Published on 16 April 2008
The Harmonograph was a 19th century curiosity for visualising the mathematics of music.
A common form of the device was to have two pendulums that swing at right angles to each other. From the top of each pendulum an arm that is attached to a pen. By changing the relative swinging frequency of the pendulums the pen will trace out some interesting shapes. An additional variation is to also attach the paper platform to the top of a third pendulum and set this spinning.
The equations that describe the behaviour and a detailed explanation of the physical devices are detailed by Paul Bourke. There is also a superbly illustrated book by Wooden Books dedicated to Harmonographs.
Last updated: 5 October 2008