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Classical musicians and music lovers believe that prized string instruments are enriched by the generations of virtuosi who have played on them. In the case of the great Cremonese instrument maker Antonio Stradivari, whose violins and cellos have been the choice of the world's best musicians for three centuries, this belief is coupled with the theory that Stradivari was an inimitable genius on the scale of Mozart and Beethoven. What else could explain why Stradivari's instruments remain the best in the world so long after the death of their creator?

Try varnish. That's the theory of Joseph Nagyvary, a professor emeritus of biochemistry at Texas A & M University. In a study published last week in the scientific journal Public Library of Science ONE, Nagyvary argues that Stradivari probably had no idea what made his instruments special because the crucial factor, an externally applied varnish on the wood, was beyond his apprehension or control. (See pictures of things money can buy, including a violin.)

Using the ashes of minute wood samples, Nagyvary analyzed the chemical makeup of violins made by Stradivari and a contemporary Cremonese maker Giuseppe Guarneri del Gesù, whose violins are thought to be near equals to Strads. The ashes of the Strad's wood contained numerous chemicals — most notably borax and chromium — that suggest it had been aggressively treated with a varnish designed to protect against infestation. The analysis also found that the organic matrix of Stradivari's wood was damaged and weakened, almost certainly by the application of the mineral preservative, leading Nagyvary to speculate that the wood's porous quality allows Stradivari instruments to resonate with a rich, powerful tone.

"There is a possibility here that Stradivari received the wood pre-treated and so did not even know these minerals in his wood were the crucial factor for the sound, and this is why, despite almost surely having apprentices, the art of his instrument making was not passed on," he says.

Nagyvary believes this evidence upends the widespread belief among instrument makers that only the strongest wood can produce a lush, full sound. According to Nagyvary, the opposite is true. He also says it casts doubt on the working hypothesis of many scientists that Stradivari worked during Europe's "little ice age" of the 15th-17th centuries, in which low summer temperatures led to slow but uniform growth in the Spruce trees used for instruments, and that the wood's uniform density explains the instruments' high quality of sound. Last year, researchers in The Netherlands and the U.S. used medical imaging technology to confirm that the wood came from slow-growing trees, and researchers in Sweden have argued that Swedish Spruce in the country's cold North are the closest specimens Europe now holds to the wood of the Stradivari era. But Nagyvary doesn't believe the growing conditions of local forests to be an important factor.

"The problem with the Little Ice Age Theory," he says, "is that the same wood was available to French, German and other violin makers in Europe, but only instruments made in Cremona were any good. I believe that's because of the special, preservative varnish used there."

Perhaps. But American concert violinist James Ehnes says that while varnish may be one of the keys to Stradivari's greatness, it can't be the only one, for the simple reason that not all Strads sound the same. Ehnes recently released a DVD, Homage, in which he performed on 12 instruments in the Fulton Collection in Seattle — probably the greatest collection of Stradivari and Guarneri violins in the world. Each Strad had its own voice, he says, although there also existed a "family resemblance" throughout the collection. "When I played these instruments I got the feeling that there were a thousand reasons why they were so great. There will never be one secret," he says.

For musicians, the debate over what defines the Stradivarius sound and the underlying causes for this uniqueness may soon be academic, as private collectors drive the price beyond their reach. "The era when musicians could afford their own Strad is coming to an end," Ehnes says. The concert violinist Cho-Liang Lin says the Stradivarius he bought for $300,000 25 years ago is probably worth $3 million now. He points to the sale of recently deceased cellist Mstislav Rostropovich's Duport Stradivarius, which trade publications recently put at $20 million. "There's no way even a highly successful young musician could afford that," he says.

But Lin's dismay is tempered by excitement over a new generation of instrument makers who, utilizing research by Nagyvary and others, are producing violins, cellos and violas almost indistinguishable in quality from a Stradivarius. Lin himself often plays on a violin made by a Brooklyn-based luthier, Sam Zygmuntowicz. Idaho-based cello maker Christopher Dungey has made instruments for the world's top cellists. Lin says, "We don't know whether the modern instruments we're using will be, after 100 years of vigorous playing, equal to Stradivarius. They already sound pretty darn good right now."

Yet even if scientists were to establish a unified theory for Stradivari's greatness, musicians will always be inclined to spiritual explanations that reflect the numinous and otherworldly qualities of classical music itself. In October 1987, my father, Lynn Harrell, a cellist, performed at London's Royal Festival Hall a week after the death of Jacqueline du Pre, the beautiful and extravagantly talented British cellist whose career was cut short at 28 when numbness in her fingers turned out to be Multiple Sclerosis, a disease that eventually killed her. It was an emotional experience: by that time, my father was playing one of du Pre's cellos — a 1674 Stradivarius — and he was due to use it to perform Edward Elgar's Cello Concerto in E Minor, a piece of barely restrained mourning that took on added power in the memory of du Pre's playing. "I dedicated the performance to her," my father recalls. "For years after I bought the Strad I could hear Jackie's [artistic] voice when I played, especially when I played Elgar. Perhaps all the hours she spent working on projecting a certain coloring and style minutely warped and changed the wood so that it more readily put forth her particular style. I don't know. But I'm sure of this: her musical presence remained in that instrument."

See pictures of the New York Philharmonic Orchestra playing in North Korea.

Read a TIME story about Stradivari.

• Eben Harrell
• The maker of the most prized — and expensive — violins and cellos in history may not have known the secret to their exquisite sound