Apollonius diagrams and the Representation of Sounds and Music.

We introduce the use of weighted medial graph structures to represent sounds and musical events. Such structures permit the building of hierarchical neighborhood relationships (symmetries) while mapping time to a weight (of a note, or event). This is useful to relate perceptual organisations (groupings in the sense of Gestalt theory) both visually and aurally. We treat time in a cinematographic way, effectively using a space- time representation. The use of colour, modulation (of waveforms), orientation, speed, etc., allows us to integrate multiple musical features in our dynamic diagrams. We provide illustrations, including animations, of our ideas.