The abstract artist, Hannah Ferguson, paints using a pendulum and her artworks have particular significance for my music. An example is the third movement of the 'Momentous Quartet', Strangeness and Charm, with the accompanying video featuring Hannah at work.
It's a simple idea. Attach a sphere with a hole in it to a length of cord and fill it with paint. Let the pendulum sphere swing and uncover the hole so that as it swings lines and drips of paint cover the surface below. The resulting patterns are individual and visually interesting.
The swing of the pendulum is a fundamental physical phenomenon and its repetitive harmonic motion can be represented graphically by a simple sine wave graph. The sine wave is also a mathematical representation of a pure sound.
Any complex sound, such as made by a bow sweeping across a violin string, or a hammer hitting a gong, can be represented by a set of these sine waves, each with its own parameters. Any sound made by a musical instrument is not just a random collection of these simple waves, but consists of a fundamental, for example, a tone oscillating at 100 Hz, plus a series of waves having a simple relationship with this fundamental: 200, 300, 400 Hz, etc. This is called the harmonic series and seems to be a natural phenomenon.
All of this was subject matter for the ancient Greeks, most notably Pythagoras, and our understanding of it has subsequently been refined through history, culminating (for geeks) with the work of Joseph Fourier in the 19th C, which led to the sophistication of modern sound sythesisers. In parallel, discoveries in astronomy revealed that orbiting planets follow the rules of harmonic motion. When it was thought that the planets orbited in circles, their relationship with harmonic motion was easily demonstrated. A corresponding 'music of the spheres' was based on the idea that planetary movement and sound vibrations conformed to harmonic motion.
With the revelation that planetary orbits were elliptical, this still held true but became more complex. If a circular orbit represented a particular harmonic movement, i.e., a particular tone, then an elliptical one meant a change in its harmonic frequency as it orbited, translating not into a continuous tone, but into a glissando. Heady stuff!
This is tough going without a clear visualisation of what is going on mathematically and treatises have been written explaining the subject, but my point is that harmonic motion is fundamental to the way the universe and everything in it looks (light waves have harmonic motion), moves and sounds. Music and art can be created to demonstrate and represent this, hence my Strangeness and Charm piece.
I know Hannah probably won't view her abstract artworks this way, but I do.