A functor is a rule which associates to structures of a certain type structures of another type in such a way that structural equivalence is preserved. Musical functors are often applied to scales or melodic elements in order to simplify their analysis. For example, a melody described using a quantum scale can be transformed into a classical one using a semi-classical limit, and this transformation takes isometric melodies to isometric melodies. Functors can also be used to transform sonic material into optical or algebraic matter. When a collection of functors span a complete set of invariants for a given class of objects, they are said to comprise the theory lens. Central to the point of view espoused here is that music can be truly appreciated only when the full scope of the theory lens is displayed.

Melodic

Functors