For centuries, string instrument makers have labored in pursuit of the Holy Grail — a perfect sound. In their quest for some kind of ideal instrument, one fit to rival an orchestra, violinmakers have tried light and heavy wood, wider and narrower faces, longer and shorter necks, tailpieces and bridges and strings of many sizes and materials, and infinite varnish recipes. The smallest alterations in the design of the instrument make a sound more tinny or darker, quieter or sweeter. Even when willing to share their techniques, violinmakers have themselves been unaware of exactly how alterations in design change the instrument’s sound, and have therefore reached new sonic heights through a lot of trial and error.
A new study coming out of the department of mechanical engineering at MIT investigates the fluid dynamics and mechanics of instrument sound production. The paper proposes an answer to the long-debated question of how the violin sound has been dramatically improved over time. A violin releases sound through two holes cut on either side of its face. Shaped like an elongated letter F, these so-called “f-holes” frame the area above the bridge where the bow crosses the strings. The elegant swirls have marked the faces of violins since the 17th century, when they were carved in the workshops of the great Cremonese violinmakers Amati, Stradivari, and Guarneri. It is widely accepted that f-shaped holes, as opposed to cuts of any other shape, enable the largest, richest, most nuanced sound.
The MIT research team sought to find out why this particular geometry, in terms of the mechanics of sound production, is sacred above all others. By measuring sound holes of many instruments of various ages, they found that acoustic power increases with the length of the incision’s perimeter. In other words, the surface area of the incision does not play a critical role. Rather, the factor that determines strength of sound is the length of the hole’s edge.
The modern f-shape is like an integral sign from calculus class. It has a long central shaft with notches on either side of its central point. The tight curves on the top and bottom lead into tips rounded like dangling dewdrops. The border of this complex shape is about three times longer than that of the original 10th century circles of the fithele. Though the perimeter is long, the surface area of the opening is quite small: any violinist who has tried to peer into the dark inner body of the instrument — to read the maker’s label or spot the sound post — knows f-holes as slender windows that frustrate most attempts to see.
Over the course of the past millennium, violinmakers have slowly but surely altered their designs to shrink the surface area and expand the perimeter of the carved openings. In the 10th century, the fithele, an early ancestor of the violin, boasted two simple circular holes on either side of the fingerboard, like overlarge dimples on the instrument’s face. Two centuries later, the circles had become semi-circles, and by the 13th century, they had been pinched into C-shapes. During the Italian Renaissance, the incisions became narrow crescent moons with small orbs hanging from each tapered tip, and later a small peak was added in the middle of the crescent. Finally, in the 17th century, the crescent was twisted into a slender f-shape.
The MIT study used complex mathematical analysis to isolate the design secrets of the violin’s sound. But violinmakers have never had such objective powers of interpretation to show them which features of a sound hole enable an instrument to produce a deeper tone. How and why, then, did designs change over time?
The MIT team offers a fascinating answer. Like organisms, violins evolved. The subtle variations that have led to more slender sound holes over time are a result of random mutation, to use the genetics term, caused by craftsmen’s small errors. These inevitable mistakes — an extra cut here or there — created a range of slightly different sound holes in each generation of instruments. The next violinmaker to come along chose to model his instruments on the specimen from the previous generation with the largest sound. Over the course of hundreds of years, this random mutation and selection for the best-sounding instruments led up to Stradivari and his contemporaries, who are widely agreed to have produced the most extraordinary instruments in history.
It is interesting to note that since that golden age of violinmaking in the 17th century, sound hole geometry has remained almost unchanged. It seems as though the engine of evolution ran its natural course until it achieved the optimal solution. And then it quietly disappeared.
Cover Image: Though many of us may not think of acoustics as a science, engineers have discovered that there is a lot that goes into producing a violin’s optimal sound. Image courtesy of Damon Criswell.