Mark Wieczorek

The 1800s were a rich period of exploring and understanding sound through physics. Hermann von Helmholtz wrote his seminal classic On the Sensation of Tone, in which he lays out the single most important improvement on the theory of why certain musical notes work together since Pythagoras.

Here are two tools used to visualize sound in a way that’s utterly unforgettable. You can see the relationships of the harmonic ratios (2/1, 3/2, 4/3, 5/4, etc.) clearly focus for an instant and then disappear.

Chladni Plates

German physicist Ernst Chladni improved a technique developed by Robert Hooke (”the father of the microscope”) where you put sand on a plate & vibrated the plate with a violin bow. The sand would form patterns based on the harmonics of the plate. Chladni Plates (youtube video) create startlingly beautiful patterns when the notes you strike are in harmony with the plate. This allows you to actually see the harmonics tht are the basis of music.

If you’re interested in Chladni Plates, this website and this website have very brief introductions.

Harmonographs

Harmonographs are multi dimensional pendulums. In addition to just the pendulum swing, the surface it swings over is also allowed to swing. Pendulum patterns can already be beautiful, but by creating this dual action, you can explore ratios. What if the ratio of swinging pendulum to swinging paper is 3:2 or 4:3 - all sorts of beautiful patterns emerge, but only at the right frequency ratios.

These two online virtual harmonographs allow you to play with the two settings. The first is fairly simple and allows you to create patterns based on simple ratios. Here you can see the interaction of the pendulum and the moving sheet of paper - each indicated a moving line on the grid. The Second is much more complex, and you may not immediately understand what’s going on. Again, there are two elements here, this time labeled Major Axis 1 and Major Axis 2 - one represents the pendulum moving, the other, the paper moving. Here are my settings, which should get you to the point where you can start playing with ratios. I suggest you test the following ratios & notice the harmonies created.

1st harmonic: 2 (2/1)
2nd Harmonic: 1.5 or 3 (3/2)
3rd Harmonic: 1.33 or 4 (4/3) (note: 1.33 is an approximation of 1-1/3 so 4 is more beautiful)
4th Harmonic: 1.25 or 5 (5/4)

If you’re interested in Harmonographs, the Anthony Ashton book is highly recommended.

Harmonics

If you’re interested in music based on harmonic overtones and not the “equal tempered” scale that we’re so used to, I highly recommend the book Lies My Music Teacher Told Me by Eskalin, as controversial as the Amazon reviews make it out to be, I found it to be very well accessible and much easier to understand than Helmholtz. Also I highly recommend the free Intonation Helper by Tom Ball. It’s a series of MP3s based on a pure overtone series. By listening to these tones, you’re hearing pure chords and not the tempered chords of pianos and guitars. These are much more beautiful and it’s much easier to learn pitch by using such a tool.

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