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:
“The conclusion suggested by these arguments might be called the paradox of theorizing. It asserts that if the terms and the general principles of a scientific theory serve their purpose, i. e., if they establish the definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretive statements establishing such a connection should then be replaceable by a law which directly links observational antecedents to observational consequents.”
—C.G. (Carl Gustav)
“... many of the things which we deplore, the prevalence of tuberculosis, the mounting record of crime in certain sections of the country, are not due just to lack of education and to physical differences, but are due in great part to the basic fact of segregation which we have set up in this country and which warps and twists the lives not only of our Negro population, but sometimes of foreign born or even of religious groups.”
—Eleanor Roosevelt (1884–1962)
“The theory of the Communists may be summed up in the single sentence: Abolition of private property.”
—Karl Marx (1818–1883)