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Levent Şentürk

Published Jul 24, 2020

Harmonograph is a forgotten Nineteenth-Century mathematical drawing entertainment, which used to attract masses who were gathering to see the performance of the ghost in the machine, the harmonograph. The harmonograph is basically a pendulum device and when its pendulums start to swing, within seconds the machine draws surprising mathematical graphics. Purchasers produced even dismountable, mobile versions of harmonographs. Today although there are no mass-produced harmonographs anymore, one can build one with minor difficulty. The simplest version would be a singular pendulum, made of a string and a tube, mounted at the top to the ceiling with a hook, and to the bottom end having a container with a hole, slowly leaking paint to a large sheet of paper. Satisfactory results can be gained with acrylic or oil paint. Mathematics, music, and physics are the soil of harmonograph; thus the reintroduction of harmonographs to the architectural studio may have substantial results and not only in craftsmanship. Based on transferring the gravitational harmonious movement to a graph or a stylus on one hand and to the plate on the other, the initial movement can result in complicated drawing patterns when everything works properly. As far as the weights of the pendulums are well distributed, the machine well balanced and frictional forces are kept at a minimum, a harmonograph can work properly (Ashton, 2003). The modus operandi of mono-, di- or tri-pendulum harmonograph a simple, yet a variable and thus a developable; even an inventive one. The mechanism is based on the concurrent oscillation of the multiple pendulums which gives the drawings mathematical complicity at such an extent that one may be shocked by the delicate quality and precision of them; and it may seem hard to believe to have these three dimensional, repetitive quantumic orbital patterns drawn without the aid of a computer but just by gravity. A harmonograph is today still an item of a rarity at an age of online gaming. One can trace only extremely rare copies of a once purchased pendul-art game set. But even this 1970s product has become a ghost itself. So not only the ghost in the machine but the machine itself shares this destiny of vanishing. By introducing this odd device to the architectural studio, plenty of creative productions could be accommodated: Harmonography has its roots in music and was originally devised as a medium for vibrations and notation. Today, after the burden of post-structural de-harmonising, rhizome theory, and an outburst of the digital neo-baroque, harmonographs can be new sources of inspiration for all.


Ashton, A. (2003). Harmonography. A Visual Guide to the Mathematics of Music. Walker Publishing, New York.

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