A theremin is an electronic musical instrument which is operated without touch by utilising the varying capacitance that exists between the player's hand and an aerial. However, the variation in capacitance produced is sufficiently small that it can only alter the frequency of an oscillator by a few percent at most: not sufficient to produce a range of musical pitches, that must vary in frequency by a two orders of magitude or so.
The audible sound is produced by heterodyning the output of two high-freqency sinusoidal oscillators, one of fixed frequency and one with a frequency controlled by the aerial. The heterodyning essentially multiplies the two oscillator outputs together, producing frequencies at both the sum and difference of the oscillator frequencies. For oscillator frequencies of around 100KHz, the sum frequency is up at around 200Khz, but the difference frequency varies with the position of the player's hand in the required audible range between zero and a few kilohertz. The sum frequency is filtered out, and the remaining audible difference frequency is amplified for output.
This particular theremin uses the circuit of Arthur Harrison's 203 Theremin. The oscillators are of the Wien-bridge type operating at around 84KHz, with gain controlled by transconductance op-amps. To increase its sensitivity, the voltage at the aerial is increased by a charge-pump voltage inverter. Since this could otherwise introduce noise at high frequencies, which would be made audible by the hetrodyning stage, the charge pump here is synchronised with the fixed-frequency oscillator.