Of the Theremin and Futurist Stringed Instrument Making

Linearity

The critical point of even the best-made theremin remains the ability of the player to control its expressive potential. RCA’s advertising brochures of the 1930s claimed that playing theremin was as easy as whistling: but this is not really true.

The first difficulty to overcome is the absence of tactile control: there are no bows, keys or pluckable strings; only two hands that move towards or away from two antennas. The only connection between the instrument and the human brain controlling the movement of the hands is what is called aural feedback, which means nothing more than the fact that listening is the only way of knowing what note we are playing.

In order to understand these concepts better and therefore give some idea of what can be done with a theremin, a brief description of how it is played may be useful.
As designed by the inventor, conventional theremins consist of a box placed at medium height in front of the instrumentalist, who has a vertical antenna on the right that is used to control pitch by horizontally moving the right hand towards (higher notes) or away from it (lower notes) and, on the left, a roughly U-shaped horizontal antenna that is used to control the volume of the sound by vertically moving the left-hand closer (to the point of complete silence) or farther away (up to maximum volume).
The maximum pitch range is usually 3-6 octaves.
It is immediately obvious that the melody is uninterrupted, in the sense that it necessarily involves a continuous glissando between one note and the next, unless the notes are separated by rapid movements of the left hand that reduce the volume to zero between one note and the next by means of what is known as a staccato technique.
Another fundamental technique is the vibrato: in this case, rapid movements of the right wrist harmonically modify the note in the same way as a singer modulates her voice or a violinist oscillates his finger on the pressed string. By means of this technique, the already rich sound created by good circuitry becomes even more expressive… hearing is believing!

But this description gives rise to a spontaneous question: how do you know how far you need to move your right hand in order to change from one note to the next?
Only practice allows an instinctive answer, but thereminists have developed some facilitating techniques. On the basis of their knowledge of their instruments, they know that beginning from a closed fist, gradual sharp finger movements until the hand is fully open allow them to increase the pitch note by note (and obviously vice versa).

In technical terms, the physical principles underlying the theremin (i.e. the creation of a virtual capacitor between the hand and antenna) are not sufficient to put what has been said into practice because the frequency of the sound produced by the instrument is not linearly but exponentially dependent on the distance between the hand and the antenna, which means that the movement necessary to pass from one note to another in the lower octaves is much greater than that used in the higher octaves.
This situation has been electronically improved by the insertion of a large value coil (usually of about 40-50 milliHenry) between the antenna and the resonant circuit of the oscillator leads to the formation of a second resonant circuit consisting of the coil itself and the virtual capacitor. The hand movements modifying the capacity of the virtual capacitor also change the resonance frequency of the new circuit, which in turn magnifies the resonance frequency of the oscillator circuit. The final result is an increase in the extension and linearity of the produced sound, which allows the movement of the hands to produce roughly similar variations throughout the pitch range. During the design phase, the inductance of the antenna must be calculated in such a way that the inductor-virtual capacitor circuit resonates at a slight frequency than the resonant circuit of the oscillator connected to the antenna.

In addition to this increase in the linearity of the response, it is also important to underline the considerable increase in the range of pitch. When the working frequencies of the oscillators are approximately 200 kHz, the variation in frequency induced by the virtual hand/antenna capacitor is of a few hundred Hz, whereas the introduction of a second resonant circuit by means of antenna inductance allows a beat with a range of some thousands of Hz, which generally correspond to 4-6 musical octaves. It has to be said that, without using antenna inductance, a greater range can be reached by increasing the working frequency of the oscillators to 600-800 kHz but, in this case, there may be binding problems and, in any case, the linearity of the response will be completely lost.

After this technical digression, we can say that another indispensable requisite of a good theremin is its linearity of response and consequent range of pitch.
Léon Theremin understood this from the beginning and, for what is here called antenna inductance, he used coils that were 4-6 cm wide and had a height of sometimes more than 20 cm. They were totally wound by hand, which ensured the optimal linearity of the instrument: the RCA theremins were also built using these techniques.