An interval is the distance in pitch between two notes, described by a numeric value that indicates how many letter names are spanned, and a quality that specifies the exact number of half steps. The perfect intervals are the unison, perfect fourth, perfect fifth, and perfect octave. These are called perfect because of their strong consonance and because they have no major or minor variants; they are classified only as perfect, augmented, or diminished.
Major and minor intervals differ by a single half step. A minor interval is one half step smaller than its corresponding major interval; for instance, a major third spans four half steps (as in C to E), while a minor third spans three half steps (as in C to E♭). Augmented intervals are one half step larger than a perfect or major interval, so a perfect fifth of seven half steps becomes an augmented fifth of eight half steps. Diminished intervals are one half step smaller than a perfect or minor interval; reducing a perfect fifth yields a diminished fifth of six half steps, which is also known as a tritone.
The tritone, an interval of three whole steps or six half steps, holds particular significance in tonal music. It divides the octave exactly in half and produces maximum dissonance. Tritones appear prominently in dominant seventh chords, where they create the harmonic tension that resolves to the tonic. Tritones have two common spellings: an augmented fourth and a diminished fifth. These two spellings are enharmonic intervals, meaning they sound identical but are notated and analyzed differently because they belong to different keys. For example, an augmented fourth from C to F♯ and a diminished fifth from C to G♭ both span six half steps but carry distinct theoretical functions.
Intervals can also be inverted by moving the lower note up an octave or the upper note down. The numeric sizes add up to nine, so a third inverts to a sixth and a fourth inverts to a fifth, while the qualities invert as well: major becomes minor, augmented becomes diminished, and perfect intervals remain perfect. When an interval exceeds an octave, it is called a compound interval: a ninth is a compound second, a tenth is a compound third, and so on, sharing the same quality as its simple counterpart. A major sixth, for instance, spans nine half steps and is the inversion of a minor third.