What makes the world's great violins from Italian masters like Stradivarius and Guarneri sound so good? Researchers say it's down to something not there, the wood that's been cut away for the instruments' signature "f holes."

Those are the distinctive curled holes in the violin's surface out of which the sound created within from the bowing of the strings escapes, researchers at the Massachusetts Institute of Technology explain.

The scientists conducted experiments in the lab to see how air flows from the f-shaped holes of hundreds of violins made in the 17th to 18th centuries in Cremona, Italy, where the acknowledged masters of the violin craft, the Guarneri, Stradivari and Amati families.

After studying technical drawings, CT scans and X-rays of the instruments to determine how air flowed through the holes, they found that the length of the perimeter of the holes, not the width, and the strength of the violin's back plate opposite the holes had the biggest impact on sound quality.

The shape of the violin's holes may have gradually evolved to create improvements in acoustic power, the researchers report in the Proceedings of the Royal Society A.

When sound waves escape from the violin, "most of the airflow is coming around the edges" of the holes, says lead author Nicholas Makris, an engineer at MIT.

That means the longer f-holes could produce a stronger sound than the rounded sound holes of medieval fiddles and lyres, ancestors of the violin, the researchers say.

Over a period of almost 800 years the sound holes of stringed instruments evolved from a simple round hole to a semicircle, and from there to a c-shape that gradually grew more elongated, finally arriving at the f-shape sound holes of the violin. Testing shows the sound that comes out the narrow f-shaped holes is louder at lower frequencies than it is coming out through round holes because the air accelerates faster, making a sound difference the ear can pick up.

While the Italian violin makers obviously had a good ear for the best violin sound, whether they understood the exact design requirements needed to create that sound is not clear, the researchers say.

"People had to be listening, and had to be picking things that were more efficient, and were making good selection of what instrument to replicate," Makris says. "Whether they understood, 'Oh, we need to make [the sound hole] more slender,' we can't say."

Even tiny differences in the length of a violin's f-hole can affect its acoustic power, the researchers say, which could explain why Amati violins, with shorter f-holes and less reverberating power, are preferred in small chamber ensembles while Guarneri violins, with longer f-holes and more resonating power, are the choice of most musicians when playing in larger ensembles or in concert halls.

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