Digitized Stradivari: CT Scanning the World's Greatest Violoncello

In 2016, Computer Science Professor Harry Mairson received a Provost Research grant to to work on his software for classical stringed instrument design.

Last April, I got into a taxi in Cremona, the Italian city that is the past and present world center of liuteria (violin making). In the car with me was the most distinguished of travelling companions: the renowned 1700 Stauffer-ex Cristiani violoncello, made by the greatest Cremonese liutaio (violin maker), Antonio Stradivari.violin

In the very early morning, we were off to Modena and TEC EuroLab, a CT (computerized tomography) scanning facility serving the aerospace and automotive industry. But that day's client was something else. Strad's progeny, three centuries old, was due for a full-body, 3-D scan.

Accompanying us in the taxi was Fausto Cacciatori, the conservatore of Cremona's Museo del Violino. The remarkable museum that he curates serves as the home of the Cristiani, together with a collection of stringed instruments crafted by the illuminati of seventeenth-century Cremonese violin making. Also making the trip from the Museo was its CEO, Paolo Bodini, the ex-mayor of Cremona. And the Cremonese taxi driver, Luca Voltolini, is a music maven who I see regularly at Museo concerts and events.

Everyone is a little bit crazy about liuteria in Cremona. Cremona is violin making's Vatican City. And the Museo del Violino is its sanctum sanctorum, housing a treasure trove of instruments by Stradivari, members of the Amati and Guarneri families, and other luminaries of the Cremonese tradition. When Oxford's Ashmolean Museum loaned the Museo the 1716 Stradivari Messiah--the most famous violin in the world--for its tercentenary last year, the excitement shown on its arrival was palpable. You'd think that an Italian movie starlet had just shown up, with a gaggle of paparazzi in tow.

In addition, violin making is a business. Cremona has over 160 professional liutai working all over the city, in storefront workshops next to clothing bottegas, bike stores, pastry shops and cafés. The consorzio liutai (violin making association) travels around the world to sell its instruments--from San Francisco to Shanghai, Seoul, and Taipei. A violin "Made in Cremona'' carries a revered imprimatur.

The most famous violoncello of the Venetian liutaio Domenico Montagnana is called the Sleeping Beauty (La bella adormmentata). Our beauty, the Cristiani, has been sleeping comfortably in its plush, padded, strapped-in case during the hour-long drive to Modena, through the heart of an immense plain, the Po River valley. The springtime is magnificent here--lush green fields and fertile farmland, a crisp morning air with the hint of summer, amidst the Italian architecture that bestows on this country a cultivated charm and allure. It is simply a breathtaking place of sights and smells and especially sounds, and the taxi ride with this remarkable violoncello is a moment to reflect also on that magnificence.

I've been trying to persuade the Museo to CT scan the Cristiani for nearly three years. Now, after many megabytes of email encouragement, and finally my moving to Cremona for four months to make the case in person during my sabbatical, it's actually taking place. Why would a computer science professor like me be interested in doing this?

From Classical to romantic: instrument making, designing, and copying

To understand why, you first have to understand something profound about the art of violin making. Modern composers venerate Mozart, but do not aspire to write opera in the idiom of Le Nozze di Figaro. Contemporary painters revere Tiziano and Tintoretto, but don't want to paint like them. Today's scientists put Galileo in their pantheon, yet prefer to stand on his shoulders to see further--to repeat Isaac Newton's famous words--rather than stand shoulder-to-shoulder with him. But in contrast, modern violin makers aspire to copy famous instruments by Nicolò Amati, Antonio Stradivari, Giuseppe Guarneri del Gesù, and other luminaries from the Golden Age of Italian liuteria. These celebrated liutai were not copyists. They were designers.

Somewhere along the line--whether it was the ravages of the plague and consequent loss of communal knowledge, the emergence of new technologies of measurement, or social fealty towards (if not fetishism for) the past--the classical age of design gave way to the romantic age of copying. This year, Cremona's Museo del Violino featured homage to both: its storied son, the 1716 Stradivari Messiah, on loan from Oxford, was displayed next to a remarkable copy of it by Jean-Baptiste Vuillaume, the preeminent French luthier of the nineteenth century.

