Editing Set theory (music) (section)

==Comparison with mathematical set theory==
{{Unreferenced section|date=November 2023}}
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 (music)|transposition]] and [[Melodic inversion|inversion]] where mathematicians would use [[translation (geometry)|translation]] and [[reflection (mathematics)|reflection]]. Furthermore, where musical set theory refers to ordered sets, mathematics would normally refer to tuples or sequences (though mathematics does speak of [[ordered set]]s, 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 {{var|n}} objects, such as [[pitch class]]es, is called a [[combination]], and an ordered subset a ''permutation''. Musical set theory is better regarded as an application of combinatorics to music theory than as a branch of mathematical set theory. Its main connection to mathematical set theory is the use of [[naive set theory|the vocabulary of set theory]] to talk about finite sets.