Visualization of musical structures is a powerful tool to assist composers and improvisers in their creative processes. Interpreting the Tonnetz as a simplicial complex it is possible to visualize notes and chords as subcomplexes endowed with particular topological and geometric properties. The software HexaChord developed at the IRCAM by Louis Bigo will be used to show how the topological information provided by the real time interaction among the composer and the "simplicial Tonnetz" can be used either as a didactical instrument and a facilitator.
In addition to the planar representation of the Tonnetz, a 3-dimensional version obtained considering the consonance relationship among the theme and the harmony will be described. The anisotropic and dynamical nature of this model allow to identify sonorities as Tonnetz's extended shapes, characterized by their extrinsic and intrinsic geometrical features.