By James N. McKean

Riddle me this: What is the only part of the violin that serves absolutely no function at all—and yet, without it, the instrument can lose up to 25 percent of its value? Believe it or not, of the more than 120 parts of the violin, the only one that is completely dispensable is the scroll.

The scroll, actually, consists of two parts—the pegbox and the volute, which is the seashell-like carved knuckle that surmounts it. And while it’s perfectly true that you do need something up there to hold the end of the strings and be able to tune them, a quick glance at the truncated stub that holds the pegs on a carbon-fiber instrument shows that it doesn’t have to be a scroll.

Considering that it’s such an afterthought, the sophistication of the design that has gone into the scroll is remarkable. Looked at from the side, the curves unwind from the eye in a perfectly opening spiral, culminating in the long swoop of the pegbox, itself shaped by two curves that play off each other as they open up.

The design itself is shrouded in mystery. The first classical violins that we know of were made in the Cremonese workshop of Andrea Amati in the mid-1500s. While the design of the body has changed to some extent over the centuries, the scrolls on those first instruments have never been surpassed, and in fact rarely equaled. They combine the best of the early and late Renaissance. The positioning of the eye in the spiral, and then the balance of the volute with the pegbox, embody that centered sense of repose that is the hallmark of the great Florentine sculptor Donatello. But the interplay of the curves reflects the exuberance of the master sculptor and architect Bernini—which isn’t such a surprise, since he and Amati lived at the same time.

The balance of Amati’s design is so perfect that you can’t help feeling that there must be some system of design that was used to generate it (along with the rest of the instrument). However, there is no record at all of any system of design used by Amati, or any other maker of any note. A quick search online will turn up hundreds of models using theoretical methods. All of them, however, suffer from two fatal flaws. One is complexity. Violin makers, like other craftsmen, were almost without exception uneducated and illiterate, so any practical method would have had to be very simple. And yet all these drawings are bewilderingly intricate.

The bigger problem, though, is that they just don’t work. The most common framework suggested is the Golden Section, a mathematical division seen most famously in the proportions of the temple of Athena on the Acropolis. Another is the spiral of Vignola, found frequently in nature—the Nautilus shell being the best example. The mathematical proportions of the Fibonnacci series have also been tried. But here’s the problem: None of them can successfully generate a scroll even remotely as beautiful and balanced as the ones carved by Amati, or any of the other great makers, Italian or otherwise, such as Jacob Stainer.

While that might be frustrating for those intent on analyzing the violin, it reflects one of its greatest aspects: its essential mystery. The violin is the most efficient acoustic amplifier ever designed, and yet it was conceived two centuries before the field of acoustics was even invented. And all of the essentials of its design are there in the very first ones we know of. Alone in the field of human endeavor, it has stood relatively unchanged for half a millennium.

I once asked the great acoustician Norman Pickering, who died in 2015, if it might be possible to develop an electronic violin that could sound just as good as an acoustic. “Sure,” he replied. “If you had all the time, money, and resources of the Apollo moon program. Maybe you could,” he hedged. But then he laughed. “Why bother? Why not just use the money to hire musicians?”

A quick search online will turn up hundreds of models using theoretical methods. All of them, however, suffer from two fatal flaws.

Why bother indeed. The search for a system of design is as immensely seductive as trying to unravel all the other “secrets” of the violin. It’s easy to vanish into the vortex of compasses and fractions and French curves. But it’s like medieval doctors dissecting a brain, searching for the soul: You’ll never find what you’re looking for, but in the process, you risk losing what you already have.

Which is the pure joy of making a scroll, of unwinding all those lovely curves. There is no fun quite like it. You start with a big block of maple, heavy enough to break a toe if you happen to drop it on your foot. The scroll and the neck are all from the same block; the unique value of the scroll itself is shown by the fact that when the neck wears out or breaks, a new one is laboriously grafted on to save the original. Step by step, using saws, drills, gouges and chisels, knives, and finally steel scrapers, the scroll emerges, the delicate curves enhanced by the grain and figure in the wood.

If you hold your instrument by the neck and slowly rotate it, you will see why the fixation on the exact system of design is beside the point. You never really look at the profile; what grabs your eye is the interplay of all the curves, as they move and change, wind and unwind. And while it’s tempting to think of the scroll as pure sculpture, it’s not. It’s much more than that. A piece of sculpture is fixed in a spot; you walk around it, looking at it from this view or that. The scroll, however, is constantly in motion, always changing with the music, dancing as you play.

Rather than one of Bernini’s fluid sculptures, when I think scroll, I think Gershwin. Fred Astaire and Ginger Rogers, dancing cheek to cheek. And as elegant and technically accomplished as they might be, there’s a joy to what they’re creating that’s in a large part due to its utter irrelevance. No one needs their dancing anymore than a violin needs a scroll. But that’s not at all saying it serves no purpose. In fact, it’s essential. The scroll is there to remind you that, when all is said and done—the practicing, the auditions, the rehearsals, the colleagues and the audience, even the paychecks—in the end, like the music you make, the violin is a thing of beauty.