Introduction to The Stradivarius Code
“Without music, life would be a mistake” - Friedrich Nietzsche
The Stradivarius Code is the result of an international dispute over the authenticity of a legendary instrument known as the “Messiah,” which was long claimed to be the best-preserved violin by the celebrated Italian maker Antonio Stradivari.[1] Since about 1872 it has been referenced in dozens of books and perhaps hundreds of articles; in 2001 the violin’s estimated value was US $20,000,000.
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Due to this disagreement, to which I have a personal connection, I spent many years in study and research that led me to determine the principles and procedures, or codes, on which Stradivari made his celebrated violins. These codes are not restricted to the violins’ bodies; I have also devised systems for recreating the designs of his scrolls, pegboxes and sound holes, and have analyzed the proportional qualities of these plus original fittings like the bridge, tailpiece, bass bar, and fingerboard, and their placement on the violin.
My findings, derived from studying instruments by this brilliant maker along with the acoustical and aesthetic knowledge of his time, have also led to the discovery of astonishing links between the laws of nature, musical sound, and Stradivari’s violins. These include a Pythagorean triangle that represents a common musical chord, a musical mode that is the structural foundation of his violins, a surprising connection between pi and an aesthetic proportion known as the “golden section,” the role of Fibonacci and prime numbers in the measurement of musical intervals, and a concrete correlation between musical pitch and foot length. Experimentation using a monochord – an instrument with ancient origins traditionally used to ascertain harmonic proportions – revealed that Stradivari violins are designed with musical proportions as their foundation, which arise from the physics of music and, consequently, from nature.
This book elucidates the lengthy process by which I arrived at deciphering Stradivari’s codes and their variants, and the final chapters give an analysis of several violins, including the “Betts” from 1704, made on the larger forms.
Given the requisite carving skills and excellent materials, a gifted instrument maker can now recreate the dimensions of these violins exactly. More significantly, makers – and others who are intrigued by Stradivari’s brilliance – will understand why his instruments exhibit such exemplary acoustical and aesthetic qualities.
Not only will The Stradivarius Code assist violin makers in making better versions of their violins derived from Stradivari models, it will aid in determining the fake “Stradivarius” violins, of which there are many.
Based on these insights, I have arrived at a conclusion regarding the authenticity of the “Messiah” and another renowned violin.
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Antonio Stradivari and his Violins
Nearly three centuries after his death at the remarkable age of about ninety-three, Antonio Stradivari (ca. 1644-1737) remains widely renowned because his violins and other stringed instruments represent the epitome of the craft and are highly prized throughout the world for their tonal and aesthetic qualities.[2] An extremely prolific maker over a roughly seventy-year span, he gained international recognition quite early; by the 1680’s his instruments were presented to the King of England, followed a few years later by orders for instruments from Cosimo III de' Medici.
Since the mid-1700’s, Stradivari’s instruments – and especially the violins – have been studied and abundantly copied by subsequent makers who have sought to learn the “secrets” of their quality and whose research includes use of the latest technologies such as computerized axial tomography (CAT) scans, laser scans, electron microscopes, and dendrochronology.[3]
Among the many renowned violinists who have played violins made by Stradivari are Giuseppe Tartini, Niccolò Paganini, Pablo de Sarasate, Jean-Delphin Alard, Isaac Stern, Erica Morini, Jascha Heifetz, Arthur Grumiaux, Itzhak Perlman, Anne-Sophie Mutter, and Joshua Bell.
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Despite immense fame within his own lifetime, little is known about Stradivari’s early life; there is no documentation that he was born in Cremona, Italy and only scant evidence that he apprenticed with the eminent maker Nicolò Amati (1596-1684), although it seems evident that he was influenced by the perfection of the instruments produced by the Amati family.[4]
Most of his instruments have been altered over time, some quite substantially. Stradivari crafted them in the configuration of the Baroque instruments of his era; eventually, nearly all that are extant were modernized by reshaping and resetting (or, more often, replacing) the neck, among other alterations. A Milanese family of violinmakers by the name of Mantegazza developed an advisory relationship with a prominent collector named Count Cozio di Salabue and is said to have regularly thinned out the plates of instruments, including those by Stradivari. Wear and tear on the instruments often leads to repairs made by thinning out a portion of a plate and inserting new patches of wood.[5] The mere act of improperly cleaning a violin can lead to a loss of varnish, and places that make frequent contact with either the player or within the carrying case are typically worn down, sometimes leading to new edgework on instruments. The back of the scroll, too, is often worn where it makes contact when the violin is set on its back on a flat surface or was slid into and out of early violin cases. The top plates of the violins are made from spruce, which is especially subject to transverse shrinkage over the years and often develops numerous cracks that require expert repair.
