Show HN: Umbilic Torus Model of 12‑Tone Harmony (Now, Live TCP Note Tracking)

This is a real‑time, interactive model of 12‑tone equal temperament harmony, projected onto an umbilic torus. Harmonic ordering is encoded as a closed 3D curve tracing the circle of fourths; adjacency is defined along this spiral.

Previous 3D projections of 12‑tone equal temperament — including Tonnetz‑on‑torus visualizations, chord‑space topologies, and other geometric or topos‑inspired models — often represent harmonic adjacency through triangular lattices or higher‑dimensional embeddings. While these preserve the underlying relationships, the added lattice can make the global structure harder to perceive as a single, continuous form. In this model, the umbilic torus is shown without such overlays, so the harmonic spiral is seen as one uninterrupted 3D path. The smooth curvature is used purely for visual continuity and aesthetic clarity, not as a determinant of harmonic relations.

The system now supports *Live TCP Note Tracking* — meaning any external tool (DAW, MIDI parser, audio analyzer) can stream active notes directly into the visualization.

It’s built with Love2D and 3DreamEngine, and integrates with FluidSynth or any TCP‑capable backend. I’d love feedback from topologists, mathematical music theorists, and educators exploring new ways to visualize harmony.