Of the Theremin and Futurist Stringed Instrument Making

Principles

As we have seen, from a theatrical point of view, the operative approach is undoubtedly esoteric and almost metaphysical, but the instrument is actually based on well-known physical principles and makes use of essentially simple, easily understood and easily implemented electronic circuits.

The theremin is based on the principle of a beat generator: two harmonic radio frequency signals are fed into a mixer whose output consists of other signals that represent the sum and difference of the frequencies of the first two. If the frequencies of the two incoming harmonic signals are closer enough, the difference between the signal will fall within the audible range (20 Hz – 20KHz); furthermore, by controlling the frequency of oscillation of one of the two signals, we can obtain a variable audio signal.

As can be seen in the diagram, the oscillator 1 (generally operating at 175-200 kHz) is connected to an antenna. Bringing a hand closer creates a virtual capacitor between the antenna and the human body, the value of which (in the order of a few picoFarads) varies in relation to the distance between the two plates (hand and antenna). By connecting the antenna to the resonant circuit, the capacity of the virtual capacitor is added to that of the circuit capacitor in such a way that, by moving the hand nearer to or further from the antenna, it is possible to modify the working frequency of the oscillator: bringing the hand closer reduces the frequency because the total capacity of the resonant circuit increases.

The second oscillator has a fixed working frequency equal to that of the first at rest: i.e. when the hand is distant from the antenna.

The harmonic signals of the two oscillators are fed into a mixer. Radio technology teaches us that the mixing of two harmonic signals produces a third with a frequency equal to the sum of the frequencies of the first two, and a fourth whose frequency is equal to the difference between them:

f1 + f2 = f3
f1 – f2 = f4.

This technique is known as beat generation, in which the beat is the result of the mixing of the two harmonic signals.
As said above, if the working frequencies of the two harmonic signals are similar, the signal difference falls within the audible range: i.e. a low-frequency signal is generated. For example, if we set the working frequency of oscillator 2 at 200 kHz (f2) and adjust oscillator 1 in such a way that the movement of the hand varies f1 from 200 to 198 kHz, the beat of the mixer output (f4) will vary from 0 to 2 kHz: i.e. an audible signal.
It is important to note that the mixer is the real heart of the theremin insofar as it does not merely produce a simple audio signal but, as we shall see, also determines the waveform that is the voice of the instrument.

The characteristics of the volume oscillator are the same as those of pitch oscillator 1: it uses radio frequencies and controls working frequency by means of an antenna. The only difference is the different working frequency (usually about 350-400 kHz) in order to avoid interference with the pitch circuit.
The produced signal is filtered and demodulated in order to obtain a variable direct voltage that depends on the distance of the hand from the volume antenna, a voltage that is used to control the voltage-controlled amplifier (VCA), the purpose of which is to increase or decrease the amplitude (or intensity) of the audio signal.