Representation of Musical Structures and Processes in Simplicial Chord Spaces

In this article, we present a set of musical transformations based on the representations of chord spaces derived from the Tonnetz. These chord spaces are formalized as simplicial complexes. A musical composition is represented in such a space by a trajectory. Spatial transformations are applied on these trajectories and induce a transformation of the original composition. These concepts are implemented in two applications, the software HexaChord and the Max object bach, tonnetz, dedicated to music analysis and composition, respectively.