Wood, Knife, & Sound

Notes from the workshop of Jedidjah de Vries.

Posts Tagged ‘design’

Three New Sciences

Tuesday, September 19th, 2017

I think many violin makers have a mixed relationship with science. In the abstract we’re fine with it, but when science turns her all-knowing eye towards us and our instruments we get a bit squeamish. Don’t get me wrong, of course it’s wonderful to gain new insights into our favorite subject. And there are makers who are super into acoustics and other areas of scientific inquiry. On the whole, however, there tends to be a hefty dose of skepticism and aloofness mixed in with all that fascination.

Every time a new scientific study about violins comes out, there are two critiques that tend to pop-up again and again. First, there are the makers who ask “But how do I apply this to my making?”, often with the not-so-subtle implication that if it doesn’t help them make a better violin the study is basically worthless. To be honest, I don’t have a lot of sympathy for this line of criticism. I understand it though. I too am busy and don’t really have time to learn a bunch of specialized scientific jargon in order to parse some academic paper just to glean an abstract truth about the physical object already on my workbench. But I also know that that’s not science’s problem. I’m not the intended audience for these papers, and Science isn’t actually in the business of producing actionable intelligence anyway, just Knowledge1With heavy caveats.. At the end of the day I don’t actually care all that much if this or that bit of research helps me make a better violin. I think violins are cool so I am happy to enjoy any insight—however abstract—into them.

Second, there are the complaints about how the researchers didn’t take into consideration or failed to understand this or that aspect of violins or of making. These complaints chide the scientists for telling us something that we already knew, for overgeneralizing or hyper-focusing on details. A lot of this comes down to Science failing to face and grapple with the materiality of violin making. Science is a powerful tool, but so are the cumulative experiences and craft knowledge of makers and musicians. It’s with that in mind that I want to talk about three recent-ish scientific papers. I have a few thoughts on their scientific merit, but mostly I want to try to put their scientist episteme in conversation with the techne of making.

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Evolution of the outline

I’m going to start with one of my favorite recent-ish papers: Imitation, Genetic Lineages, and Time Influenced the Morphological Evolution of the Violin by Daniel H. Chitwood.  The idea of this study was to see how much can be learned about instruments by looking only at the shape of their outlines2Note that this purposefully ignores their size. The technique Chitwood employed is one he usually uses to analyze leaves and draw conclusions about their evolutionary relationship to each other. The basic approach is to learn about the relationship between shapes by asking “What is that distinguishes one from the other?” Here, instead of trying to differentiate leaves by species, he looked at instruments first by type—violin, viola, cello, or bass—and then by maker—Magini, Lupot, Degani etc.

To do this he needed a large database of instrument outlines. Luckily the Cozio archive has photos of thousands of instruments, which he was able to take and then turn them into machine readable mathematical formulas. Next those formulas were analyzed using a technique called linear discriminant analysis, which tries to find mathematical characterizations of difference (which are called linear discriminants) that can be used to categorize objects into classes. Because all of this is happening mathematically the result is very different from how we humans would go about the same task. So instead of say “the ratio between the width of the upper and lower bout” or “the squareness of the shoulders” we end up with something that is complex, abstract, and can’t really be put into words.

He first does this for instrument type—i.e. violin, viola, cello, or bass—and comes up with three linear discriminants: LD1, LD2, and LD3. LD1 captures the difference between basses and everything else, and does so very well. LD2 does an admirable job of capturing the difference between cellos and violin/violas. Lastly, LD3 sort of captures the difference between some violas and violins, but it will come as no surprise that many violas seem to basically be scaled up violin shapes.

None of this is new or surprising: many violas look like violins and basses look different from everything else. But it’s a good warm up act to show that the technique can work for instrument outlines. Also, as a maker it is somewhat interesting to think about the differences between the instruments purely in terms of outline and how they might relate to necessary differences in construction, acoustics, playability, or aesthetics, especially as we scale between different instrument types and even within instrument types, as we so often have to do with violas.

I also have three follow up questions that I wish Chitwood had addressed, specifically with regard to the violas whose LD3 values are within the violin range versus those that are different. First, one hypothesis worth looking into is whether this is driven primarily by a greater representation of Brecian instruments—which are maybe less similar to the violin average—in the set of violas vs. the set of violins he examined, or is something else going on? Second, it would be interesting to see whether there is is any sort of correlation between a viola’s size and LD3. For example, perhaps larger violas are more violin like, while smaller violas require greater alteration to get them to work. And third, I would be curious to plot out where the more common models that makers tend to copy and consider “successful” fall along the LD3 scale.