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Stradivari’s reputation is not without a few, largely self-serving, detractors: blind tests have pitted contemporary violins against fine 17th and 18th-century Cremonese instruments, including those by Stradivari, in attempts to prove that the mystique of these instruments is but a fallacy. Claimed results from “experiments” like these are misleading, however; it may take an excellent violinist well over a year to adjust to a fine violin, each of which, ideally, is matched with an equally responsive bow. Two bows of the same weight and length may produce strikingly different tonal results due to differences in their balance points and flexibility, and matching a bow to complement the qualities of a violin is a process that may take years of searching and trials. Furthermore, two violinists playing the same violin and bow, in the same acoustical environment, are likely to produce sound qualities that are dramatically different due to dissimilarities of technique and sound production by the bowing arm; therefore, a brief generic survey is completely inadequate.[6] Finally, many violins made after the mid-18th century are direct copies of, or strongly influenced by, instruments made by Stradivari.
Over the course of his long career, Stradivari experimented with the design of his instruments and was constrained only by human dimensions plus the physics of vibrating strings and their tensions. The increased tonal projection of his larger model instruments is due, in part, to a more sizeable resonating chamber, and later in his career he flattened out the traditional arching of the top and bottom plates. Many of the surviving materials from his workshop are now housed in the Museo del Violino, formerly the Museo Stradivariano, in Cremona, Italy.
A Controversy Erupts Over the World’s Most Famous Violin
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In the Cremonese tradition, violin makers design and use inner forms or molds for shaping the acoustical chamber of the instruments’ bodies. In 1992, the American musical instrument expert Stewart Pollens published The Violin Forms of Antonio Stradivarius. This groundbreaking book was the culmination of several years spent researching, analyzing, and documenting the materials used and produced by Antonio Stradivari and features life-sized photographs of the extant violin, viola, and cello forms, among other instrument types, plus documentation of the designs and tools used by the master maker and analysis of many of the techniques he used to fabricate the instruments.
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The forms were used to produce multiples of each instrument’s design prototype, and each part of the instrument – including the pegbox and scroll, neck, sound holes and their placement, and fingerboard – was conceived to complement this design. The extant violin forms and their accompanying designs and templates are identified by letters that include G, PG, P, PB, B, S, T and Q. Pollens was the first person in contemporary times to recognize and illustrate the proportional relationships of these forms.
As the Conservator of the Metropolitan Museum of Art’s collection of musical instruments from 1975-2006, Pollens was responsible for the maintenance, research, and restoration of some 5000 instruments made throughout the world, from ancient times to the modern era. He is a noted photographer of musical instruments, including for a life-scale book of the violins of Giuseppe “del Gesù” Guarnerius, and the author of many scholarly articles and books, especially on keyboard and stringed instruments.[7] With a background in instrument building, physics, and photography, plus a keen interest and expertise in exact but identifiable restoration of musical instruments – as is the standard in most museums – he has contributed immensely to the field of organology. I became aware of his work through the numerous articles he has published in The Strad magazine alongside his excellent photography of stringed instruments, and we had a few friends in common. I first met him in the mid-1980’s when I was playing concerts with The Mozartean Players, a period-instrument chamber music ensemble, at the Metropolitan Museum and used its “baroque” Stradivari violin.[8] Because the instrument could not leave the museum, this necessitated my practicing in a basement storeroom with his oversight.
In 1989, The Strad interviewed me for a feature article and Pollens was assigned to photograph me for the piece. After a somewhat rocky start, our developing relationship culminated in marriage in 1995.
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The dispute – which is described more fully in the next chapter – began in 1997, when he was invited to photograph the “Messiah” violin in England and observed that the violin did not match the description historically associated with it. A subsequent dendrochronological test indicated that the wood on the violin’s top postdated Stradivari’s death, which soon led to a huge controversy in the violin world and severe attacks on him and his reputation.[9]
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How to Identify a Stradivari Violin?