Brooklyn luthier Samuel Zygmuntowicz, who has made instruments for renowned American contemporary classical violinists from Isaac Stern to Joshua Bell, gave a lecture last year at New York's Museum of Mathematics, and joked that French violins slowly increased in size in the era of Vuillaume. Makers would slavishly trace each other's exacting templates, he said, and thanks to the pencil creep inherent in this copying, the templates slowly enlarged. I call that communication without understanding.

But the importance of design has slowly undergone a rinascimento, a renaissance. In 2006, a French luthier and polymath named Francois Denis wrote a book called Traité de Lutherie: The Violin and the Art of Measurement, where he described the design methods of the Italian masters. Denis showed how stringed instrument design was based on Euclidean straightedge and compass constructions right out of your tenth-grade high school geometry class--and not on rulers, graph paper, calipers, protractors, and other precision instruments of modern measurement.

It's one of the best books I've ever read: a polyglot pot pourri of art and architecture, mathematics and musicology, philosophy, history, and science. When Oxford's Ashmolean Museum had an exhibition of Stradivari instruments in 2013, its catalogue paid unmistakable homage to Francois's contribution: it read, "It is now recognized that what first distinguished Cremonese instruments from those made in other centers was a geometrical formality of design and proportion borrowed straight from the architects, painters and many other designers and craftsmen of the Renaissance."Book cover

For centuries, Euclidean geometry was the canonical way that people thought about form and structure. Every town had its own system of measure. But when craftsmen congregated from afar to construct a cathedral, depending on those metrics was a guaranteed recipe for disaster--a mathematical Tower of Babel. Geometry, on the other hand, is a language understood by all in exactly the same way. Half the distance means half. A third is a third. Parallel, perpendicular, tangent, bisector--these words mean the same thing to everyone. No one has to worry how many cubits there are in a furlong.

Software: A representation of practical knowledge

I'm an amateur violoncello maker. Enlightened by Denis's book and its recipes, I sat down to draw a violin. Hours later, I was surrounded by failure: my desk was littered with crumpled paper, the discarded detritus of defeat--nominally parallel lines that weren't, misplaced circles and intersections, and gaping holes in paper, dug from inserting the compass in the wrong place. Then I looked again at the directions from the book, and had a computational epiphany: Francois's violin recipes were just a suite of informally written computer programs.

If I designed a programming language in which to code--in practically the same words--exactly what is in his book, I would have a precise statement of his design formulas. I could get a computer to draw everything for me. I could modify the formulas, and immediately see what changed in the forms. I could experiment with designs, and use the software for historical research on stringed instruments.

The software I've subsequently put together to realize Francois's ideas I call "Digital Amati'', after Andrea Amati (1505-1577), the Cremonese maestro credited with making the first instruments of the violin family. (In neighboring Brescia, they claim it was Gasparo da Salò (1540-1609). But participating in this centuries-old controversy is not likely to produce a conclusion any more definitive than whether Grana Padano is really a better cheese than Parmigiano Reggiano.)

"Computational thinking''--a credo among computer scientists--means that complex processes can be described as algorithms. This should be music to the ears of a liutaio, who implicitly understands that in the complex constructional processes of violin making, there is an algorithmic method for everything. The design and the making of scrolls, pegboxes, rib outlines, arching--the entire geometric world of the violin is derived from the same family of Euclidean constructions you'd use to draw an equilateral triangle, a square, or a pentagon.

Programming languages don't exist simply to tell machines what to do. Well recognized as the engineering vernacular of software, they are more importantly the collective mother tongue of algorithmic ideas. In other words, programming languages provide a way for people to describe to each other what we know how to do. Like writing poetry, grant proposals, users manuals, and love letters, writing code is a way of getting your point across. Computer scientists call the relevant vernaculars "domain specific languages''. What that means is: alexandrine verse is for love letters, not for coding web browsers. Every domain of discourse, including the description of violin forms, has its appropriate language.

