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I've recently been looking into the Physics that went into the design of the first analog Theremins.

There's no doubt that the Theremin does indeed sound "off" and artificial compared to other instruments such as the violin, guitar or flute. I've been wondering what exactly the physical reason for this odd sound of the Theremin is.

Ive looked at the spectrum of a 500 Hz note played on both the violin and the Theremin and found that for the Theremin the main power lies in the first 4-5 harmonics. In the violin however there are many more excited harmonics (10-15) which carry significant power.

I was wondering if this could be the reason for this artificial sound, i.e. the Theremin sounds off because the sounds it produces are "too pure".

I would greatly appreciate it if anyone could confirm or refute this hypothesis and maybe also point to some resources which go more in depth on this topic.

Edit:

The violin spectrum; The audio

The Theremin spectrum; The audio

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    $\begingroup$ Certainly a violin produces a very harmonic-rich sound, compared to many other instruments. $\endgroup$ – Hot Licks Feb 25 '18 at 23:16
  • $\begingroup$ There is also the gliding transitions between notes. $\endgroup$ – Pieter Feb 25 '18 at 23:31
  • $\begingroup$ A french horn also has most of its power in the first 5 harmonics: projectrhea.org/rhea/index.php/Fourier_analysis_in_Music. $\endgroup$ – probably_someone Feb 26 '18 at 0:05
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    $\begingroup$ Most likely, it sounds artificial because you've been told it's artificial. If you had gone your whole life without hearing a french horn, and then heard one for the first time without being told what it was, I would bet that you would think it sounded "off", too. $\endgroup$ – probably_someone Feb 26 '18 at 0:10
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Comparing the Fourier transforms of various instruments is indeed the right idea, as a difference in the amplitudes of various harmonics does lead to a difference in timbre. So the answer to the question, "Why does the theremin sound odd?" is in some way answered by the Fourier spectrum of its sound. But the answer is a bit more complicated than "it has most of its power in the lower harmonics." For example, the french horn at moderate volume also has most of its amplitudes in the lower harmonics, which gives it the characteristically sweet, pure tone that it's known for. But we don't think of the french horn as sounding artificial.

So what makes us think of something as artifical-sounding? The answer is most likely just that we haven't heard an instrument with a similar set of harmonic amplitudes before. The definition of "similar" is quite complex, as our ears are characteristically more sensitive to higher frequencies, and so the particular arrangement of the upper-harmonic amplitudes plays an inflated role in the determination of the timbre. But the point is that it has very little to do with the actual design of the instrument itself, as instruments with very different designs can have very similar Fourier spectra, and thus, very similar timbres.

One point that I would like to make clear is that it doesn't have much to do with the theremin being electronic. As an example, here's another instrument that is played in a completely classical way that sounds just as artificial as the theremin: https://www.youtube.com/watch?v=i5KiodkF2m4. The instrument is known as the "musical saw," and is literally just a carpenter's saw being played with a violin bow. If you grew up listening to the singing-saw music in Dmitri Shostakovich's opera "The Nose," when you first heard the theremin, it wouldn't sound odd or artificial at all - it would sound just like the singing saw you were used to!

So the precise reason for an instrument sounding artificial is not really a function of any particular aspect of its design; rather, it's a function of you personally being used to a particular repertoire of Fourier spectra. When an instrument comes along that, for whatever reason, has a substantially different Fourier spectrum, then you'll perceive it as sounding artificial. Answering the question, "What particular instrument designs produce Fourier spectra that are substantially different than what we're used to?" isn't really possible, as there are an uncountable variety of different designs, and even an uncountable variety of types of different instruments you could conceivably make. For example, if you took a cavity of exactly the right shape and blew some pressure-modulated air into it, you could make a wind instrument that would sound exactly like the theremin.

Likewise, you could take a purely electronic instrument like a theremin and, by manipulating the particular arrangement of the harmonics produced, make it sound exactly like a violin.

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  • $\begingroup$ Comments are not for extended discussion; this (very interesting) conversation has been moved to chat. $\endgroup$ – rob Feb 26 '18 at 15:25
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I would have thought that the answer to this question lies in the humanities or social sciences, rather than physics.

