Editing Set theory (music) (section)

{{Short description|Branch of music theory}}
[[File:Z-relation Z17 example.png|thumb|upright=1.5|Example of [[Interval vector#Z-relation|Z-relation]] on two pitch sets analyzable as or derivable from Z17,{{sfn|Schuijer|2008|loc=99}} with intervals between pitch classes labeled for ease of comparison between the two sets and their common interval vector, 212320]]

'''Musical set theory''' provides concepts for categorizing [[music]]al objects and describing their relationships. [[Howard Hanson]] first elaborated many of the concepts for analyzing [[tonality|tonal]] music.{{sfn|Hanson|1960}} Other theorists, such as [[Allen Forte]], further developed the theory for analyzing [[atonal]] music,{{sfn|Forte|1973}} drawing on the [[twelve-tone technique|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.

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