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A harmonograph uses two pendulums swinging in perpendicular planes to create a graphic representation of harmonies. This device uses the same relationships found in musical harmonies, but at the much lower frequencies of pendulums. The design for this harmonograph came from "100 Amazing Award Winning Science Fair Projects" by Glen Vecchione, with minor alterations during the build and test phases. Another interesting book on this topic is Anthony Ashton's "Harmonograph: A Visual Guide to the Mathematics of Music".

The curve traced out by a point on the rim of a circle rolling along a straight line is called a cycloid. Let the radius of the circle be . Allowing the tracing point to be either within or without the circle at a distance from the center generates "curtate" or "prolate" cycloids, respectively.