Single oscillator theremin?

Question

I read that the pitch circuitry of a theremin mixes two RF oscillators, and their difference creates the audio frequency produced by the instrument.

The theremin has inside it three radio-frequency oscillators, of which two form the heart of the pitch circuitry and the third drives the volume circuitry. The pitch circuit uses a fixed-frequency oscillator operating at 260 kHz and a variable-frequency oscillator having a range of 257-260 kHz. The frequency of the variable-frequency oscillator depends on the capacitance of the pitch antenna circuit. As you bring your hand near to the pitch antenna, you raise the capacitance in the circuit, which lowers the frequency of the oscillator. Conversely, as you move your hand away from the antenna, the capacitance goes down and the frequency rises. The outputs of the two oscillators go to a mixing circuit, where they are superposed. Since the two signals are close in frequency, they produce beats whose frequency is the difference between their frequencies. Thus, as you lower the frequency of the variable-frequency oscillator, you raise the beat frequency, and as you raise its frequency, you lower the beat frequency. Depending on your hand position and the adjustment of the instrument, the beat frequency can be anywhere from around 65 Hz to about 3 kHz (260 kHz minus 257 kHz). These are audio frequencies, and they correspond to a range that spans from about two octaves below middle C to about three-and-a-half octaves above middle C. The mixing circuit extracts this beat frequency and sends it to a voltage-controlled amplifier. Source

Is there a reason why one couldn't simply use a simple oscillator in the audio range instead? What makes the pair of RF oscillators a superior choice?

Answer 1

You need the small capacitance changes caused by the vicinity of a hand to actually affect an oscillator. An oscillator at audio frequencies cannot practically be built from capacitances in the same order of magnitude as these changes.

Also, the changes in capacitance do not change the oscillator frequency by factors of 2 or more – which would be necessary for an octave of tonal range. Instead, the change is a small fraction the "nominal" frequency of the oscillator. You need to find the difference to a reference oscillation to be able to get a frequency variation that is large in terms of the base frequency.

Answer 2

The Theremin needs to work with the small hand capacity change. Using this small capacity you could not build a low frequency oscillator for audible range. If you use two oscillators and the difference frequency, then a variable frequency in the audible range is possible.