Stradivari’s Cristiani violoncello

The Stauffer-ex Cristiani cello, in the back seat of our taxi, is my innamorata--its beguiling form, wine-red varnish, and sublime sound. Like many old Italian instruments, it has an enchanting history. The most famous violoncellist to play it was Lise Cristiani, a prepossessing Parisian prodigy who toured the renowned concert halls of Europe to great acclaim. In an 1845 concert in Leipzig, at age eighteen, her virtuosity and charm caught the attention of her accompanist, none other than the remarkable Felix Mendelssohn. He then composed and dedicated to Cristiani his romantic Song Without Words opus 109, now a staple of the violoncello repertoire. During a subsquent and arduous tour across Siberia, having already given concerts in St. Petersburg, Lise contracted cholera, and died tragically at the age of twenty-six. The violoncello later passed through the hands of the famed London violin shop of William Henry Hill and Sons, the authoritative biographers of Stradivari, who called it "one of the most beautiful examples among the works of the great master.'' Exhibited in 1987 and again in 2004 in Cremona, it was subsequently purchased, with great joy, by Paolo Salvelli, the current president of the Fondazione Stauffer in Cremona. Thus the Cristiani has returned to the town where it was first played.

When I lived in Cremona last year, I was only among the latest in a succession of its star-struck suitors--I paid court to the Cristiani several times a week at the Museo del Violino, hoping that by careful and close observation, I could internalize all of its proportions. But the Cristiani has a problem: it's really too big for a modern musician to play--roughly 2 centimeters longer than the modern standard. (Imagine asking a pianist to play on a keyboard where the octaves are a quarter-inch bigger.) Violoncellos, originally used to play simple bass lines in church music, later became virtuoso instruments. Their size consequently decreased, giving the player access to more positions on the fingerboard. Pitch standards changed for musical performance. And string technology improved from gut to metal wound, so that string lengths could be shorter, with better resonance, and greater projection in large concert halls.corner of cello

To accommodate modern musicians, many early Stradivari violoncellos were taken apart and cut down in size during the late eighteenth century. But not the Cristiani. It stands unchanged, witness to Stradivari's revolutionary move from his earlier, big cello designs, to the subsequent instruments played by Yo-Yo Ma (the 1712 Davidov, once played by Jacqueline du Pre), the 1711 Duport played by the late Mstislav Rostropovich, and the 1707 Countess of Stanlein-ex Paganini played by the late Bernard Greenhouse of the Beaux Arts Trio. These latter instruments set the standard for the modern violoncello.

The Renaissance design method for stringed instruments is proportional: from an initial length, everything else is drawn with straightedge and compass using proportional sections. So I did a proportional reconstruction of the instrument from parallax-corrected photographs, inspired by Francois Denis's methods, and reduced its string length to the modern standard. The lower section of the instrument is shorter than in the modern Stradivari violoncello, but--automagically--all the other dimensions are, thanks to the proportional reduction, commensurate with the modern standard. Now I'm building this reduced-size Cristiani based on my design.

So are prominent stringed instrument makers around the world. I brought the drawings I did of this instrument to the Oberlin Violinmaking Workshop in 2015, an exclusive international summertime gathering of luthiers. The PDF of the drawings was used to program a computer numerically-controlled (CNC) router. About 35 sets of molds and templates were made for violin makers to take home--all of the infrastructure needed to build this old and new violoncello model.

The CT scan

TEC Eurolab is located in an industrial zone outside Modena, in a building without any architectural interest--it's the sort of place you'd expect to see a Silicon Valley startup. The rooms are high-ceilinged, open, and nondescript. The newly-installed CT machine we used came from North Star Imaging in Minneapolis, and is housed in a large, radiation-sealed room.

The scan involves calibration of the machine with the violoncello, data acquisition, and a lengthy postprocessing stage to produce the final output. A CT scan produces a 3-D image by taking the scanned object, and slicing it--like mortadella--into thousands of 2-D slices. Using software visualization tools, any 2-D section, at any angle and orientation, can be digitally reconstructed on a computer screen by selecting and rearranging the voxels (CT pixels) from those slices.

