Maria Larionoff (ML): For our concert in April, you are playing the lovely “Lark Ascending” by Ralph Vaughan Williams plus two of your own arrangements of works by Pablo de Sarasate that were originally for violin and piano Over the years we have played others of your transcriptions, both here and with the American String Project in Seattle. How did this interest come about?

SC: I was probably influenced by the fact that my father, Bruce Chase, was a well-regarded arranger and composer, especially of works for orchestra. He studied violin and piano as a child living in Iowa, but it appears that he essentially ran away from home in his late teens and joined a dance band in the Northwest as a pianist. The band soon realized that because they had only a few instruments their repertoire was limited, and he was elected to make music arrangements.

ML: Where did he study this? It seems as if he did not go to college.

SC: No, he didn’t, and it was interesting to learn that my father was self-taught as an arranger and composer. But following a stint in the Navy during WWII he began working for television and radio studios in Chicago, back in the days when they had resident bands and orchestras. A few years before I was born, he was writing arrangements and conducting a band for a television show called “Super Circus” – and wore a special uniform, sort of like Robert Preston in “The Music Man”! Shortly after that he spent quite a few years working for “Don McNeil’s Breakfast Club,” which was a popular, nationally-broadcast morning radio show.
By the early 70’s, however, this kind of work was fast disappearing and the “Breakfast Club” had ended its run, so he practiced the violin and joined the Milwaukee Symphony Orchestra as a second violinist, where he remained until his retirement. For their Pops programs they frequently featured some of his arrangements and had him conduct, and he became something of a mascot for the orchestra. He also wrote and published albums of music to be used in educational programs from grade through high school level, and his arrangements, especially medleys, are still performed by symphony orchestras throughout the world.

ML: So how did you get started in this field, and what kind of approach do you take?

SC: I don’t really recall, but I started imagining music that I liked and played in a slightly different setting, with an increase in its tonal effects – sort of like “surround sound” versus what comes out of a piano. I am also self-taught in this but tend to restrict what I do to string ensembles because I am less comfortable writing for full orchestra with brass, wind, and percussion instruments, and have a profound respect for high school music teachers, who often have competence in playing and teaching a wide assortment of instruments.
If I am arranging something for violin and string orchestra that was originally accompanied by piano, I start by taking its part and dividing the left and right hands into the bass and treble instruments. Often, I add little original bits or make small changes to jazz it up with the goal of making the arrangement more fun for the orchestra players and listeners. Each arrangement is very time-consuming but I generally enjoy the process, and I am grateful that Itzhak Perlman and Joshua Bell are among the violinists who have played my works.

ML: You have been working on a long-term and complex project, which you told me about when you were last here. Can you tell us about it and its status?

SC: Yes, thank you. I have been writing a book about Antonio Stradivari, the proportional schemes that he used for designing his violins, and how these relate to the properties of music and nature. This project got started many years ago but had a long hiatus, and I returned to it because I felt it was valuable and had more free time to devote to it. I am excited that it is very close to completion.

ML: What led you to embark on this?