The second part of the study applies the same approach to categorizing violins by maker. The idea here was not to see whether it was possible to train a computer algorithm to identify instruments from their outline—Philip Kaas’ job is safe—, but what can be learned about the relationship between makers from how a computer algorithm identifies instruments. Specifically they tried to (1) tease out where direct copying versus evolutionary influence or drift was responsible for similarities, if there were any, between makers and (2) they wanted to see if it was possible to build a sort of genealogical map of instrument styles based on their outline.

To answer the first question they looked for correlations between makers’ styles and when they worked. They found that one particular linear discriminant, which they called LD13Note: this is not the same LD1 from the first part of the study., had a relatively strong correlation with when the instrument was made. The reason for this appears to be mostly because of Stradivari. A low LD1 number is indicative of a Strad shaped violin. Because of this, before Stradivari all instruments had high LD1 values. During Stradivari’s life a few instruments, i.e. his, had low LD1s and then as time went on makers began copying Stradivari so more and more violins had low LD1s. It is important to note that this appears to be primarily because of direct copying, and not a general trend or convergence in making towards instrument outlines that have lower LD1 values. This is mostly clearly evidenced, first, by how sharp the rise in the number of instruments with lower LD1 values around 1800 is, and, second, by how the computer algorithm—when using all 85 linear discriminants—will often erroneously attribute violins made by later makers, such as Lupot or Bisiach, to Stradivari, i.e. while LD1 is the most pronounced characteristic of Strad it looks like later makers were copying all of his characteristics and not just happening to emulate one of them.

For us makers there is nothing particularly surprising about any of this4Perhaps the tidbit that the Deganis are a notable exception to the overall trend, is worth following up on, but I don’t know what to make of it in isolation.. Overall this just confirms the common understanding of the history of making. What it does not do, however, is offer much insight into why Stradivari copies became increasingly popular after about 1800. But it does give us a tool to start exploring that question more systematically. It would be interesting to look more closely at instruments with high LD1s, especially those made between the time of Stradivari and Lupot, to try to understand why those design elements have been largely abandoned and whether any are worth bringing back. I am particular curious what kind of correlation, if any, there may be between makers who employed baroque vs. modern neck sets and the LD1 values of their instrument designs, or if there are any other similar changes (string design, concert hall size, repertoire, etc.) whose time-line corresponds with changes in LD1 values. Of course it’s possible that the change in design preference was largely extrinsic to acoustic or other design needs, e.g. a shift in cultural preferences and attitudes towards the Italian baroque or Strad himself. Chitwood’s work on its own doesn’t answer these questions, and there is no Big Data approach that will. It would be wrong of us to collapse everything we know about Strad’s style into LD1. But this can give new approaches with which to examine the historical record that might bring out new insight that we would otherwise miss.

To answer the second question Chitwood analyzed the violins using an additional 84 linear discriminants and treated the makers as though they were species who might be related to each other by evolution. I have reproduced the tree he came up with below for easy reference. For Chitwood the main takeaway was that this evolutionary tree of instruments corresponds fairly closely with the family tree of the makers, i.e. makers from the same family tend to use similar looking models. This again reinforces the notion that instrument design is transmitted primarily by direct copying and not evolutionary adaptation or drift. As a maker what jumps out at me most are the exceptions. Perhaps most notably the split in the Guarneris between more Amati-like and more Stainer-like. Furthermore, as a maker, I would have liked to rerun the analysis but with some makers—such as Guadagnini and del Gesu—split by period, i.e. treating early and late del Gesu as two different makers. And lastly, while the tree seems like a useful tool to help conceptualize the relationship between makers, it also left me with a number of follow up questions that I’m not entirely sure how to go about answering such as: What exactly are these Stainer like instruments, and how should I understand them in the broader context of violin making history? Is there actually a Stainer school or are makers arriving at those shapes for different reasons/routes? At the end of the day Chitwood’s family tree is really more of a forest level view, which is useful but only meaningful when you understand the histories and place of the individual members that are in it.

Hierarchical clustering of violin shape.

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Ff-hole acoustics

The second study I will look at is The evolution of air resonance power efficiency in the violin and its ancestors which looked at the impact of sound hole shape on the acoustics of the violin. The bulk of this article is dedicated to building a very technical mathematical model that can describe “the acoustic conductance of arbitrarily shaped sound holes”. That is, they want to be able to calculate how good differently shaped sound holes, and thus ff-holes, are at transmitting sound. This should roughly correspond with how loud an instrument can be, all other things being equal. The big take away from their model is that it’s the perimeter, not the area, of the sound hole correlates with output. So, broadly speaking, a crinkly shape like an ff-hole will be better at transmitting sound than a circle with the same area. This key insight drives much of the rest of the study.

