| Description |
Atonal music theory borrows much of its conceptual framework from the mathematical disclipline of set theory. Several music theoretical concepts, however, exceed the scope of set theory and are ill-defined as such. This document aims to help complete the mathematical foundation of atonal music theory by constructing the basis for a definition of pitch class space: namely, that pitch class space is the quotient ring of all pitches related by octave equivalency under addition and multiplication. This definition is constructed by systematically defining a series of concepts from the mathematical disciplines of set theory, order theory, and abstract algebra, then relating those to concepts from musical acoustics and musical set theory. |
