Identity (music)

An identity function is a permutation or transformation which transforms a pitch or pitch class set into itself.

For instance, inverting an augmented triad or C4 interval cycle, 048, produces itself.

Performing a retrograde operation upon the tone row 01210 produces 01210.

Doubling the length of a rhythm while doubling the tempo produces a rhythm of the same durations as the original.

These families are defined by symmetry, which means that an object is invariant to any of various transformations; including reflection and rotation.