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:
“... feminism is a political term and it must be recognized as such: it is political in women’s terms. What are these terms? Essentially it means making connections: between personal power and economic power, between domestic oppression and labor exploitation, between plants and chemicals, feelings and theories; it means making connections between our inside worlds and the outside world.”
—Anica Vesel Mander, U.S. author and feminist, and Anne Kent Rush (b. 1945)
“The ladies understood each other, in the careful way that ladies do once they understand each other. They were rather a pair than a couple, supporting each other from day to day, rather a set of utile, if ill-matched, bookends between which stood the opinion and idea in the metaphorical volumes that both connected them and kept them apart.”
—Alexander Theroux (b. 1940)
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)