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.[2] 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.
For other uses, see Inversion (disambiguation).Inversional equivalency and symmetry[edit]
Set theory[edit]
In set theory, inversional equivalency is the concept that intervals, chords, and other sets of pitches are the same when inverted. It is similar to enharmonic equivalency, octave equivalency and even transpositional equivalency. Inversional equivalency is used little in tonal theory, though it is assumed that sets that can be inverted into each other are remotely in common. However, they are only assumed identical or nearly identical in musical set theory.
Sets are said to be inversionally symmetrical if they map onto themselves under inversion. The pitch that the sets must be inverted around is said to be the axis of symmetry (or center). An axis may either be at a specific pitch or halfway between two pitches (assuming that microtones are not used). For example, the set C–E♭–E–F♯–G–B♭ has an axis at F, and an axis, a tritone away, at B if the set is listed as F♯–G–B♭–C–E♭–E. As another example, the set C–E–F–F♯–G–B has an axis at the dyad F/F♯ and an axis at B/C if it is listed as F♯–G–B–C–E–F.[14]