GUERINO MAZZOLA, THOMAS NOLL

Extending Set Theory to Harmonic Topology and Topos Logic

Abstract

It is well known that classical logic can be interpreted in terms of set models. In music theory, Hugo Riemann introduced the principle of a musical logic, whereas Wolfgang Graeser and the American school following Allen Forte introduced set-theoretic methods to describe tonal and atonal structures.
We discuss the relation between structure and logic in these approaches and relate two lines of thought which both suggest to conceive musical logic beyond a classical boolean approach. David Lewin's way of studying of set transformations involves ideas that can be related to fuzzy logic. Our approach to a harmonic morphology models some of Riemann's concepts and is formulated in a topological language. This study leads us to a synthesis of set theory and logic, which has been developed in the framework of a musical topos theory, an application of Grothendieck's geometric logic and object-oriented conceptualization to a unified evaluation of truth and esthetics in music.

Biography of Guerino Mazzola
Biography of Thomas Noll