Set Theory (music)
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson (1960) in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte (1973), drawing on the work in twelve-tone theory of Milton Babbitt. The concepts of set theory are very general and can be applied to tonal and atonal styles in any equally-tempered tuning system, and to some extent more generally than that. One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered or unordered, and which can be related by musical operations such as transposition, inversion, and complementation. The methods of musical set theory are sometimes applied to the analysis of rhythm as well.
Read more about Set Theory (music): Mathematical Set Theory Versus Musical Set Theory, Set and Set Types, Basic Operations, Equivalence Relation, Transpositional and Inversional Set Classes, Symmetry
Famous quotes containing the words set and/or theory:
“We set up a certain aim, and put ourselves of our own will into the power of a certain current. Once having done that, we find ourselves committed to usages and customs which we had not before fully known, but from which we cannot depart without giving up the end which we have chosen. But we have no right, therefore, to claim that we are under the yoke of necessity. We might as well say that the man whom we see struggling vainly in the current of Niagara could not have helped jumping in.”
—Anna C. Brackett (1836–1911)
“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical theory will abandon that point of view.”
—Thomas Nagel (b. 1938)