Study reveals the accidental origins of the violin

Researchers at MIT have gleaned new understanding of a centuries-old musical instrument.

Could violins, like animals, have evolved?

The answer is yes, according to a team of researchers led by MIT professor Nicholas Makris.

Dr. Makris collaborated with the violin making and repair program at North Bennet Street School to study the acoustic properties of violins and violin ancestors. Their research, which appears in Proceedings of the Royal Society A, shows that a violin’s acoustic power is linked to the shape of the holes in its body.

Perhaps more surprisingly, it also suggests that the violin’s distinctive, f-shaped sound hole came not as a result of human ingenuity, but rather a series of random mutations.

In 17th century Italy, master builders – the Amati, Stradivari, and Guarneri families most notably – ushered in the golden age of violinmaking. This era, called the Cremonese period, produced some of the most sought-after musical instruments of all time. Many players and makers assert that the quality of these  instruments are unmatched by modern successors – although that notion has been heavily disputed.

Violin design has changed relatively little since the Cremonese period. So it is surprising, to say the least, that researchers are still working to understand their intricacies.

“We have looked back over a couple of hundred years of literature on violin acoustics,” Makris says. “There are formulas, derived by [Victorian polymath] Lord Rayleigh about one hundred years ago, for the resonance frequency of circle and elliptical sound holes, but nothing for power. And that seems to sum the previous knowledge.”

Makris’ research focuses on violins, but was spurred by a different, older instrument. The lute is a medieval stringed instrument with a round sound hole. They look a little bit like guitars – except many lutes feature intricate carvings called rosettes over their sound holes. After being approached by a professional player who wanted to understand the effects of the rosette on sound and volume, Makris took the case.

In musical instruments, volume and power are related to airflow – in other words, instruments that push a greater volume of air through their sound holes will be noticeably louder. With the help of Yuming Liu, a principal research scientist at MIT, Makris’s team modeled airflow through sample sound holes. In doing so, they were able to determine the power efficiency of different lutes.

In time, Makris realized that air would flow faster near the perimeter of a sound hole and much slower at the center. So it didn’t matter if the sound hole was open or covered in rosette carvings – there was virtually no difference in volume.

Further testing on more diverse sound holes – like those of Cremonese violins – confirmed the notion that airflow was maximized at a sound hole’s perimeter and negligible in its interior.

“So more perimeter and less interior area is better,” Makris says. “That is, for the same area of wood you cut to make the sound hole, a shape that has larger perimeter and less interior area will lead to more sound generation. The circle has the smallest perimeter for the same area, and so is the least power-efficient.”

Slender f-holes minimize interior area, so they are naturally more power efficient than round sound holes of the same perimeter. As a result, violins tend to be much louder than lutes.

“One way to understand the efficiency is to think about what happens near a tall building on a windy day,” Makris adds. “It tends to be far windier at the perimeter of the building rather than some distance from the building, because all the air flow obstructed by the building escapes in a concentrated region at the edges. Something similar is going on with the sound holes of musical instruments.”

The thickness of a violin’s back plate also factors into power efficiency, the team found. Violins expand and contract as they are played, thereby generating sound within the body. As the instrument expands, it pushes air through the f-holes.

“The problem is that when the violin contracts, its body sucks air towards it,” Makris says. “This has a canceling effect on some of the air being squeezed out of the f-hole, which reduces the sound. A thicker back plate reduces this cancellation by [reducing] the expansion and contraction of the violin body, and so makes the net acoustic power radiated outwards greater.”

The finding is supported by chronology – from Amati to Stradivari to Guarneri, violins slowly developed thicker back plates and more slender f-holes. But it wasn’t so much a conscious transition as it was natural selection, Makris says.

For most of human history, instrument making was a deeply personal, individual art. Every lute and violin would have been made by hand – none could be exactly the same as another.

“We found that if you try to replicate a sound hole exactly from the last one you made, you'll always have a little error,” Makris said in a press release. “You're cutting with a knife into thin wood and you can't get it perfectly, and the error we report is about two percent ... always within what would have happened if it was an evolutionary change, accidentally from random fluctuations.”

Makris’s personal fascination with musical instruments belies him. As a professor of ocean engineering at MIT, he focuses on ocean exploration by way of acoustics, not on musical design. But according to Makris, these two interests aren’t as disparate as they might seem.

“It all comes from the same first physical principles of physics,” Makris says. “Experience in one definitely helps with intuition in the other. I think there is a tendency nowadays to overspecialize or to expect overspecialization. Go back to the times of Lord Rayleigh and you will find musical acoustics prominently at the beginning of his classic books on the mathematical physics of the theory of sound. What we have done to help understand musical instruments also answers questions about more general sources of sound, including those underwater.”

But it takes more than textbook physics to design a Stradivarius-level violin. Some, including Makris, believe there’s something almost intangible about a well-crafted instrument.

“There is something very beautiful in the natural sounds of wooden instruments that is difficult and will be difficult to quantify over a wide frequency range,” Makris says. “What we have done pertains to a lower frequency register that is an important starting point.”

Lutherie, the art of building stringed instruments, is still an imperfect study. Makris hopes his research will meet a “growing demand” from musicians who seek to understand the properties of wooden instruments.

“I think our work actually can help many players and makers with simple practical decisions about sound hole size and shape,” Makris suggests, “and perhaps also certain choices of wood type and thickness. I have also heard from violin makers who know about our findings that design changes they made based on them have led to happy customers.”

“But the makers have the magic and I try not to interfere for the most part,” Makris adds. “They know so much, but so much of their work is an art form that is not so easy to communicate. But I still try to ask questions and learn as much as I can.”

Consumer interest in luthier-made instruments has rebounded in recent years, but most players still get their axes off the assembly line. If the evolution of violins was caused by human error, could mass production halt the progress of instrument design?

“When I was younger, I could not afford to have an instrument made and had to have mass-produced ones, which clearly serve an important niche,” Makris says. "So you essentially need a portion of the population that is capable of supporting arts and high level craftsmanship to maintain progress.”

“It makes you wonder if a big corporate committee might one day be determining if change is good for sales or not,” Makris adds. “But so long as there are independent instrument makers, progress will not stop.”

[Editors note: A previous version of this story misstated the position of Yuming Liu.]