Physics of course can describe the quality of the sound produced by a theremin, but it cannot account for it's perceived "oddness".

I would punt that one of the reasons humans dislike sounds that are "too pure" is because they have a quality that is simply unfamiliar to the ear. And theremins (or sounds similar to them) have often been used in contexts that imply menace - such as in depictions of aliens landing.

But another way of conceiving the same quality of "purity" is that the sound lacks complexity, and therefore people find it easy to analyse, and in turn shallow and unstimulating. An instrument that imposes purity also means that players lack the ability to be "expressive" (a byword for subtle auditory complexities and variations) and therefore lack the ability to compose more satisfying pieces.

A related point on "purity" is that appreciation of music has a certain aspect to it which is related to the difficulty of production and respect for the skill of a musician. People may appreciate purity when they know it implies difficult-to-achieve precision, but less so when it implies rank simplicity and lack of difficulty.

Another thing I've noted about theremins is that they have an amplitude control that is unlike any mechanical instrument. They produce a sound that fades in and out as if someone has their hand on the volume control of a speaker - which of course is exactly how they work, but that gross control of volume is not a familiar technique in playing a musical instrument - and again, the control it exerts is "too pure".

As @Pieter notes in the comments, there is also a perfect glide between notes. Some instruments are fretless, but very few are played consistently in a fashion that gently blends between every note - most pieces of music have at least some sharp transitions.

A related point is that theremins tend to have no apparent "beat" (if played on their own outside a band of other instruments), and there tends to be no apparent percussive element to each note (which even fretless instruments can have on account of how they are plucked or otherwise played). Rhythm is an important and pleasing aspect of music.

Those are my off-the-cuff thoughts on the matter, anyway.

I would remark in closing however that perfectly good and pleasing music has been created with a theremin, with no apparent odd quality when it supports other instruments. "Good Vibrations" by the Beach Boys is an example - apparently, Brian Wilson used to refer to the theremin as "that damn woo-woo machine".

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    $\begingroup$ "That gross control of volume is not a familiar technique in playing a musical instrument" - any wind instrument player will vehemently disagree with you here. "Very few [instruments] are played consistently in a fashion that gently blends between every note" - this is a function not of the instrument's design, but rather of the particular playing style. I would argue that it's quite common for "normal" instruments to allow this gliding (especially if you count the human voice), and the only reason we don't hear it more is because Western musical tradition mandates sharp transitions. $\endgroup$ – probably_someone Feb 26 '18 at 1:07
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    $\begingroup$ I'm also not entirely sure what you mean by theremins having no "apparent beat." If you mean that a solo theremin performance inherently lacks rhythm due to the design of the instrument, there are plenty of examples to disprove that. Here's one of Bach's Goldberg Variations being played on a trio of theremins, in which the rhythm of the piece is clearly discernible (youtube.com/…). $\endgroup$ – probably_someone Feb 26 '18 at 1:22
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    $\begingroup$ Regarding theremin notes having no "apparent percussive element" at the beginning of each note, neither do violins, so that seems like an odd criterion to choose to separate normal and abnormal instruments. In fact, the Goldberg Variations arrangement above was originally written for a string trio, and the theremin was able to adapt it quite well. But assuming you still want to keep that criterion, it is definitely possible to articulate notes percussively on a theremin, as this demonstration shows: youtube.com/watch?v=VsMQXdHCVFk $\endgroup$ – probably_someone Feb 26 '18 at 1:26
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    $\begingroup$ Ah, but that's the whole reason I replied. You're taking the stance that most people think the theremin sounds odd because of some aspect of the design of the theremin, when it's far more likely that people think the theremin sounds odd because it's constantly enlisted to play pieces that sound odd. $\endgroup$ – probably_someone Feb 26 '18 at 1:41
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    $\begingroup$ The fact that acceptable pieces are extremely difficult to play is also a quality that the theremin shares with the violin. One could even argue that the violin is even harder to make acceptable sounds with, since in addition to the finger-positioning practice that the theremin and violin both require, the violin requires in addition several years of bow technique to avoid being a squeaky mess. So why doesn't the violin only play odd pieces, if it's so difficult to play an acceptable piece? $\endgroup$ – probably_someone Feb 26 '18 at 1:50

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