They then go on to verify their theoretical model experimentally, checking it both against a sound hole set in an idealized rigid body—which is not a violin—and an elastic body—like a violin whose top and back move. The study is careful to point out that their model only accurately describes the case of a rigid body. It gets close for an elastic body, so it’s still useful for a general comparison between instruments with different sound holes, but might be slightly off, which might be important for the fine tuning of a violin’s acoustic behavior. This is a good example of a case where the simplification necessary for a robust scientific model doesn’t quite line up with the specificity needed for making. But, as makers, while we need to keep such caveats in mind, they shouldn’t distract us from the broader points.

Having established both the theoretical and experimental validity of their model the authors then use it to address two questions. First, they look at changes in sound hole design over the course of pre-violin instruments and, second, at changes in ff-hole design in the violins of Cremonese makers.

The authors begin by pointing out that from the 10th century to the violin in the 16th century instruments display sound holes with increasing perimeter to area ratios and they calculate the corresponding increase in air resonance power. They then speculate the evolution of instruments is being driven, at least in part, by a desire to maximize projection culminating with the claim that:

The lute in fact became effectively extinct, perhaps partly due to its relatively low radiated power. This occurred as the violin’s prominence rose, at least partially because its greater radiated power enabled it to project sound more effectively as instrument ensembles and venue sizes historically increased.

Increased power as sound holes evolved.

The overall trend in sound hole shape towards designs that correspond with increased power is very convincing. However, I wish that they had provided more historical evidence to backup their evolutionary claims. For example, if their claim is true why wouldn’t viola da gambas with violin like ff-holes instead of the more traditional cc-holes have become popular? But instead each step in sound hole evolution seems to come only with an entirely new instrument. And while volume may be part of the lute’s decline, this was also a time of changing musical styles from polyphonic madrigals to the monody of the figured bass. If anything, I would frame their findings the other way around, namely that the historical changes in sound hole design lends weight—though not proof—to the notion that the instrument builders of the past cared about increasing the ability of their instruments to project and carry, which is relevant to how we think about making copies of those instruments today.

Before we follow that thread into the world of Cremonese violins there are three side issues the paper brings up in passing that I think are worth highlighting. First, they point that the fact that output correlates with sound hole perimeter and not area complicates linear scaling of instruments. As noted above, this is an issue that we makers often encounter. Digging into this study may help us better match our ff-hole choices to the air volume of our instruments, especially when attempting new viola models. Second, they note that the output of two ff-holes is less than their sum, especially as they get closer to each other. I am curious how sensitive this affect is and whether the range of variation commonly seen on instruments is big enough to make a difference. And third, they explain that rosettes, such as those seen on some lutes and baroque guitars, end up acting essentially the same as undecorated circular sound holes, which while not useful information is interesting.

After looking at different instruments the authors turn their attention to the violins from three generations of Amati, from Stradivari, and from Guarneri del Gesu. The approach here is the same as before. They begin by noting that there is a trend of increased ff-hole size over time, which in principle corresponds to an increase in power output. The authors, however, are quick to acknowledge that violins are complex so they check to see whether changes in back plate thickness, top plate thickness, thickness near the ff-holes, mean air cavity height, or air volume might be having a greater affect than the changes in ff-hole size. Their conclusion is that the combined effect of all six parameters is an increase in power output over time and that the increased ff-hole size is by far the single largest contributor to this. The other very interesting, and somewhat stunning, conclusion from this additional step is that while larger ff-holes would in principle have led to a rise in the frequency of the A₀ mode, other changes—especially increases in cavity air volume—balanced this out to keep the A₀ mode relatively constant over time 5With the notable exception of late del Gesu violins, which are outliers in so many way.. What part of the process classical makers were paying attention to I don’t know, but to me this clearly suggests that they cared about the acoustical properties of their instruments and knew how to manipulate them.