SC: My husband, Stewart Pollens, is a musical instrument expert and researcher who worked for the Metropolitan Museum of Art for over thirty years as its conservator in that department. In 1992 he published a groundbreaking book on Stradivari’s instruments, which included an analysis of the extant materials that encompassed the forms on which they were built through designs and patterns for the necks, scrolls, fingerboards and bridges. Much of this material is preserved in the Museo del Violino in Cremona, Italy, and his book was the first to present life-sized photographs of the forms, which provided the acoustical foundation for his violins.
In 1997 he was engaged to photograph a famous instrument from 1716 called the “Messiah,” which has been housed in the Ashmolean Museum in Oxford, England since about 1939 and is reputed to be the best preserved and most perfect Stradivari violin ever built. Its provenance ostensibly leads directly back to the maker and in 2001 it had an estimated worth of $20,000,000. After photographing it, Stewart made a brief examination of its interior and realized that the violin did not match a description by one of its alleged historial owners, who was an Italian count. He theorized, among other possibilities, that it might have been repaired since the description was written in the 19th century but was mystified by this discrepancy and some others. With the goal of at least ascertaining the violin’s age, he asked a renowned German wood expert named Peter Klein to date it, using a growth-ring analysis, in a blind test from his life-sized photograph of its spruce top. It turned out that the wood was dated slightly after Stradivari’s death, which excluded it from having been made by him.
Stewart confided this to the publisher of his book on Stradivari, who was also a noted English violin dealer, but word got out shortly thereafter and the whole violin world was set ablaze, leading to terrible attacks on him and Dr. Klein. The Ashmolean then got someone – who, in my opinion, was unqualified due to bias, a lack of training, and improper testing techniques – to redo the dating based on the wood growth. This fellow claimed to come up with a “correct” date and “matched” it to two other Stradivari instruments but would not share the data. Another dendrochronologist independently confirmed Klein’s findings.
Meanwhile, the violin dealers banded together and presented their reasons for believing that the “Messiah” was a genuine Strad. Gradually, through my own investigation I realized that there was no concrete proof of its provenance before 1872 and that they could not satisfactorily answer why or why not it, or any violin, might be authentic to Stradivari. This led me to the theory that there must be some design philosophy behind his instruments, perhaps related to the properties of music, that was now lost. For example, manmade structures that include Stonehenge and pyramids in Mexico represent lost knowledge, because these are now mysterious artifacts although they appear to relate to astronomy. To determine if the “Messiah” was genuine, I needed to learn, understand, and recreate Stradivari’s basis for his designs and offer proofs of this. I also wanted to indicate how this knowledge would have been present in northern Italy in the mid-16th century, which is when the earliest of the great violin makers – the Amati family – were active.

ML: What are some of the properties of music that apply to his instruments?

SC: Compared to having a nice meal, for instance, in which we smell, taste, see, and touch our food, music can feel ephemeral and intangible. We can watch a concert but our hearing is what should be principally engaged. We also know that music affects how we feel but we’re not sure why.
But sound has physical structures, starting with its rates of vibration and how they are created. What we call musical intervals – the distances between the notes that we play – have properties, first apparently recognized by Pythagoras, that relate to their masses. These are most readily seen on stringed instruments like violins and cellos: for example, to play a higher pitch on the same string, we shorten the vibrating length of the string and reduce its mass. If we shorten it by eight notes – an octave – the vibrating string length is halved but the frequency of vibration is doubled. For the octave, this ratio is therefore 1:2 and reflects the mass (one part out of two) that is vibrating. For the fifth, it is 2:3, and for the fourth it is 3:4. We can also observe these in the string lengths of a harp or inside a piano. There are many other factors but these physical manifestations form the basis of how music is created. Therefore, music is entwined with, and influenced by, the facts of the natural world and these exist independently of instruments.
As for other aspects of vibration: for practitioners of yoga, the colors of the different chakras are associated with different vibrations, with red as the slowest and violet as the fastest, and the “red shift” in astronomy indicates a slower rate of vibration and that the object is moving further away. This principal also applies to the “Doppler effect” (such as a blaring car horn that drops in pitch as the car moves away from the observer) and in weather radar. Music features consonance and dissonance, which is defined by the ratios of vibration and is also observable in comparing colors side by side that either complement or clash.
I theorized that in designing and building his instruments, Stradivari “tuned” them in terms of their proportions, which turned out to be correct. I also sought to define his system and usage of measurement, which was not simple – if you look at closely at a violin you will see that it consists nearly entirely of curved surfaces. I ended up using an ancient measure called the braccio, which was a principal building unit of measure in Cremona, Italy, starting by the Middle Ages. It relates to the length of the human arm – like the cubit, which makes sense – and there is documentary evidence that Stradivari used it, but I had to successfully figure out a way to have it work for a multitude of his violins that can differ quite a lot dimensionally.

ML: Do these ideas apply to just the body of the violin or to the whole instrument?

