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Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen , 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. 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 which can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well. ==Mathematical set theory versus musical set theory== Although musical set theory is often thought to involve the application of mathematical set theory to music, there are numerous differences between the methods and terminology of the two. For example, musicians use the terms transposition and inversion where mathematicians would use translation and reflection. Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences (though mathematics does speak of ordered sets, and although these can be seen to include the musical kind in some sense, they are far more involved). Moreover, musical set theory is more closely related to group theory and combinatorics than to mathematical set theory, which concerns itself with such matters as, for example, various sizes of infinitely large sets. In combinatorics, an unordered subset of ''n'' objects, such as pitch classes, is called a combination, and an ordered subset a ''permutation''. Musical set theory is best regarded as a field that is not so much related to mathematical set theory, as an application of combinatorics to music theory with its own vocabulary. The main connection to mathematical set theory is the use of the vocabulary of set theory to talk about finite sets. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Set theory (music)」の詳細全文を読む スポンサード リンク
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