The theremin is played by carefully moving your hands near 2 antennas, one for volume and one for pitch. But how does it work? If you mix the signals of 2 rf oscillators, you will get many output signals. The most important signals are the sum and difference of both frequencies. (This principle of mixing two signals to get a 3rd one is called heterodyning.) Lets say we have one oscillator on 500 kHz and another on 501 kHz, the sum will be 1001 kHz and the difference 1 kHz. This 1 kHz is audible.
Now why would you want to use the difference from 2 rf oscillators if you only want a single audio frequency? That, has everything to do with how the theremin is played: by moving your hand near an antenna. By doing so you de-tune an LC oscillator. In an LC oscillator the frequency is determined by the value of an inductor (L) and capacitor (C). If you would connect an antenna to the capacitor, the antenna will work as an extra capacitor and so have influence on the frequency. If you move your hands near the antenna, its capacitance will change, and the frequency will change with it. These changes are, however, very small, less than 1 percent. Suppose an oscillator works on 1 kHz, the variation would only be 10 Hz. However at 500 kHz a 1% variation would be 5 kHz. Then when you mix the 500 kHz to 505 kHz oscillator with a fixed 500 kHz one, you would end up with an audiosignal of 0 to 5 kHz. This doesn’t only allows us to play music, but has another advantage: its possible to make an instrument with a range of 3-5 octaves.
Now we have a variable audio tone, but it has the same volume all the time. To change that another oscillator is build. Again at a high frequency, lets say 200 kHz. And again there is a antenna connected to the capacitor in this oscillator, so its frequency will change if you wave your hand near the antenna. Now the signal of this oscillator is fed to an inductor and capacitor connected in parallel, tuned to 200 kHz as well. Such an LC circuit acts as a short circuit for frequencies other then 200 kHz. This means that the more you de-tune the oscillator, the weaker the signal gets. This signal is then rectified and used to regulate the volume of the audio signal. This can be done in various ways.
In theory a theremin would produce a pure sine wave. Yet it often doesn’t sound that way. This can have various reasons. In modern designs the audio often gets distorted on purpose to get a ‘more interesting sound’. But there is another reason, especially with more traditional build theremins. As we now know the pitch oscillator contains 2 rf oscillators at nearly the same frequency. With the large, unscreened inductors in traditional theremins the radiation of both oscillators is all over the place. And for some mysterious reasons, because they nearly operate at the same frequency, the have the tendency to pull towards each other. Like they want to go operate on the same frequency. This distorts the pure sinewave and all sorts of non-harmonic signals appear. This gives a very special sound, much more interesting as simply adding distortion by clipping. If you have a modern theremin with those little screened coils in it, the effect is much less. However you can connect a small capacitor (say 1-5 pF) between both oscillators to create the same effect. Some people use a resistor (about 10k – 100k) instead. If both frequencies get very close both oscillators might actually lock on eachother. When this happends, they will operate on the same frequency, and there will be no difference frequency (audio signal). This means you will have to experiment with coupling both oscillators, if there is to much coupling your theremin might go silent below 200 Hz for example. More on theremin sound at Dave’s Theremin Homepage. There are even more reasons why a theremin sounds the way it does, like the behaviour of the mixer circuit and the transformers in the audio path (of tube theremins), but those go beyond the scope of this article.
You now know how the antenna influences the frequency of the oscillator. But how can you make the influence more or less. What if the theremin only does 2 octaves and you want it to do three? Well You can build an oscillator at, say, 500 kHz with different combinations of L and C values. As long as their product remains the same. Within limits you can decrease the L and increase the C or the other way around. The antenna has a certain capacitance. This is added to the capacitance of the C in the oscillators LC circuit. The smaller the C in the circuit is, the larger is the influence of the antenna. Thus if you want to add an extra octave, you will have to decrease the C and increase the L. If you want to reduce the range, its exactly the other way around. Btw, It’s not wise to go to extremes here, a large range will make it very hard to find the exact notes. Want to read more about this? See Fred Nachbaur ‘s site. To get a good sensitivity one has to use a small capacitor and large inductor, which has its disadvantages. Therefore another method is often used with a series inductor between the LC circuit and the antenna. More info on this (with a lot of math) is at the Brown Crow website.