Harmonic Geometry Lab

A Three.js sacred geometry visualizer with a dark holographic UI. Renders the six Platonic solids (Tetrahedron, Hexahedron, Octahedron, Icosahedron, Dodecahedron, Merkaba), lets you click vertices to connect and measure them, and includes a real audio-reactive cymatics engine — play a tone and watch the solid deform into a genuine standing-wave pattern, not a decorative wobble.

Also included: Voxluminara (voxluminara.html) — a companion conlang app whose phonemes are tied to real Solfeggio frequencies. Click a phoneme there and the Lab reacts live, in real time, in a separate window.

Single-file apps — everything lives in index.html / voxluminara.html, no build step, no backend.

Running it

Because of browser file:// restrictions on ES modules, serve the directory rather than opening the files directly:

python -m http.server 8000

Then open http://localhost:8000/index.html.

How to Use

The basics

• Pick a solid from the SPECIMEN CATALOG on the right (Tetra, Hexa, Octa, Icosa, Dodeca, Merkaba).
• VIEW — just look at it, orbit the camera.
• CONNECT — click two vertex dots to draw a line between them and measure the distance, angle, and edge direction. DISCONNECT removes a link.
• CUT — slice the solid with a plane to inspect its interior.
• SKETCH — draw freeform lines independent of the solid's native edges.
• CUSTOM — place your own points on a construction plane and drag them with a gizmo; they measure and connect just like native vertices.
• Every connection you make logs to the MEASUREMENT LAB panel and persists across reloads — EXPORT downloads the full log as JSON/CSV, CLEAR DATA wipes it.

RESONANCE mode — making it breathe

Switch to RESONANCE (or press 7). This is where the solid stops being static:

1. Pick an input: UPLOAD an audio file, or MIC for live input. With nothing connected, the manual frequency dial drives things instead.
2. Pick a deformation mode with the MODE button — it cycles through three:
   • RADIAL — a simple pulse, driven by the audio's beat frequency. The original, baseline effect.
   • HARMONIC — real spherical-harmonic math. Each Solfeggio frequency (396–963 Hz) maps to a genuine vibration mode, so different tones produce visibly different deformation patterns, not just different speeds. Node/antinode coloring shows you exactly where the solid is staying still versus swinging wide.
   • EDGES — classic Chladni-style standing waves along the edges themselves. Higher frequencies show visibly more nodes per edge — 396 Hz bows each edge once, 963 Hz shows a dramatically spikier multi-node pattern.
3. Play a real tone and watch — the CARRIER/BEAT/AMP readout tells you what's actually being detected.

The Voxluminara Bridge — the full instrument

This is the part worth trying end to end:

1. In RESONANCE mode, click BRIDGE. A new window opens with Voxluminara.
2. Scroll to THE PHONEME SYSTEM — 18 glyphs, each tied to one of the Solfeggio frequencies and a specific deformation mode.
3. Click any phoneme card. It plays its tone and the Lab window reacts immediately — same frequency, same mode, live, no file uploads, no manual steps.
4. Click SILENCE in Voxluminara (or another phoneme) to change or stop it.

Try Α (963 Hz, "Source") for the busiest edge pattern, or Ζ (852 Hz, "Crown") for a distinct harmonic shape — then compare against Σ (396 Hz, "Void") to see how different the same solid can look.

Features

• Six Platonic solids with net/ortho/face-detail stencil projections
• CONNECT / DISCONNECT — click vertex dots to measure distances, angles, and edge directions between them
• CUT / SKETCH — freeform edge sketching independent of the solid's native geometry
• CUSTOM mode — place your own points on a construction plane and drag them with a TransformControls gizmo
• Specimen log — every measurement persists to localStorage and exports to JSON/CSV
• RESONANCE mode — three real deformation engines, not one:
  • Radial — scalar potential field gradient (∇φ), not a hand-tuned wobble
  • Harmonic — real spherical harmonics (Y_l^m), closed-form Cartesian polynomials, each Solfeggio frequency mapped to a genuine vibration mode, node/antinode coloring
  • Edges — true interior standing waves along each edge, node count scales with frequency, derived via Gram-Schmidt projection for a well-defined bow direction
  • Input via file upload or microphone (stereo-aware, extracts carrier/beat frequency for binaural/Hemispheric Sync audio), or a manual dial fallback
• Voxluminara bridge — a companion conlang app's phonemes drive the Lab live via postMessage, no shared backend required

Project status

Version	What it covers	Status
v0.1	Data model, persistence, export, CUSTOM mode, SKETCH integration	✅ Built & confirmed
v0.2 (Phase 2)	Audio input pipeline, RESONANCE mode, vertex deformation	✅ Built & confirmed
v0.2.1	Gradient-driven deformation addendum + audio-analysis flicker fix	✅ Built & verified
v0.3	Cymatic Resonance — real spherical harmonics, wireframe/mesh follow-through, node/antinode coloring	✅ Built, verified w/ real audio, user-confirmed
v0.4	Edge Standing Waves — true interior nodes along each edge, Chladni-style	✅ Built, verified w/ real audio, user-confirmed
Voxluminara Bridge v1.0	Live cross-app instrument — phoneme clicks drive the Lab in real time	✅ Built, verified, user-confirmed

Full spec documents for each stage are tracked alongside this repo (see harmonic-geometry-lab-spec-*.md and voxluminara-lab-bridge-spec-v1.0.md).

Tech

• Three.js (ES module, no bundler)
• Web Audio API (AnalyserNode, ChannelSplitterNode) for real-time frequency/beat extraction
• Real spherical harmonics and Gram-Schmidt-derived edge geometry — no physics engine, just the math
• Cross-window postMessage bridge — no server, no shared origin required
• localStorage for measurement persistence — no backend