Fiddle Physics
POSTED 27 SEP 2001


The science of music

The science of art

Isaac Stern, shown playing his violin in his New York studio in this Jan. 28, 1997 file photo, died Saturday, Sept. 22, 2001. Stern, the master violinist who saved Carnegie Hall from the wrecking ball, was 81
AP Photo/Adam Nadel



Brown wooden violin with a label reading "Copy of/Antonius Stradivarius/Made in Germany."
Courtesy National Park Service






click to listen
To sustain a note, a musician uses "slow bowing," pulling the bow across the strings near the bridge. Sure, it sounds simple, but if the bow moves even slightly away from the bridge, the result is less than pleasant -- causing even obsessed Why Filers to question the limits of their scientific and musical curiosity. The sound deteriorates further when the bow is moved further from the bridge.

All musical performances by Suzanne Beia, School of Music, University of Wisconsin - Madison.


click to listen: wolf tone
It comes as little surprise that the better the instrument, the better its ability vibrate and create a pleasing tone. On the flip side, better-vibrating instruments are prone to the dreaded "wolf tone." This happens only when playing certain notes and involves a sound so unpleasant that would be foul even to Why Filers deafened by years of listening to atonal compositions from blasting headphones. Interestingly, humid conditions make wolf tones more common.



close-up of Stern playing the violinIsaac Stern is dead.
Violin is alive.

Stern, who died this week at age 81, was one of the great violinists of the 20th century, a master who could coax sounds of unbelievable subtlety and intensity from an odd-shaped wooden box with four strings.

All of which got us Why Filers asking a basic question. What is the relation between bow, string, violin body, and vibrating air? How does a violin make noise -- or music? Fortunately, just as flutes lure lobster-lovin' biologists, fiddles attract physicists.

We talked with Colin Gough, a professor in the department of physics and astronomy at the University of Birmingham (United Kingdom) about the problem. Gough, a might-have-been violinist who opted for science instead, wrote an elegant description of violin physics.

Sounds good
The best way to understand how an object makes sound is to bake it tackwards. Violin sits with bow laid across it.Sound reaches the ear as repeating waves of compressed and decompressed air. These sound waves are created by something vibrating -- the vocal cords of Howlin' Wolf, the tongs of a tuning fork, the body of a violin. The violin body is stimulated to vibrate by the bridge, which is wedged under the vibrating strings. The strings, in turn, are moved by the bow.

If we want to fake it torwards, the arm moves the bow, which moves the strings, which moves the bridge, which moves the violin body, which moves the air, which moves the ear drum, which makes nerve signals, which cause the brain to instruct the parental yap to whine, "Keep practicing! You're a tad flat!"

Either tay you wake it, sound production starts with the bow's slip-and-grab act on the string. As Gough explains, the bow's friction moves the string to the side. Eventually the friction is overcome, and the string slips. The bow grabs again, and slips again, repeating the cycle.

The slip-and-grab routine divides the string into two straight-line sections with a kink, or bend, between them. This kink moves along the string as many times as the note's frequency -- 200 hertz, or oscillations per second, for the note G.

The violin family includes the viola and cello, shown in various sizes and tuning. Courtesy NASAThe violin family includes the viola and cello, shown in various sizes and tuning.

Kinky sound
Although sound waves are generally depicted as curves, the string actually transmits a saw-tooth wave to the bridge. Between the large peaks are smaller peaks that carry a subtler form of sonic information that helps set the timbre -- distinctive tone -- of the instrument and musician. These smaller peaks reflect factors like bowing pressure and speed.

Until the bridge stimulates the violin body, there is little sound, as the string and bridge vibrate precious little air directly.

It's at this point, as we factor in the astoundingly complex acoustic shape of the violin body, that things get really complicated. As you know, solid objects can resonate -- or vibrate freely -- at certain frequencies. The resonant frequency of a violin string, for example, is determined By its mass, length and tension. Similarly, the resonant frequency of a violin body reflects its size, shape and mass.

This may sound straightforward, but the sexy curves of a violin body create an uncountable number of resonances, and they give the fiddle -- in a master's hands -- its unmatchable tone.

To understand tone, we need one more factor in the equation -- vibrato. Produced by a gentle, sideways flexing of the left hand, vibrato changes the string's length, and hence its pitch.

Vibrato, a repeated fluctuation of pitch, is an important part of most music. Note the visible and audible differences between vibrato and straight tones. Musicians can vary the speed and/or the "width" of the vibrato. Width is the rate of pitch fluctuation.

click on each tone to hear the difference: fast vibrato, wide vibrato, and straight tonefast vibratowide vibratostraight tone

Sparkling sound
That alone would lend interest, for, as Gough points out, "There's nothing more boring than a sound that does not vary."

But changing pitch is just the start. "Because the violin has an enormous number of resonances, as you change frequency, you pass over these resonances at random," Gough says. "The sound quality in a single note is changing all the time, and the ear is always interested."

Over the past century or so, Gough says, scientists have come a long way in finding how fine fiddles are fashioned, and why the 17th-century Italian masterworks still sound so satisfying.

Boy playing the violinNational Institute of Health

But there's been less progress, he says, toward helping the modern counterparts of Stradivarius and Guarnari make better instruments.

The violin, he says, is so complicated, there's no way science can predict and control every resonance: "It's fairly safe to say that basically science has illuminated how they work without improving them."

Good news. Gough says there's no reason for us humans to feel inferior to electronics just yet: "The ear is probably the world's most sophisticated spectrum analyzer."

-- David Tenenbaum


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