PHY 212 Net Research Project for 2/23/04

LC Resonance in Music

Leon Theremin was a Russian physicist who is credited with invented many innovative electronic devices. However, he will probably be remembered primarily for inventing the world's first electronic musical instrument. It was dubbed the theremin when he brought it to America in 1927. He spent many years in Europe and the United States touring with an "orchestra" of theremins until he disappeared (possibly kidnapped by the KGB) just before World War II. Theremin was a well-liked, affable character who never quite understood man's social constructs. (Yes, he did look a bit like Tesla and was undoubtedly just as peculiar in his own way.) While in the US, he fell in love with and married Lavinia Poole-Williams, a dancer in the first black ballet company in America. His seemingly blissful marriage ended when he mysteriously disappeared a few months later. He wasn't heard from for nearly sixty years! There are numerous web sites which describe various aspects of the fascinating history of this man. For starters, check out Robert Moog's description and history. (Moog, one of America's first innovative techies, invented the synthesizer. This page was probably created in the first few years of the internet!) Also look at the 1989 interview with Theremin by Olivia Mattis. For a real treat, watch the award-winning film documentary which is available on both VHS and DVD. This is one of most interesting, moving and well-edited documentaries I have seen. If you have a DVD player, you may borrow my copy. (A small blood sample may be required for security purposes.)

Although you may never have heard of the theremin, you have probably heard the theremin. It is the source of the "eerie music" that has been used in many horror and sci-fi movies since Theremin brought his instrument to America. It has shown up periodically in the music scene, from the famous early recordings of theremin virtuoso Clara Rockmore (the premiere protege of Leon's) to the current Led Zepplin tour. Even the P-Funk band, The Politicians use the theremin on one track.

What makes the theremin different from any other instrument is that you don't physically touch it! Look at the photos of Leon and Clara. The left hand (near the loop antenna) controls the volume while the right hand (near the straight antenna) controls the 5 octave range of pitch. This is a very difficult instrument to play since even slight movement creates a noticeable change. Clara Rockmore would change pitch primarily by changing the shape of her hand. You would see her translate her right hand only during changes in octave.

To understand how the theremin works, you need only a basic understanding of resonance in LC circuits. As you are learning this week, the there is a natural angular frequency of oscillation in an LC circuit given by . If you change either L or C, the value of the frequency will change. Consider control of the pitch of the instrument. As the right hand moves, one of these quantities changes (see question #3 below). This changes the resonant frequency of the circuit and it is this frequency that determines the pitch that you hear. The volume is also controlled by the changing resonant frequency in the "left hand" circuit, but how that is done involves a bit of clever circuitry.

The hand actually makes only a very small contribution to changing the L or C value in the circuit. This means the hand can make only a small fractional change in the frequency. Yet the theremin's 5 octave range (~100 to 3200 Hz) represents a factor of 32 change in frequency! So how does the theremin achieve this feat?

It does it in the same way your FM radio tuner extracts the audio signal from the carrier wave. Isle 95 broadcasts at a carrier wave frequency of 95 MHz (95.1 actually). That means the wave frequency is 95 MHz when there is no audio signal (those moments of silence between songs.) When music is present the broadcast frequency ranges roughly from 94.09 to 95.01 MHz, covering the 20,000 Hz range for sound. (Actually there's two stereo channels to broadcast and the full range is closer to 15k, but you get the idea.) This represents a measly ±.01% change in frequency! Your FM radio generates its own steady 95 MHz carrier frequency (that's why you are asked to turn it off during airplane takeoff and landings) which is electronically mixed with the broadcast wave. The difference of these two waves leaves the audio signal (remember beat frequencies?), which is then amplified and sent out to the speakers. The theremin uses this same technique. (See the bonus question!)

For those of you with a little more experience with electrical circuits, you might want to check out a hand scribbled schematic for one of the newer transistor designs . See if you can identify the LC oscillation portions of the circuit. If you'd like to hear what it sounds like, I have stored a sound sample by Denny Genovese of the Southeast Just Intonation Center on the WebPhysics server. The download time should be short, but the computer you are using may or may not have the software to play it. (Give it a try. If it doesn't work, drop by my office and I'll play it for you.) You should also check out MouSing to turn your computer into a theremin. It's totally cool, but it only works if you're on a PC.

For a very reasonable price (unless you want a vintage version) you can buy or build a theremin. If you think you might like to become a theremaniac, a good starting point for the plethora of theremin links is the Theremin Enthusiasts Club International.

May your hand be steady and your melody smooth.

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