Why has it taken 250 years for us to make musical instruments that can rival those of Stradivari? The answer, says Thomas Levenson, is a lesson in the limits of science

Sometime in the 1650s, in Cremona, a small town near the Po river, southeast of Milan, a 12-year-old boy began his apprenticeship. It took perhaps a decade, but in 1666 came the proof that his training was complete: a finished violin signed by its maker, Antonio Stradivari.

For almost 70 years more, Stradivari would produce violins, cellos and a handful of other designs - in all probably more than 1,000 instruments. (About 700 survive, though perhaps as few as 50 are in first-class condition.) These instruments, along with those of a few other makers, mostly from Cremona, are still considered the best ever made. After Antonio's death in 1737, his sons continued his work for a few years, as did his most talented apprentices. But by about 1750, it was all over. Violin making shifted to Venice and elsewhere, and the quality declined precipitously. Ever since, the Stradivari's "secret" has eluded all those who sought to emulate or surpass the champion. Only now, in the past two decades, have a number of top makers produced instruments whose quality approaches that of the Cremonese masters.

Why has it taken so long? The question takes on a sharper edge in the context of what was happening just as Stradivari honed his art. Pierre Simon de Laplace, perhaps the most beamish of Sir Issac Newton's disciples, expressed how many thought Newton's revolution would end: in the ability to "embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom". There would be no limits. Ultimately, "nothing would be uncertain".

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But if we are so smart, if science so capable, why is the musical landscape not littered with great fiddles? The answer, and the story of how modern makers have begun to crack the Stradivari problem, is an object lesson in what one can and cannot ask science to do.

The story of the violin family predates Stradivari, of course. In the mid-16th century, the violin was still seen as cheap and nasty, fit only for vulgar use. As Jambe de Fer wrote: "We call those viols with which gentlemen, merchants and other virtuous people pass their time. The other type is called (the) violin. It is commonly used for dancing." The Cremonese helped change all that, starting in the 1550s with Andrea Amati, grandfather to Stradivari's teacher. Amati and his successors developed the violin, the cello and the viola to the point where they possessed a range of expression far beyond anything the viols could produce. Stradivari continued that invention. He changed the dimensions of his violins almost every decade. In 1707, he produced a more compact version of the cello, whose basic pattern is still the standard.

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The common element in Stradivari's work, and that of the best of the other Cremonese masters, was the range of sonic colour, the tone and the dynamics their instruments produce. The immediate cause for the decline in quality after 1750 was obvious enough:in the space of eight years, Stradivari; his greatest rival, Giuseppi Guaneri del Gesu; Stradivari's former apprentice Domenico Montagnana; and Stradivari's two sons all died. Cremonese production shrank, and new materials and methods emerged. The biggest change was in the varnish. The old one was slow drying and difficult to use; the new version was spirit-based, quick-drying and easy to apply. No written recipe for any Cremonese varnishes survived, and by 1800 the formula was thought to be lost. With that, and the realisation that newer instruments did not sound that great, came the notion of Stradivari's "secret" and the start of the search. On one level, the hunt should have been simple. From the physicist's perspective there is no real mystery. The production of musical sound has been studied since the early 19th century. With the advent of modern measuring instruments, the sound of old violins can be quantified with extraordinary precision. In the effort to recreate the older sound, each element of a violin has come in for scrutiny. Stradivari's varnish has been a particularly tempting target. Texas A&M university professor Joseph Nagyvary has proposed that the varnish was made of a compound found in the bodies of insects. Mayne Coe, a retired chemist, believed that the secret was a varnish that contains tung oil. The most promising approach came from the luthier Simone Sacconi, who argued that the varnish was a version of a well-known two-stage furniture treatment: an undercoat of glue and a top coat of oil-based varnish.

Stradivari's wood has been another focus. Professor Nagyvary has argued that a fungus may have altered the wood's structure and suggested that wood used in Cremona was stored in water for long periods. Modern luthiers agree that the quality of the wood is critical. Mario Miralles and his wife, Brenda, are Los Angeles-based makers with a record of producing prized old-master copies. They get their maple from the Balkans and their spruce from Italy - always trying to find old wood to work. They recently built a copy of a Domenico Montagnana cello used by world-famous cellist Yo-Yo Ma. Mario Miralles says: "I cannot emphasise too much how important it was to find what I would consider good wood."

The wood, however, is only the start. The Miralles' approach rejects the notion that there is a single, simple physical secret that Stradivari used. What success they have had comes from a marriage of scientific discoveries, such as the exploration of the Cremonese varnish, and a dedicated re-creation of the craft that Stradivari would have absorbed in his master's shop.

The Montagnana project illustrates the process. It began with a two-week study of the original instrument, whose tone Ma characterises as robust and earthy. Mario Miralles began by measuring each component with great precision - numbers that he immediately began to change as he built his own cello. The reason: such measurements guide but deceive. An old instrument, distorted by static stresses and centuries of use, cannot be translated directly into a template for a new cello that will sound like the old. For Miralles, that is the point at which the search for Stradivari's "secret" fails. There is no law of Stradivari that in itself can generate reliably wonderful violins and cellos. The quality of such instruments turns on mastery of the variability, the intractably detailed real world of wood and time. One can know what is desired and study the methods that will produce certain effects. But it is impossible to predict exactly how the work of art that is a master instrument will take shape. "You can't be a slave to copying," Miralles says. "What we do is figure out how the old makers would have thought. We spend a lot of time looking at great instruments. We try to get close to Stradivari, to imagine we are living in his town."

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The test of that feat of imagination came when Ma brought his cello to Los Angeles to compare it with the finished copy. Miralles says the Montagnana sounded a shade darker than the new cello, the older instrument displaying a slightly richer suite of lower overtones. "I can hear the differences," Miralles says, "but it's close."

In other words, 250 years after the last Cremonese masters died, we can now produce instruments that in blind auditions rival the old ones. They do not precisely replicate a master's individual instrument, but they approach the standard of the Cremonese instruments, Miralles says. The key has been the advance of science. Advances in chemical analysis and the detailed study of violin family sound over the past 20 years have yielded the data that describe what goes into a top instrument. But ultimately, the success or failure of an individual instrument turns on the marriage of that scientific knowledge with the craft skill required to know when and how to depart from the original.

Laplace's arrogance lay in his belief that certain knowledge was achievable. He and many since have thought prediction and mastery over the material world the goal of science. But the success of some of today's best makers in producing beautiful instruments marks the limit to the extreme ambition of the scientific revolution. The best of contemporary science cannot eliminate the unpredictability that is inherent in such commonplace stuff as wood or glue. The last step in the creation of the work of art that is a finished instrument remains a singular act, as it has been since Stradivari began to learn his craft.

Thomas Levenson's Measure for Measure, Oxford University Press, explores the historical connections between music and science.

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