What's happening
Each note, played alone, is simple harmonic motion — smooth back-and-forth oscillation at a fixed frequency, the same motion as a swinging pendulum or a mass on a spring. The dot on each track below the curve traces exactly this.
Why the shape matters
A Lissajous curve plots two or three of these oscillations against each other, one per axis. Its shape is decided entirely by the ratio between the notes' frequencies. Simple ratios — like 2:3, a perfect fifth — draw a curve that closes into a clean, repeating loop. Complex ratios, like a tritone, never quite close, so the curve keeps slowly evolving instead of repeating.
That's not a coincidence: those same simple ratios are what make an interval sound consonant. The "f : …" line above shows the nearest small-integer (just intonation) approximation for the current chord — the simpler the numbers, the more consonant the interval, and the cleaner the curve.
Tuning note
Playback uses real equal-tempered tuning (what a piano or guitar actually plays), which only approximates those simple ratios. Consonant intervals still draw a near-closed curve, but it slowly precesses instead of exactly repeating.
Chord name
The badge above the stage detects the interval (2 notes) or triad quality (3 notes) — major, minor, diminished, augmented, sus2, sus4 — straight from the notes you've picked, including inversions.
Controls
In 3-note mode: drag to orbit, scroll to zoom, and click a face of the small cube (bottom right) to snap the camera flat onto a plane. The grid traces the cube that bounds the curve, for a clearer sense of scale and rotation.