Local and global limit denotators and the classification of global compositions

Abstract

It is shown that the module complexes used for the classification theory of global compositions are denotators of limit type, a special instance of which is also encountered in the network theory of David Lewin [Music Theory Spectrum 12 (1990), no. 1, 83–120] and Henry Klumpenhouwer. We then sketch a theory of global limit denotators and show that there is a canonical functor into the category of global compositions. This provides us with invariants for the classification of global limit denotators