Editing Music theory (section)

===Serial composition and set theory===
[[File:Berg's Lyric Suite Mov. I tone row B-P.PNG|thumb|Tone row from [[Alban Berg]]'s ''[[Lyric Suite (Berg)|Lyric Suite]]'', movement I[[File:Berg's Lyric Suite Mov. I tone row B-P.mid]]]]
{{Further|Serialism|Set theory (music)|Arnold Schoenberg|Milton Babbitt|David Lewin|Allen Forte}}
In music theory, serialism is a method or technique of [[Musical composition|composition]] that uses a series of values to manipulate different [[aspect of music|musical elements]]. Serialism began primarily with [[Arnold Schoenberg]]'s [[twelve-tone technique]], though his contemporaries were also working to establish serialism as one example of [[atonality|post-tonal]] thinking. Twelve-tone technique orders the twelve notes of the [[chromatic scale]], forming a [[tone row|row]] or series and providing a unifying basis for a composition's [[melody]], [[harmony]], structural progressions, and [[variation (music)|variations]]. Other types of serialism also work with [[set (music)|sets]], collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions (often called "[[parameter (music)|parameters]]"), such as [[duration (music)|duration]], [[Dynamics (music)|dynamics]], and [[timbre]]. The idea of serialism is also applied in various ways in the visual arts, design, and architecture<ref>{{harvnb|Bandur|2001|loc=5, 12, 74}}; {{harvnb|Gerstner|1964|loc=passim}}</ref>

"Integral serialism" or "total serialism" is the use of series for aspects such as duration, dynamics, and register as well as pitch.{{Sfn|Whittall|2008|loc=273}} Other terms, used especially in Europe to distinguish post-World War II serial music from twelve-tone music and its American extensions, are "general serialism" and "multiple serialism".{{sfn|Grant|2001|loc=5–6}}

Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by [[Howard Hanson]] (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as [[Allen Forte]] (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally tempered tuning system, and to some extent more generally than that.{{Citation needed|date=July 2015}}

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 (music)|transposition]], [[Melodic inversion|inversion]], and [[Complement (music)|complementation]]. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.{{Citation needed|date=July 2015}}