Two pendulums swinging at right angles, with a pen between them, draw the ratio of their speeds. Simple ratios, the same ones that sound consonant in music, make simple and beautiful figures. Pick an interval, set the pendulums swinging, watch the pen draw, and listen to it. Curious? Read about harmonographs.
Interval
Pendulums
Watch and listen
Look and save
Seeing consonance
When two pendulums swing in a simple ratio, like 2:3 for a fifth, the pen comes back to where it started after a few swings and the figure closes on itself. The simpler the ratio, the simpler the figure, just as the simplest ratios sound the most consonant. Detune one pendulum slightly and the figure slowly turns, the way two nearly matched notes beat.
Lissajous and harmonograph
A Lissajous figure is the ideal case: pendulums that never slow down, so the pen runs around the same closed curve forever. A real harmonograph's pendulums lose energy, so the figure spirals in toward the center. A third, rotary pendulum moving the paper in a circle adds the loops and rosettes.