I wanted to know what kind of sound would be produced from geometries that cannot exist in reality, if they were granted some special permission to exist.
Take the Klein bottle, a type of non-orientable manifold, as an example. While it is not inherently a self-intersecting manifold, representing it in our reality (3D Euclidean space) makes self-intersection unavoidable. Consequently, the “true” Klein bottle (free from self-intersection) cannot exist in the real world, rendering it impossible for us to either see or hear it. However, if we assume it exists — that is, if we are permitted to completely ignore the physical singularity at the self-intersection and treat it as if it were not intersecting — how would it sound like?
This project is a demo intended for the presentation on my DAFx paper “Modal Structuer of Plate Boundaries and Klein Bottle Reverberation”. This paper discusses a digital effect that represents acoustics on a non-orientable manifold using modal forms and utilizes this representation for reverberation. As demonstrated in the examples, the non-orientable manifolds considered include the Möbius strip, the Klein bottle, and the real projective plane.
This project is currently underway, having just broken ground. We began with preliminary research in a two-dimensional quotient space (ignoring factors such as curvature or cavities) and plan to uncover more fascinating insights moving forward. Stay tuned!
