Theremin: What the world’s purest sounding instrument can teach us about heavy metal music

Recommended listening: The Beach Boys – Good Vibrations

The previous instalment of this music technology series introduced some ways in which audible oscillations could be generated using vacuum tubes. The instrument featured this time also generates its sound using vacuum tubes but does so in a completely different – and highly innovative – way. 

The instrument in question is the “theremin”, which was invented by Soviet scientist Lev Sergeyevich Termen (Leon Theremin) in the 1920s. Uniquely, the theremin is operated without any physical contact with the musician; the pitch and volume of the generated sound can be controlled – seemingly by magic – using only the position of the user’s hands relative to the instrument.  It also produces a very pure sound, much like the Armstrong oscillator covered in the previous article. However, a careful (Fourier) analysis reveals that there is not just one frequency being created but also a number of additional frequencies (known as “harmonics” of “overtones”) at integer multiples of the lowest frequency. It is these additional harmonics that give the sound its distinctive warmer timbre, similar to a human voice.

There are two aspects to the theremin that warrant further investigation. Firstly, how does it detect the position of the user’s hands and use it to create a sound? Secondly, how does it create those distinctive additional harmonics? These questions can be answered with reference to Theremin’s patent (US1661058A, granted in 1928).

Regarding the generation of sound, the theremin includes two high-frequency vacuum-tube oscillators (2, 4) that operate simultaneously at about 500kHz. Although these frequencies are too high to be audible individually, the proximity of the user’s hand to the control-element (1) causes the frequency of the first oscillator (2) to deviate from the frequency of the second oscillator (4). When these two almost-identical frequencies are “mixed” together in a vacuum tube (5), an audible pitch corresponding to the frequency difference between the oscillators is produced.

The creation of this new frequency (in a process known as heterodyning) is due to the non-linear amplitude response of the vacuum tube 5. The term “non-linear” means that when the two signals are input simultaneously in the vacuum tube, they do not simply add together but also “intermodulate” with each other to create new frequencies including the audible difference frequency. Since the oscillators (2, 4) operate around 500kHz, even a very small relative change to the frequency of the oscillator (2) (due to the “body capacitance” from the user’s hand) can lead to a meaningful change to the audible pitch. This pitch is then amplified and output via a speaker, with the amplification amount also being controlled by the position of the user’s other hand in a similar way.

So, the generation of the lower pitch can be explained by the non-linear mixing, but what about the generation of all those other harmonics? Surprisingly, the answer is exactly the same – the non-linear behaviour of the amplifying vacuum-tube provides subtle distortion to the signal that produces additional harmonics in the output. According to Theremin’s patent, “the variation of the quantitative composition of the over-tones in the sound may be effected … by utilizing the curved parts of the amplifier characteristics”. What Theremin had noticed here (arguably far ahead of his time) was not just that vacuum tubes may distort input signals when amplifying them, but also that this distortion can be a good thing.

This counterintuitive fact would go on to become a critical tool for audio processing and is foundational to many genres of music. The genre that best exemplifies the beneficial properties of non-linear distortion is rock music, where almost all of the iconic guitar sound is provided by the distortion. Especially in heavier subgenres like metal, a guitar amp can transform even a gentle melody into a squealing lead guitar solo rich in high harmonics; to achieve this the amplifier is overdriven in a similar (albeit much more extreme) way to the tube amplifier in the theremin.

Rock guitarists also make particular use of the “intermodulation” property in a technique known as the “power chord” – this refers to a chord formed from two notes spaced apart by a musical interval of a perfect fifth. In exactly the same way as the vacuum tube (5) in Theremin’s patent, distorting two notes at different frequencies produces a lower oscillation corresponding to the frequency difference, and below is a video showing this in action.

The resulting weighty sound of distorted power chords arguably provides a core component of the rock genre (e.g. as heard in the guitar riffs in Deep Purple’s ‘Smoke on the water’ in 1972 or Blink-182’s ‘All The Small Things’ in 1999). Of course, Theremin would have had no idea of these later uses, especially since the electric guitar had not yet been invented and the rock genre was not established until the 1960s.

Now would be a good time to return to my song recommendation, Good Vibrations, released in 1966. This song remains one of the most expensive singles ever produced, with some estimating that it cost $50,000 at the time — in today’s money that’s more than $500,000 (or about $2000 per second of playback). This astronomical cost can be explained by its novel approach to the production process. In most music released before that time, the role of the recording engineers was simply to document the sound of the musicians, thereby leading to music that sounded comparable to live recordings. However, in the approach pioneered by musicians like The Beach Boys and The Beatles, the recording process was seen as a creative opportunity to experiment with new technology like synthesisers and combine different recordings together to produce something completely different to any live performance.

Therefore, if you are familiar with Good Vibrations, then you’ll no doubt have assumed that the ghostly whistling tone that appears in the chorus is a theremin… well actually, no. This is technically a later variant invented by Paul Tanner known as the ‘electro-theremin’. Although it produces a similar sound, it uses a controllable sine-wave generator that outputs a note at a single frequency rather than the harmonically rich combination of frequencies produced by the original theremin. As a result, although the electro-theremin was certainly able to produce good vibrations, better vibrations could have been achieved if The Beach Boys had simply followed the original design in Leon Theremin’s patent!

Unfortunately, despite its arguably superior sound, the original theremin was not a huge commercial success. This was perhaps in part due to its release coinciding with the Great Depression, but also in part due to its difficulty to play. I remember visiting a museum in Oxford where the attendant offered a prize to any visitor who could get the theremin to produce a recognisable melody.

It seems the Beach Boys could relate to this struggle; when they wanted to perform Good Vibrations live, they enlisted the help of an engineer, Robert Moog, to modify their electro-theremin to use a more tactile ribbon controller for selecting pitches. This was by far from Moog’s only contribution to the world of synthesisers, and the next instalment of this series will explore his most well-known invention, the world’s first commercially available synthesiser.

If you would like to discuss anything in this article further, or you have an invention that you would like to protect, then please contact the author, or get in touch with our patents team at gje@gje.com.