SC: The interior of the violin’s body is shaped somewhat like a figure eight – the corners are just decorative – and this forms the acoustical heart of the instrument. Although there have been many makers of violins, traditionally in Western Europe but more recently in Asia and the Americas, since about the mid-1700’s they have been largely copyists of the outer dimensions of well-regarded instruments and tend to treat them like a paint-by-numbers project, without regard for – or knowledge of – the underlying philosophies of their design. For instance, the necks of most antique violins were either reset or replaced so they are no longer in their original configuration and are usually ignored in an analysis. Additionally, I could not locate any information whatsoever on how to design the sound holes, which feature reverse curvatures, including in historic books on how to build a violin. It became clear that these have long been copied from extant examples and transferred to the instrument being built.
Gradually, I realized that the entire instrument needs to be considered from the top to bottom and that a kind of theme and variation exists in Stradivari’s violins: certain elements like the vibrating string length, position of the bridge, and complete length are immutable in their length proportions, but there is room for variance in some of the other dimensions, including the inclination of the sound holes.
In my book I provide instructions for designing nearly all aspects of Stradivari’s violins. One exception is in the thicknesses of the top and back plates – unfortunately, nearly all of these have been thinned since Stradivari made them, which I consider terrible vandalism, and this was done to “improve” the violin’s sound, which is a fallacy. I have attempted to recreate a “map” of his original thicknesses, based on the other data of the instruments.

ML: What was your process like, and what kind of equipment and materials did you use in your research?

SC: The goal was to reverse-engineer his violins, and the basis was formed by Stewart’s life-sized photographs of Stradivari’s violin forms plus accurately scaled full-sized photos of violins. I first needed to match these, however, which was a long process because the effects of aging on a violin include shrinkage, especially of its top, and wear on its edgework. I also read many books and articles about the properties of music and the history of its measure, plus those on violins and their characteristics. I also studied the materials that were left by Stradivari, which included some designs, although how they originated is not indicated.
This research led me into another realm, which is the “music of the spheres.” Starting in ancient times the proportions of music were used to calculate the motions of planets and major stars, among other applications. Why was this important? It was because determining a travel route – especially at sea – required a reliable positioning technique that referenced these, plus knowing the exact time that the reckoning occurred. For things from business transactions to conquering foreign lands, it was a vital need, but the timepieces of the era were inexact. Devices such as astrolabes were helpful, but it took until 1737 for a precise chronometer to be built that enabled the accurate calculation of longitude and made this travel safer and more efficient. That year happens to be the final year of Stradivari’s life.
Once I realized the role that the properties of a taut vibrating string plays in his measurements, I started experimenting on my violin but faced some limitations in accurately measuring the non-vibrating portions of the string, so I asked my husband to build a monochord for me. This is a simple instrument that features usually one or two taut strings and was a measuring device in the era of Pythagoras, used especially for determining proportions in musical instruments. In addition to this, my principal tools included a divider, an accurate ruler, a compass, and a calculator, along with tracing paper, pencils, erasers, and a computer for writing. Because I needed to make technical drawings for illustrations, I learned how to use a computer-assisted drawing program, which also took a while. Some of these tools were developed thousands of years ago and others just in the past few years.

ML: What are some other techniques or ideas that you used?

SC: Well, an early challenge was to reconcile the braccio length with violins of different lengths that do not relate easily to straightforward divisions. Eventually, I experimented with using its inch length – a 1/12th division at 40.294 mm – and creating a total length that matched the various lengths of the instruments, which in turn became its own foot length with 12 divisions. The test, of course, was that it worked throughout the violin models, and it did.
Another challenge was to discard entrenched ideas, such as measuring something in a linear fashion using a ruler with regular divisions. This realization led to a special ruler using measures from a vibrating string, which has characteristics that include nodes – which string musicians usually call natural harmonics – that are spaced irregularly, and these are present in both directions of the taut string. This ruler is derived from the monochord and determines the linear proportions of the violin, from the bottom edge through divisions of the body up to the top of the scroll. The full string length of the monochord represents the full length of the violin, and small bridges are used to find interior proportions. These measures are then used to create the nonlinear body parts of the violin, as in the curvatures of the bouts. Unlike a regular ruler, these measures are defined by the full length, the portion that is vibrating and the portion that is not, so there are three terms.

