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 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.
Read more about this topic: Set Theory (music)
Famous quotes containing the words mathematical, set, theory and/or musical:
“What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
—D.H. (David Herbert)
“When I married Humphrey I made up my mind to like sermons, and I set out by liking the end very much. That soon spread to the middle and the beginning, because I couldn’t have the end without them.”
—George Eliot [Mary Ann (or Marian)
“We have our little theory on all human and divine things. Poetry, the workings of genius itself, which, in all times, with one or another meaning, has been called Inspiration, and held to be mysterious and inscrutable, is no longer without its scientific exposition. The building of the lofty rhyme is like any other masonry or bricklaying: we have theories of its rise, height, decline and fall—which latter, it would seem, is now near, among all people.”
—Thomas Carlyle (1795–1881)
“Sometimes a musical phrase would perfectly sum up
The mood of a moment. One of those lovelorn sonatas
For wind instruments was riding past on a solemn white horse.
Everybody wondered who the new arrival was.”
—John Ashbery (b. 1927)