Inversion (music)

In music theory, an inversion is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of contrapuntal lines of music. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.

An interval is inverted by raising or lowering either of the notes by one or more octaves so that the higher note becomes the lower note and vice versa. For example, the inversion of an interval consisting of a C with an E above it (the third measure below) 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.

The tables to the right show the changes in interval quality and interval number under inversion. Thus, perfect intervals remain perfect, major intervals become minor and vice versa, and augmented intervals become diminished and vice versa. (Doubly diminished intervals become doubly augmented intervals, and vice versa.).

Traditional interval numbers add up to nine: seconds become sevenths and vice versa, thirds become sixths and vice versa, and so on. 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. See also complement (music).

A chord's inversion describes the relationship of its lowest notes to the other notes in the chord. For instance, a C major triad contains the tones C, E and G; its inversion is determined by which of these tones is the lowest note (or bass note) in the chord.

The term inversion often categorically refers to the different possibilities, though it may also be restricted to only those chords where the lowest note is not also the root of the chord. Texts that follow this restriction may use the term position instead, to refer to all of the possibilities as a category.

A chord is in root position if its root is the lowest note. This is sometimes known as the parent chord of its inversions. For example, the root of a C-major triad is C, so a C-major triad will be in root position if C is the lowest note and its third and fifth (E and G, respectively) are above it – or, on occasion, do not sound at all.

The following C-major triads are both in root position, since the lowest note is the root. The rearrangement of the notes above the bass into different octaves (here, the note E) and the doubling of notes (here, G), is known as voicing – the first voicing is close voicing, while the second is open.