Roll Over, Segovia – research on physics of guitar design
A scientist turns up the volume on classical guitars-without using amplifiers
A GREAT GUITAR IS LIKE A beautiful woman–no, really, it is. Antonio de Torres Jurado, the 19th-century Spanish carpenter who gave the acoustic guitar its modern form, is said to have been inspired by the figure of a young woman in Seville. Torres made the guitar much larger than it had been before, especially in the hips, and thus made it loud enough to compete at a time when it was rapidly losing market share to the piano. He stiffened the vibrating top plate of the guitar, the thin and all-important soundboard, with internal struts that fanned out from the sound hole like the pleats of a skirt. Today the finest classical guitars are still made according to Torres’s basic design, by individual craftsmen toiling in garden-shed workshops that smell of sawdust and shellac.
Like living organisms, no two guitars are the same, and each one is made of living material: wood. “That’s the problem,” says physicist Joe Wolfe of the University of New South Wales in Sydney. “Wood is not a predictable material.”
A guitar is very like a woman, then (oh, all right, or a man)–but it is also, to a physicist, like a bunch of pendulums connected by springs: It is a system of coupled oscillators. The first oscillator is the string, but a plucked string doesn’t move enough air to emit much of a sound. So the bottom end of a guitar string is attached to a hardwood bridge, which transmits the vibration to the top plate, which transmits it to the rest of the guitar, which transmits it to the air in and around the instrument. Together these oscillators augment the string’s feeble output and make it audible.
Their coupled motion patterns are very complex, and each note on the guitar corresponds to a particular pattern. But each vibration pattern is made up of a sum of simpler vibrations, called modes. Play an F sharp on the bass E string, for instance (or a G, or G sharp; it depends on the guitar), and the whole instrument will swell and contract like a balloon, albeit indiscernibly, with the top and back plates moving a few microns closer and then apart, roughly a hundred times a second. About an octave higher–at the fourth, fifth, or sixth fret of the D string–the top and back plates move roughly twice as fast, at 215 hertz or so, but now they move in parallel, forward and back at the same time. Another octave or so higher and the bottom end of the soundboard inflates, while the neighboring area next to the sound hole deflates, and vice versa.
The soundboard is the most important source of sound on a guitar, and so selecting the wood for it takes care. It has to be so light that a vibrating string can move it, and stiff enough so that it won’t pollute the sound with a wobbly mess of overtones. It is usually spruce, sometimes redwood or cedar. A tree that has grown slowly on cold mountain slopes works best, because slow growth, with its closely spaced rings, ensures more even properties. A good luthier picking a board will flex it with his hands and rap it with his knuckle; the sound it makes is an indirect indication of its density.
But even the best luthier will not get perfectly consistent results. “Each piece of wood is a bit different,” says Wolfe. “One piece turns out to be a bit stiffer than the last piece from the same tree. You make something exactly the same shape and size, using the same techniques, and you measure it and one of the resonance frequencies is up to hertz, and another one is down to hertz. And it’s a completely different instrument.”
This lack of reproducibility makes it difficult to do a controlled experiment in luthiery–you can never be sure of changing just one thing about a guitar and holding all the other variables constant. That’s one reason luthiers as a bunch are not scientifically inclined; another is that a lone craftsman producing only one or two guitars a month can’t afford to do a lot of experimenting. “The way guitars are made is to formula,” says Rob Armstrong, a luthier in Coventry, England. “There is nobody questioning what’s going on.”
Armstrong is an exception; he has been helping Owen Pedgley, an industrial designer at Loughborough University in England, design a guitar made of injection-molded polycarbonate. Another, more controversial freethinker is Michael Kasha, a chemical physicist at Florida State University and a member of the National Academy of Sciences. Kasha got interested in guitars 35 years ago, when he looked inside his 8-year-old son’s instrument with a bicycle mirror and was horrified by what Torres had wrought–specifically, by the symmetrical fan of internal struts that are glued to the inside of the top plate. “The traditional soundboard, which was arrived at by accident and never changed,” Kasha explains, “has no tuning from bass to treble.”
Kasha’s theory is that a soundboard vibrates in local modes: The treble strings stimulate more vibration on the treble side of the plate, and ditto for the bass. “People say the whole soundboard vibrates together, but it’s not true,” he says. “When you drive it locally, it vibrates locally in the predominant pattern.” It follows that you should be able to tune the soundboard to respond optimally at a range of frequencies by dividing it into resonating zones of varying diameters. Torres’s fan bracing doesn’t do that; it divides the soundboard into more or less equal areas. The result, Kasha says, is that many notes are not brilliant: The fundamental frequency of a note doesn’t dominate the overtones. Kasha’s radically asymmetrical design, in which the struts are in a herringbone pattern and the sound hole leers from one corner of the guitar like the eye of a Cyclops, is designed to be brilliant.
Although a few luthiers have followed Kasha’s precepts, and at least one stirring recording has been made with his guitars–Kurt Rodarmer’s guitar version of Bach’s Goldberg Variations–Kasha has not really shaken the Torres tradition in three decades of trying. And he certainly hasn’t convinced other physicists. They question his basic theory (“The notion that there’s a bass side and a treble side to the top plate–there isn’t any such thing,” says Bernard Richardson, a physicist and guitar-maker at the University of Cardiff, Wales) and fault him for publishing no experimental evidence. Lately Kasha has been testing guitars, including those of top luthiers, in an anechoic chamber, and he says he will soon publish measurements that will demonstrate the superiority of his design. One famous maker is going to be especially shocked, Kasha thinks: “His basses are woofy. They have no fundamental at all.”
That particular luthier has said that the inspiration for his successful design came to him in a dream–which is perhaps an indication of one of the obstacles faced by anyone hoping to organize a scientific revolution in luthiery. Last August Kasha spoke at a guitar festival in Healdsburg, California, that was attended by many luthiers. “There was a panel discussion,” he recalls, “and one of the guys on the panel was a pure mystic. He said, `These are things beyond man’s ken–only God can understand these things. We have to go by the spirit of the music.’ Well, I’m not a mystic.”
Even if it were possible to banish mystics, there is another reason luthiery will always remain more of a craft than a science: Tastes differ. Kasha may have succeeded in making guitars sound more brilliant, but some people find his guitars loud. There is no such thing as a perfect guitar, says Richardson: “Saying that you’re going to produce the perfect guitar is like saying you’re going to produce the perfect wine from a batch of chemicals.” Or Juliette Binoche from scraps of flesh and bone. Beauty, after all, is in the ear of the beholder.
COPYRIGHT 2000 Discover
COPYRIGHT 2000 Gale Group