Technique · Geometry
Harmonograph
The drawing of a pen pushed by swinging pendulums, spiralling inward as friction slows them; the phases drift so the rosette keeps morphing.
Harmonograph is drawn geometry, rebuilt as it changes. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- Joseph Goold, Charles Benham and Richard Kerr published a book of harmonograph designs, Harmonic Vibrations and Vibration Figures, in 1909, treating the machine as a way to draw musical harmony.
- The sounds of an octave (2 to 1), a fifth (3 to 2) and a fourth (4 to 3) are the simplest musical ratios, and they make the simplest, most symmetrical harmonograph figures.
- The first electronic equivalent was the oscilloscope: in the 1950s the American artist Ben Laposky photographed the traces of two oscillators and called them oscillons.
- Hugh Blackburn, a Scottish mathematician, described the pendulum harmonograph in 1844, and it became a popular parlour amusement in Victorian homes.
- Jules Lissajous studied the same figures in 1857 by reflecting a beam of light off two tuning forks vibrating at right angles.
The mathematics
- Each swing dies as e to the power minus 2.20 t over the whole drawing, so the pen ends at about 11 percent of its first swing.
- The ratio 1.500 to 1 is a fifth in music: the pendulums come back into step after a few swings, which is why the figure forms a closed, symmetric rosette.
- If the ratio is a fraction of whole numbers the line closes after a fixed number of swings; any detuning makes it miss by a little each time, so the rosette turns slowly, which is what the drift of the phases here imitates.
In art
- A harmonograph drawing has no author in the line: the artist chooses the pendulums, and the physics draws the curve.
- Spirographs, oscilloscope pictures and plotter drawings are all cousins of the harmonograph: a few simple periodic motions combined and traced out.
More ways to use it
Related techniques
L-system · Space colonisation · Diffusion-limited aggregation · Flow ribbons · Ridgelines · Curve families · Streamlines · Paint strokes