When Virtual Reality Helps Fathom Mathemusical Hyperdimensional Models

Abstract

Mathemusicians have always produced models for understanding, analyzing or computing music. We are used to visualize some of them on paper, in a theater or on a computer screen. Even if they refer to multidimensional spaces (3D-4D), while displaying these models on a computer screen the viewer ends up with a 2D picture, or a movie. Planar projection limits the perception, nowadays, in the era of virtual reality, we propose tools and solutions to better apprehend these models and give the viewer an improved immersive experience. Taking advantage of methods used in air traffic simulations, we are developing techniques that we will apply to existing mathemusical visualizations, beginning with Tonnetze and Hyperspheres. We herewith introduce two recently revealed mathemusical models that we have created: 2D: The Shadow Tonnetz, our latest extension of the Tonnetz that keeps trace of a harmonic path. 4D: The Entangled Hyperspheres, a combination of two Planet-4D models that enables us to visualize microtonal music. The images in this paper are extracted from immersive virtual reality world; during MCM we intend to presented the movies with adapted 3D equipment. All videos including virtual ones will be available on www.mathemusic.net.