The defensive “evidence” provided by the violin experts, who are also dealers, was largely empirical and I was left pondering a question; if the specialists cannot tell us factually why a violin is authentic, then how can they tell when it is not? By consequence this led to; what makes a Stradivari violin?
Instruments restorers have developed a body of knowledge about certain characteristics that are associated with makers or their region; these include interior details of craftsmanship, the shape and placement of the sound holes, decorative elements like the purfling, and the varnish. Because many violins are heavily restored, however, some of these details may be obscured. Furthermore, they generally do not address the question of why a violin might demonstrate an exceptional acoustical capability.
Over the years, scientists and pseudo-scientists have posited various theories and claims about the qualities of the wood and how it was treated (these include immersion in pondwater for years before use or the absorption of minerals while being floated down a river), or that the varnish contained, among other things, crushed gemstones.[10] Very few have attempted to determine what acoustical properties – especially using knowledge and techniques available from the mid-16th century through the first quarter of the 18th century – might have been at work. Many violin makers that include Jean-Baptiste Vuillaume (1798-1875), have claimed that their instruments are equal if not superior to the “old makers,” yet they were usually slavish copyists of these very instruments.[11]
I began with a theory: that despite the varieties of sizes and shapes among Stradivari’s violins, there is a foundation upon which they are built that is derived from acoustical properties; in other words, certain irrevocable truths that are linked with physics and, consequently, with nature. I then started to closely examine the life-sized photos of the forms and look for any proportional clues found on them. The more I learned, the more I found that I needed to learn, so I began reading numerous books about sound and its physical properties, leading in turn to learning about proportional aesthetics – and associated mathematics – along with many related topics. I especially sought out the information in these fields that would have been available in northern Italy in the 17th century or earlier.
Due to professional and personal obligations, although I had arrived at much of the basic knowledge I needed to complete this project in the early 2000’s my work was largely on hold until late 2019, when I was able to devote significantly more time and attention. The arrival of the Covid-19 pandemic led to the cancellation of my scheduled concert work for a full year and a half, but the prolonged self-quarantine allowed me to focus closely on this project and complete it.[12] The final part of the process, which was the most complex and time-consuming, focused on synthesizing a substantial amount of information and reducing it to as simple a procedure as possible, with the goal of recreating the violins’ designs.
The Foreword to a book that I have consulted, Mathematics from the Birth of Numbers, contains the pertinent observation that technology has become detached from philosophy and that today’s mathematicians are virtuosi who are usually divorced from the contexts and history of their field.[13] The same could be stated of many instrument makers of the past 250-plus years, who are often copyists of known and respected instruments; while they may change a detail or two, they do so often in a largely-arbitrary manner and are generally unaware of the original design concepts of these instruments.
More recent technologies, such as laser scanning, are contributing to greater knowledge of the acoustical responses of fine violins that, when combined with a thoughtful structural analysis, can lead to insights about design elements that include the sound hole placement and arching of the top and bottom plates. It is obvious, however, that these design elements were originally achieved through other means.
The roles of sound, nature, and physics are deeply intertwined with the design of these violins; therefore, The Stradivarius Code contains a certain amount of mathematics that explore how pitch is generated on a vibrating string, the physical properties of musical intervals, and the roles of proportion and aesthetics. There is also an examination of historic measuring systems and how they relate to a violin made in the 17th or 18th century. Although the information may appear to be a bit dense at times, these principles are readily understood by a focused reader with a high school education. It is necessary, too, to provide this evidence as a form of scientific proof for the conclusions that I draw.
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Although I have no background in organology, my lifetime has been devoted to interpreting music on the violin, which is based on symbols and their meaning – much like language and mathematics – and I have a demonstrable interest in science and mathematics. My overviews of some topics related to the physics of sound and pitch, such as the characteristics of organ pipes, are necessarily brief and there are many excellent sources for additional information.
My principal concert violin is by a Cremonese make named Petrus Guarnerius, who relocated to Venice, but I have played several violins made by Stradivari and noted their tonal focus, resonance, response, and exceptional beauty. Having perfect pitch also aided me in doing research: because I theorized that the designs of the violins themselves have musical properties, I turned ultimately to the monochord to “play” the harmonic proportions of Stradivari’s violin designs.
