The physics of fiddling

Isaac Stern, master of the complex physics of waveform generation, vibrating wood, and acoustical analysis, died last month.

Stern, of course, didn’t think of himself in those terms: he thought of himself as a violinist. But violins are remarkably complex devices.

On the surface, they look pretty simple: the bow vibrates the strings, which vibrate the violin, which sets up a sound wave which impacts on the listeners’ ears.

The details, however, are much more complex. To begin with, the bow doesn’t vibrate the strings smoothly. Instead, it alternates gripping and slipping. As a result, the string is actually divided into two straight-line sections with a kink between them, which moves along the string at the frequency of the pitch: for example, 440 times per second for the note A.

It’s not easy maintaining this kind of wave without destroying it. Beginning players can’t, which is why beginning players are painful to listen to. Skilled players like Stern, however, control this complex waveform with ease.

Another element in the sound is the vibrato, produced by a gentle, sideways flexing of the left hand. This changes the string’s length, and hence its pitch, so that the sound actually moves back and forth to either side of the “correct” pitch rather than clinging to it tenaciously. This makes the sound more interesting to listeners.

The strings’ vibrations are transferred to the front plate of the violin via the bridge. The front plate of a violin is usually carved from a solid block of fine-grained pine. Pine is also used for the sides, while the back plate is usually made of maple. The front plate includes the beautifully shaped “f-holes,” which alter the way the plate vibrates, affecting the instrument’s tone, and more importantly, boosting sound output at low frequencies. The shape and size of these holes is key to the instrument’s tone.

Inside the violin, close to the feet of the bridge, is the sound post, a solid rod connecting the back and front plates. The force exerted by the bowed strings causes the bridge to rock back and forth on the sound post, resulting in a larger vibration of the front plate and a louder sound. There’s also a “bass bar” glued underneath the top plate, which dampens some of the smaller vibrations, also strengthening the violin’s sound.

Every violin’s sound is unique because violins are enormously complex shapes. Every object has resonant frequencies at which it vibrates freely. But violins are so complex they have an enormous number of resonances–and as the pitch of the note being played varies, these resonances are activated at random. The result is that the sound quality of even a single note is changing all the time, keeping the ear constantly interested.

Some experts believe that Stradivarius violins and other great old instruments sound much better than even exact modern copies because of some lost “secret.” Some have suggested it was the use of carefully seasoned wood, because the way wood vibrates changes with the amount of moisture in it–but measurements of the growth-ring patterns in the wood of a Stradivarius show that the makers sometimes use planks of wood that had only been seasoned for five years. (Of course, now that wood has been seasoned for 300 years. Maybe modern violins will sound just as lovely in three centuries.)

Others have suggested that there was something special in the varnish. But ultraviolet photography shows that the varnish used on the Stradivarius violins is simply ordinary carpenter’s varnish of the day. In any event, most of these old instruments were revarnished in the 19th century. They were also altered in other ways–with stronger sound posts, for instance–to make them better solo instruments, which means most old violins don’t sound at all the way their makers intended.

There is, then, no strong scientific evidence that Stradivarius and other great violins of the past are significantly different from the best violins being made today. But the lack of scientific evidence really settle the question. The human ear and the human brain can detect nuances of sound that machines can’t. Maybe there really is something unique about a Stradivarius.

Or maybe there’s just something unique about people like Isaac Stern.

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