of "perfect fourth".
She was like the perfect fourth-grade teacher, a woman whose natural authority did not inhibit a sense of humor that, in its sly appearances, hinted at the existence of a private life more raucous and freewheeling than could be revealed in the public one.