Structurally, violins made by Stradivari should be considered on two bases: the acoustical design of the interior and the aesthetic qualities of their visual balances. In the case of the sound holes, each of these applies as there is an evident acoustical consideration yet they must be visually balanced. These two elements are addressed in detail in The Stradivarius Code.
Like many physicists, astronomers, philosophers and, perhaps, theologians, I was searching for a “grand unification theory” that would answer, quite simply, why this maker and his instruments represent the epitome of violin making. I also sought to devise a master design system that would account for all aspects of his violins, including the curved surfaces and the scroll spiral in profile, and tried out countless theories before arriving at the most beautiful and simple templates imaginable that are directly derived from the properties of music and nature. These final revelations coincided closely with the publication of stunning photographs that were taken by the James Webb Space Telescope and reveal our universe – and well beyond – in gloriously rapturous detail. A solution for the riddle of the sound hole design was inspired by a pivotal work by Leonardo da Vinci, which he created ca. 1409 in homage to the influential Roman architect and engineer Vitruvius
The foundation for this investigation is Stradivari’s violin forms as photographed by Stewart Pollens, who provided extraordinarily helpful knowledge in addition to his vast library, writings on Stradivari and other makers, and measuring equipment. These, combined with life-sized photographs of violins, much self-education and consideration plus a trial and error methodology, gradually led to an interpretation of the information found on the forms and the violins. During this process, I had three mottos: “observe and learn,” “look to the forms,” and “simplify, simplify,” and I learned to avoid entrenched theories.[14]
Without his work – and the insults hurled at him by violin dealers – my astonishing adventure would not have taken place; therefore, I dedicate this book to Stewart Pollens, who has always sought the truth.
The search for The Stradivarius Code begins with a legendary violin housed in the Ashmolean Museum in Oxford, England. Is it worth at least $20,000,000 or is it a fake “Stradivari” made as a hoax? If the latter, then is there a true “Messiah” Stradivari violin?
Stephanie Chase, 2022. All Rights Reserved.
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[1] Antonio Stradivari used the Latinized form of his name, Antonius Stradivarius, for his labels.
[2] In mid-2022, the highest public price paid for a Stradivarius violin was $15.9 million US.
[3] Dendrochronology is the science of dating artifacts by identifying patterns of annual growth rings in tree trunks and objects made from them.
[4] For a detailed biography of Stradivari’s life and work, as well as information regarding his materials and their provenance, see Stewart Pollens’ Stradivari and The Violin Forms of Antonio Stradivarius.
[5] Probably the most invasive of these repairs is a “patch coming through” the back or top plate.
[6] In 2015, Stewart Pollens gave a talk, “When Science Goes Bad,” that discussed this and other experiments at a joint conference of the Galpin Society, the Institute of Acoustics, and the Royal Musical Association.
[7] In 1994 the Metropolitan Museum of Art held a two-week exhibition of 25 violins made by Giuseppe “del Gesù” Guarnerius, which included the violins used by Niccolò Paganini and Jascha Heifetz. These violins were photographed for the book, “The Violin Masterpieces of Guarneri del Gesù.”
[8] This large model instrument was reconfigured in 1975 to approximate a Baroque style violin.
[9] Dendrochronology is a scientific technique for dating certain woods by the characteristics of their growth rings.
[10] In 2009, Pollens and another researcher, Jean-Phillipe Echard, determined independently that Stradivari’s varnish is based on a simple formula consisting of linseed oil and pine resin, with the addition of coloring agents like dragon’s blood, which is a red resin derived from plants.
[11] Although violin makers put paper labels inside their instruments identifying their work and the year, throughout the centuries these have been commonly removed by unscrupulous restorers and dealers for their own collections or, possibly, to help “authenticate” a fake instrument. The removed labels are usually replaced by facsimiles.
[12] The word “quarantine” refers to the Italian practice of isolating for 40 days during an outbreak of disease such as plague. In 1630 the city of Cremona was especially hard hit by an epidemic and lost perhaps 70 percent of its population.
[13] Jan Gullberg, Mathematics from the Birth of Numbers. New York: W. W. Norton and Company, 1997, PAGE
[14] “…look to the forms” was inspired in part by the “Seinfeld” episode on black and white cookies.