With a high-resolution CT scan, we can learn more about this remarkable instrument, and have better data to serve as a foundation for better design. Curators and instrument historians can see in full detail both the damage and the repairs that have been made over centuries--expert restoration and repair may be invisible to the human eye, but the scanner sees everything.Cristiani 3D CT image

Additionally, the scan data and software tools can help us put together what I like to call a "computational art history'' of the evolution of instrument forms, and how ideas about design migrated between violin makers in the seventeenth and eighteenth century. More and more, historians are interested in what's called "material culture'': it's not enough to know who Benvenuto Cellini worked for, or fought with--each described copiously in his famous autobiography. We should also understand what he knew about the design and making of his masterpieces. That's equally true for Antonio Stradivari.

An industrial CT scan takes much longer than a medical scan, since for higher resolution images, larger and longer radiation is required. A full working day was needed for an overall scan, including a higher-resolution focus on areas of interest: near the soundpost, the f-holes, and the scroll and pegbox. But this being Italy, we couldn't forsake lunch, and for the security of the violoncello, members of our research team were required to remain with this most famous of Stradivari instruments.

So we roughed it: our research team was served a catered lunch in the laboratory, abutting the CT scanning room. After antipasti, we had tortellini con maggiorana e ricotta, macaroncini con asparagi e salsiccia, parmigiano reggiano con aceto balsamico di Modena, all with a choice of lambrusco or prosecco, pasticcini, fruit, and coffee. "È uno lavoro sporco, ma qualcuno deve farlo'' is not an Italian idiom--I had to teach it to my Italian colleagues--literally, "it's a dirty job, but someone's got to do it.''

The first part of this Italian soggiorno is straight from the seventeenth century, and its complement is entirely modern. The former is situated in a Renaissance world of art and craft, the latter in our world of contemporary technology. But it is only our modern misperception that these are really disparate components of a disjointed story.

The 2013 film Tim's Vermeer told the story of Tim Jenison, a software engineer who became convinced that Johannes Vermeer painted his famous work, The Music Lesson, aided by optical devices. Jenison built a replica of Vermeer's studio, ground his own lenses, mixed his own paints, and reproduced the picture. In the film, he tells the famous painter David Hockney, "There's this modern idea that art and technology must never meet. You know, you go to school for technology, or you go to school for art, but never for both--but in the Golden Age, they were one and the same person.''CT example

Similarly, the Milanese musicologist Renato Meucci, at a scientific conference in October 2016 devoted to Stradivari's Messiah violin, added further emphasis to Jenison's point of view: What is needed is an expanded collaboration between historians of art and provenance, violin makers, and scientists, which together could lead to greater and more reliable insights--indeed possible if there were a commensurate willingness and openness of mind by all parties involved, and if violin expertise were welcomed with dignity into the academic world, instead of being confined to the benches of violin workshops.

Among the sainted shibboleths of the academy are the importance of interdisciplinary research and experiential learning. For years, I've groaned at the mention of either. It's hard enough to learn to do one thing well, I believe, and immeasurably harder to learn two--and, moreover, put them together. Besides, everything is experiential: there simply is no learning without doing.

But this project has forced me to put my extreme-vetted academic cynicism aside. I embarked on this work not because it was interdisciplinary or experiential. I just wanted--enormously so--to do it. In turn, it's given me a hands-on appreciation of some of the great artistic creations of the late Italian Rinascimento. And more than that. It's been a renaissance for me too.


Harry Mairson is a professor of computer science at Brandeis University. He studied mathematics at Yale College, graduating in 1978, and received the Ph.D. in computer science at Stanford University in 1984. His research has been on algorithmics, logic, and programming language theory. He was an apprentice to harpischord maker Mark Stevenson in Cambridge, England, during the late 1970s. His current research project on historically-motivated software for stringed instrument design, supported by both the National Science Foundation and the National Endowment for the Humanities, is described further at digitalamati.org.