A three-pendulum harmonograph

Harmonograph with harmonogram on a wall
digitally processed harmonogram evoking a UFO
A harmonogram that has then treated digitally, printed and framed
A harmonograph is a mechanical apparatus that employs pendulums to draw images. The devices began to appear in the mid-19th century and Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly credited as the official inventor. We wanted to build a harmonograph with an authentic aspect, that would not look out of place in the laboratory of a 19th century inventor. Except for the pendulums and arms, we used wood found in skips in our street (old construction timber and pieces from a children’s bed frame).

On this page

Discover our harmonograph
See our harmonograms

Description of the apparatus

general view of a harmonograph
The principle
Two pendulums control the movement of a pen on a drawing platform, which is itself mounted on its own pendulum. By adjusting the frequencies and phases of the pendulums in relation to one another we obtain different patterns.
arrows showing the movements of the arms and drawing platform of a harmonograph

The general structure

The arms holding the pen are at a 90 degrees angle. Each arm is given a simple back-and-forth motion by its pendulum. The pendulum of the drawing platform is mounted on a more sophisticated joint (a gimbal) that allows for an ellipsoidal trajectory. The relative position of the pendulums and the need for their weights to move freely (without hitting one another or any leg of the device) gave us the idea for the general shape for our harmonograph: a horizontal rectangle triangle supported by a potence with a single leg that meets the triangle at its centre of mass.

joint of a harmonograph's pendulum

Joint of a “back-and-forth” pendulum

A horizontal dowel traverses the shaft of the pendulum. A nail protrudes under each end of the dowel and its point rests inside the hollow head of a screw inserted in the top of the potence. That allows the pendulum to rock with very little friction.

gimbal on a harmonograph

The gimbal
At the front of the triangle, square plate is allowed to rock back and forth. The pendulum goes through a hole in the centre of the plate and rests on two screws placed one in front of the other. That allows for a sideway swing of the pendulum.

The combination of those back-and-forth and sideways motions produces the elliptical trajectory of the drawing platform.

The notches on the pendulums follow a precise logarithmic progression, like frets on a guitar’s neck, and the interval between any two consecutive notches is the equivalent of a semitone. That allows to draw visual representations of musical intervals and chordsA weight is maintained at a specific height simply by resting on an element that slides inside a notch.

peg immobilising a pendulum on a harmonograph
Pendulum blocking mechanism
The pendulums can be immobilised individually with a horizontal peg. That allows to experiment with two active pendulums.
hand of a harmonograph holding a pen
The hand
The pen is hold by a wooden hand whose ‘thumb’ is a flexible blade that presses the pen against a vertical slot. There are two slots to cater for different sizes of pens.
magnetic joints on a harmonograph
Magnetic joints
The joints at the ends of the arms are made of cylindrical magnets and nails bent in the shape of crescents. That allows a wide range of motion, similar to ball joints, but with the advantage of minimal friction.
drawing platform of a harmonograph loaded with a bundle of sheets

The drawing platform

The raised corners of the platform have two roles: they maintain the paper in place during operation and they allow to store a bundle of sheets on the platform.

feet of a harmonograph

The feet

To achieve maximum stability, the device has three points of contact with the floor.

storage compartments on a harmonograph
double-framed display on a harmonograph
On the left, a storage space hidden under a removable panel contains a bunch of pens. On the right, a few pens rest in a recess.
At the back, two A4 drawings are displayed on a reclined double frame.


The drawings produced by a harmonograph are called harmonograms. By adjusting the height of the weights we change the frequencies of the pendulums and we obtain a great variety of drawings. Furthermore we can start the harmonograph with one pendulum motionless (but free to move) while the other two are set in motion. The moving pendulums will then transfer energy, through the friction of the pen on the paper, to the third pendulum, which will start moving. Thus we obtain more complex drawings of 2-pendulum patterns that progressively transition into a 3-pendulum patterns.

Here are some harmonograms that have been processed digitally.

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