Set theory (music)

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music.[2] Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music,[3] drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that.

Example of Z-relation on two pitch sets analyzable as or derivable from Z17,[1] with intervals between pitch classes labeled for ease of comparison between the two sets and their common interval vector, 212320
Set 3-1 has three possible rotations/inversions, the normal form of which is the smallest pie or most compact form

One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and can be related by musical operations such as transposition, melodic inversion, and complementation. Some theorists apply the methods of musical set theory to the analysis of rhythm as well.

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