In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and (in counterpoint) inverted voices. The concept of inversion also plays a role in musical set theory.
Focusing on intervals, an interval is inverted by raising or lowering either of the notes using displacement of the octave (or octaves) so that both retain their names (pitch class). For example, the inversion of an interval consisting of a C with an E above it is an E with a C above it – to work this out, the C may be moved up, the E may be lowered, or both may be moved.
Under inversion, perfect intervals remain perfect, major intervals become minor and vice versa, augmented intervals become diminished and vice versa. (Double diminished intervals become double augmented intervals, and vice versa.) Traditional interval names add together to make nine: seconds become sevenths and vice versa, thirds become sixes and vice versa, and fourths become fifths and vice versa. Thus a perfect fourth becomes a perfect fifth, an augmented fourth becomes a diminished fifth, and a simple interval (that is, one that is narrower than an octave) and its inversion, when added together, equal an octave.