Connections To Set Theory
Musical set theory uses some of the concepts from mathematical set theory to organize musical objects and describe their relationships. To analyze the structure of a piece of (typically atonal) music using musical set theory, one usually starts with a set of tones, which could form motives or chords. By applying simple operations such as transposition and inversion, one can discover deep structures in the music. Operations such as transposition and inversion are called isometries because they preserve the intervals between tones in a set.
Read more about this topic: Music And Mathematics
Famous quotes containing the words connections, set and/or theory:
“A foreign minister, I will maintain it, can never be a good man of business if he is not an agreeable man of pleasure too. Half his business is done by the help of his pleasures: his views are carried on, and perhaps best, and most unsuspectedly, at balls, suppers, assemblies, and parties of pleasure; by intrigues with women, and connections insensibly formed with men, at those unguarded hours of amusement.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“The moral earth, too, is round! The moral earth, too, has its antipodes! The antipodes, too, have their right to exist! There is still another world to be discovered—and more than one! Set sail, you philosophers!”
—Friedrich Nietzsche (1844–1900)
“The theory of truth is a series of truisms.”
—J.L. (John Langshaw)