by John Simonton
The 1929 RCA theremin is often used as a touchstone to assay the timbre of presently manufactured instruments. Nearly everyone notices that classic theremins have a very “string-like” voice. Also, like natural instruments, different pitches have subtly different timbres; the lowest registers can speak in nearly a vox humana. Some listeners find the sound of the current crop to be lacking in this kind of character, but if you are willing to experiment and spend some time voicing your theremin you can do a lot to replicate the characteristics that gave the originals their distinctive tone. You may even discover unusual voicings of your own. Here are some of the things that I learned while designing Theremax:
A lot of the unique theremin tone comes from interactions between the oscillators. An electronic circuit that has multiple oscillators has to fight their natural tendency to lock to the same frequency. Like pendulums that may couple through a common support structure, multiple oscillators can couple through a lot of sneak paths. Power supply and ground lines are common sources. Also magnetic coupling between the coils of the oscillators, even induced EMF between components that are close together.
In a theremin, the most apparent result of the oscillators locking is that the tone disappears. Since the two oscillators are locked to the same frequency, the difference frequency between them is zero. Most theremins count on the oscillators locking to provide a mute when the performer is not present.
Only slightly less apparent is the fact that the frequency difference at which the oscillators lock represents the lowest pitch that the instrument can produce. If they lock when there is less that 250 Hz difference in their frequencies then you won’t be hitting any notes below about middle C.
Not apparent at all, in fact getting onto obscure, is the effect that oscillators have on one another as their frequencies approach lock. Before they actually synchronize, they “pull” one another toward the lock frequency. They do this by distorting each other on a cycle-by-cycle basis so that their outputs are no longer pure sine waves, or even truly periodic except at their difference frequency.
Instead of just one sum frequency that will be rejected by filters and one difference frequency that is the audible pitch, there are now difference frequencies between all the harmonics of the two oscillators. Rigorous analysis gets hairy, but you can get some surprising insights into the results using some simple rules of thumb.
For example, you might intuitively expect that since the oscillator outputs are not pure sinewaves in this regime, the result would be a tone with the sort of dissonances usually associated with balanced modulators. Loads of inharmonic partials; clangorous, atonal timbres and so on. And, in fact, this is the result when individual cycles of the oscillators are simply clipped or squashed but still periodic.
But this is not at all the case with pulling distortion. Since the only periodicity is at the difference frequency, all harmonics will be multiples of the difference frequency. Instead of an unruly mish-mash of components, there is a neat series of odd and even harmonics of the fundamental pitch frequency. A harmonic series with both odd and even overtones of the pitch fundamental is the signature of a bowed string, hence the string-like voicing.
Notice that this distortion is pitch sensitive. At higher pitches the oscillators have less tendency to influence one another, so at high pitches the audio output waveform is nearly sinusoidal. As pitch falls and the oscillators get closer to the same frequency they begin to pull one another and harmonics begin to show up. First the second harmonic begins to come in. Then as pitch continues to fall and interactive effects get greater, the second harmonic gets stronger and other harmonics begin to appear. This is why the timbre changes at different pitches.
The effect of coupling interactions on instrument tone provides fertile ground for experimentation. The Theremax Builders FAQ shows how to increase coupling to provide a small dead zone where the oscillators lock. Further coupling, either by increasing the size of the gimmick or even using a larger fixed or variable capacitor will begin to show the sonic effects of oscillator interactions. Different coupling networks (RC, LC, etc.) and coupling points may also produce interesting results.