ML: Why are these nodes spaced irregularly?

SC: There are two principal factors. The first is exemplified by a Greek philosopher named Zeno, who is credited with a paradox: “Atalanta wishes to walk to the end of a path. Before she can get there, she must get halfway there. Before she can get halfway there, she must get a quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on.” The question is, when will she arrive? The answer is, never: the goal is for these fractions to add up to 1, which represents the end of the path, and this series will never achieve it, although it will eventually be infinitely close. This illustrates how a vibrating string works. If a full string length is divided by octaves, the first octave will be at 1/2 its original length, the next at 1/4, the next at 1/8, and so on. As we shorten the vibrating string length in playing our notes, they get closer together. This affects all intervals but is easiest to understand using octave divisions. The second factor is that nodes also reflect the presence of standing waves and antinodes, and these are present not just in stringed instruments but in others such as brass horns.
I also devised a similar ruler based on the original playing range of the violin, as demonstrated by the lengths of Stradivari’s fingerboards, and the positions of the principal notes on it. This forms the foundation for designing the scroll, pegbox, and sound holes.

ML: What are some additional insights that you gained?

SC: There were many, some of which astonished me, but one of the most useful was the role that triangles and parallelograms play in the design of these instruments, especially the curved lines!

ML: Violins should be beautiful in their sound, but they also have a lovely appearance. Do these ratios of music play a role in the visual aspects?

SC: Yes, some elements, especially the sound holes, unite the tonal and visual qualities. Another interesting aspect is the aesthetic proportion known as the “golden section,” which is associated with Fibonacci numbers and widely featured in nature and elsewhere, such as human anatomy, the growth of flowers and trees, and even electric current. A wonderful example is found in the chambered nautilus shell, which features golden section growth along a curved line, and violin scrolls in profile often closely resemble this. The golden section plays a simple length role in the violin’s proportions, and there is even a remarkably pleasing musical chord that is derived from early Fibonacci numbers! Finally, because a violin’s structure features ellipses and partial circumferences, it was clear that radii and pi played important roles that needed to be defined. Due to these factors and the role of musical proportions in these instruments, there is quite a lot of simple math in my book.

ML: What are some of your conclusions?

SC: My research reveals the ideas, contexts, and techniques behind Stradivari’s designs, how these originated, and that this knowledge was present in Cremona at least one hundred years before Stradivari’s era but lost shortly after his death, when makers became principally copyists. And I hold an even greater appreciation and gratitude for his work as he was a complete master of every aspect – not just technical but interpretive, like a fine musician.
There were other intersections between being a musician and this project: for instance, we are trained to recognize patterns in music but each composer tends to use these differently, and I needed to do this for Stradivari’s patterns before I really understood his ideas. Another was that much like practicing a piece of music with the goal of perfecting it, I sought to find the truth in his work – rather than impose myself on it – and reduce it to the simplest forms possible. Late in the process I learned that this is known as “Occam’s Razor,” named for a friar from the 14th century who held that when given a choice between two solutions for a problem, the simpler one is better and extraneous information is thereby cut out.
This research was much like solving a very complex puzzle and required a vast number of ideas and experiments, and I’ve held onto its history through notebooks plus innumerable tracings and sketches as I tried out theories. My husband was an enormous resource through his knowledge, research materials, and measuring equipment, but my approach is unique compared to that of anyone else, because I treated Stradivari’s work like that of a master composer whose music is created through the media of wood and strings.
This conversation condenses some 350 pages of material from my book, so thank you for indulging me! It includes a lot of historic contexts plus recreations the designs of two well-known violins, the “Betts” (1704) and the “Dancla” (1708). And I reached a conclusion as to the authorship of the “Messiah” – and hope that people will buy the book to learn it! My goal is to publish sometime this Spring.