Structure and Interpretation of Computer Programmers

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Sunday, June 21, 2009

Reverse-engineering stringed instruments

Despite being able to play some instruments, I probably couldn’t do a good job of making any of them. I don’t have the patience required to boil a horse for long enough to stick a fiddle together, for instance. Luthiers would probably get incredibly bored by the following post but for fellow apart-takers, it’ll hopefully be quite interesting.

I once made a stringed synthesiser, when I was at college. The basic principle is that of an electric guitar running in reverse. A metal string is stretched between two bridges, and sits inside a horseshoe magnet. Now rather than plucking the string and letting the magnetic pickup detect the vibrations, we pass an alternating current through the string and use the magnetic field to cause the string to vibrate. Mount the whole shooting match on a soundbox roughly the shape of an appalachian dulcimer, so it makes a decent amount of noise. And there you go!

Well, there bits of you go, anyway. While you can drive the string at any frequency you like, it’ll be really quiet on any note which isn’t a natural harmonic – it’s being forced at one frequency, and trying to vibrate at a bunch of other frequencies, so can’t really resonate. Assuming that the materials of the string aren’t up for grabs, it’s the length and tension which choose the fundamental frequency. What you currently have is capable of playing bugle tunes. Put a few different bugles together and you can play chromatic scales, so putting a few different strings together increases the likelihood that our synthesiser has the ability to play some notes in the tune we want.

In fact, it’s still going to have a fairly nasty volume characteristic, because most of the noise doesn’t come from the string, it comes from the soundbox. In that regard, violins and pipe organs have quite a lot in common. But they differ in that pipe organs have one soundbox per note – the pipe itself – and violins have a single box. So it’d better be possible to get it to resonate at a whole bunch of interesting frequencies, which is one of the reasons for making them (and acoustic guitars) the shapes that they are. Now what the real acoustic characteristics of a fiddle body are, I’m not entirely sure. But what I do know is that a violin is surprisingly small – the “concert pitch” A pipe in an organ is a little under 40cm and the lowest note a violin usually has (a ninth lower) will therefore be almost a metre long. Even though an enclosed box like a violin needs to be half the length of an organ pipe playing the same note, it will still naturally accentuate the higher frequencies that the strings have on offer because it isn’t big enough to do much else. And it’s that which gives the instruments their sound. My synth’s soundbox was cuboid-ish, so had two characteristic “loud” notes and their harmonics. The z-axis wouldn’t have resonated much as the box was on a table which absorbed the momentum.

The remaining interesting point is that the violin is forced to extract the sound from a rubbish part of the string. The bridge is both responsible for translating the motion of the string into the wood and for stopping the string from moving. The string moves most somewhere out toward the middle (it’s mainly vibrating at its natural wavelength, which is twice the length of the string) and not at all near the ends. That’s why pickups on electric guitars sound “warmer” further away form the bridge. There they pick up more of the lower harmonics, but the nearest pickup (and the bridge) get proportionally more of the higher harmonics.

posted by Graham Lee at 19:47  

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