Harmonograph Maker

See musical intervals drawn by pendulums. Pick a ratio, from the octave (1:2) and the fifth (2:3) to the whole tone (8:9), set the phase, detune and damping, and watch the pen draw a harmonograph figure or a Lissajous curve. Listen to the two pendulums as two tones, and save the drawing as an SVG or a PNG. No sign-up and no libraries.

• Draw a harmonograph

What it does

A harmonograph draws with pendulums: one swings the pen from side to side, another up and down. When their speeds are in a simple ratio, the same ratios that sound consonant in music, the drawing closes on itself in a simple, regular figure.

• Interval: harmonograph or Lissajous, ten musical intervals (unison, octave, fifth, fourth, major and minor thirds, major and minor sixths, whole tone, twelfth), or any ratio from 1 to 12 for each pendulum.
• Pendulums: phase, detune (a small mismatch that makes the figure turn), and for the harmonograph damping, a rotary pendulum with its speed, and the swing time. Surprise me picks random settings.
• Watch and listen: Draw it traces the figure the way the pen would, Turn the phase animates it, and Listen plays the two pendulums as two tones, one in each ear, at the same ratio.
• Look and save: five color schemes (ink on paper, gold, neon, spectrum, blueprint), line width, Download PNG (2400 pixels square) or Download SVG.

The equations

Lissajous: x = sin(2π a t + δ), y = sin(2π b t).

Harmonograph: x = e^(−dt) [sin(2π a t + δ) + m sin(2π r t + δ/2)], y = e^(−dt) [sin(2π b′ t) + m cos(2π r t + δ/2)], where b′ is b slightly detuned, d the damping, and m and r the size and speed of the rotary pendulum.

How it is built

The pages are plain HTML, CSS and JavaScript, with no dependencies and no build step. Just open index.html. The sound is made with the Web Audio API. It is also a small installable web app: add it to your home screen or desktop and it works offline.

• The figures, animation, sound and export are all in js/harmonograph.js.
• Three color themes (dark, light and blue) are shared with my other projects.
• Your settings are kept in the browser's local storage.

Harmonograph is open source at GitHub with MIT license.

Had fun browsing the app? Buy me a coffee by becoming a sponsor.

You may also be interested in my other projects Music-of-the-Spheres (demo) and Cymatics (demo). For more mystic arts as small web apps, see Esoterica.

Copyright (c) 2026 Olivier Giulieri.