Epicycles.

Put a pencil on the rim of a spinning circle, put another spinning circle on that one's rim, and so on. If each circle turns at its own whole-number speed and you pick the right sizes, the pencil can draw any closed shape. That's a Fourier series: z(t) = Σ cₖ eⁱᵏᵗ.

The tool walks the outline, takes 4,096 evenly spaced points and works out every circle at once with a fast Fourier transform. Then it draws with the N largest. A treble clef has four contours (the outside and three holes), so they're joined by bridges with no width: the pencil crosses over, goes round the hole and comes back the same way. A picture works the same way: it's split into dark and light, and every patch becomes another contour.

The error is the widest gap between what the circles draw and the real outline, as a share of its height. For the treble clef it falls from 36% with one circle to 0.25% with 256.

With the sound on, the tip's distance from the centre becomes a note: the farther out, the higher, rounded down to C major over two octaves. One circle never changes its distance, so it plays a single note. With more circles, the tip ends up playing almost the same tune the outline itself would.

The idea came from this post by matharium, which does it with a treble clef. The clefs come from Bravura, Steinberg's open music font.