Having established the historical trend of increased ff-hole size and increased power the authors offer a theory to explain how this may have happened. Their “… key assumption is that the instrument makers select instruments for replication from a current pool within their workshop.” From this they speculate that an evolutionary model may be at play, where small variations in making means that some instruments are more successful than others and that makers then pick those successful instruments as the templates for their next instrument. While this idea is certainly consistent with the available evidence I have two reasons to be unconvinced. First, given the number of paper templates that have been preserved from Stradivari’s shop I am not sure that their key assumption can be granted. Why would makers copy existing instruments instead of continue to use their ready made templates? As with the changes in sound hole shape from instrument type to instrument type, looking at the graph of ff-hole size over time it looks to me that much of the change is driven by moving from one maker to the next, with late del Gesu as a clear outlier. Second, while perhaps the overall trend of increased ff-hole size yields a louder instrument by the time we move from Andrea Amati to del Gesu, I feel that the paper could have benefited from some psychoacoustic backing to show that the smaller variations from one instrument to the next by the same maker are enough to be noticed and acted upon. Expanding the study to more makers and a broader time span may help illuminate what’s going on. None of which invalidates, or even diminishes the importance of, their findings with regards to how ff-holes function acoustically. On the one hand, one could see this as an example of how looking at “the numbers” alone can be misleading, and more generally a lesson on the limitations of hard-science to the violin world. On the other hand, I like how a study focused on “pure” acoustics can point towards insights into our understanding of historical making, in this case by adding to our picture of what historical makers might have known and cared about when it comes to sound.

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The Paris Experiments

The last paper I will discuss is probably the best known and most controversial: Soloist evaluations of six Old Italian and six new violins, better known as “The Paris Experiments”. This study arose out of a desire to address the commonly held belief that old (i.e. 17th & 18th century Italian instruments) possess a “fundemental […] tonal superiority” over contemporary instruments and claims that its findings “present a striking challenge to near canonical beliefs about Old Italian violins”. Let me first briefly summarize their process before examining whether their results support that conclusion.

The authors chose to approach the question of instrument preference from the perspective of the player because “it is violinists who choose their instruments, and whose judgments are therefore most consequential.” They therefore set about mimicking, to the extent practical, a typical setting and scenario in which a soloist would go about choosing an instrument for themselves, while also maintaining the double-blind standards needed to make it a valid scientific test. There were 6 “old” and 6 “new” instruments for a total of 12. Each of the 10 soloists were first given 50 minutes to try all 12 of the violins in a practice room, as they might while first trying instruments at a shop. They were then later asked to try the same instruments in a large concert hall. After each session they were asked a number of questions both about general preference and about specific qualities such as loudness, playability, etc. And lastly, they were asked to play a subset of the instruments again for no more than 30 seconds each and asked what kind of instrument they thought it was, to ascertain whether they could differentiate old from new. The double-blind standard was maintained throughout by having everyone wear welder’s goggles and keeping the ambient lighting low.

While criticism of the study’s methodology could easily be found in blogs, on Maestronet, and presumably around both orchestra and violin shop water coolers following its publication, I actually think their approach was basically sound. I doubt that any change to the set up, short of doing an entirely different experiment, would have produced a significantly different outcome. It is rather in the framing of the question and interpretation of the data that I think the study’s main weaknesses lie.

The pervasive problem of this paper is that it keeps slipping into treating qualitative data as though it were quantitative. This lack of conceptual clarity makes it difficult to draw clear conclusions, which ultimately weakens the impact of this important study. On the one hand the authors openly acknowledge that no conclusion can be drawn that goes beyond the specific instruments and soloists studied. But the use of language such as: “A surprising result is that while old and new violins have similar ratings for overall quality, the old are on average lower for the other five criteria,” makes it sound like they might be trying to make a broader claim. Something like “A surprising result is that while the set of old and new violins have similar ratings for overall quality, the old instruments in the study are on average lower for the other five criteria.” would have been clearer and made discussing and analyzing the results easier.

This problem is especially acute when they attempt to generate preference “scores” for each instrument. Even if we grant their somewhat arbitrary approach of assigning 4 points for being chosen first, 3 for second and so on, and then subtracting a point for each time it was rejected, to then sum the scores of the old and of the new instruments respectively in order to compare them crosses the line into statistical analysis that just isn’t very meaningful. After going through a few permutations of this the authors conclude, “We can find no plausible scoring system by which the old fare any better than this.” However, removing just the highest and lowest “rated” instruments—which could very well be outliers—yields a “score” of 25 to 27, instead of 4 to 37, and a radically different picture where old and new instruments are preferred essentially equally.

The problem here is not that they tallied the scores in a flawed manner, but that tallying scores isn’t a fair way to analyze or convey the type of data they collected. A qualitative description of each soloists interaction with each instrument, a sort of anthropological ethnography, would have been more honest while pointing, I believe, to essentially the same conclusion.

I do understand that the authors’ desire to bring together all of the data in a manageable form. I have re-graphed the preference generated “scores” in a way that I think somewhat more accurately portrays the data. I have chosen to remove dimension markings from the y-axis because while the relative ordering of all the instruments might be meaningful the relative distance between them cannot be taken as particularly meaningful. I also believe that this graph suggests a more fruitful framing of the question than “Do musicians prefer old or new instruments?” Namely: is there any correlation between musician preference and instrument age.

My regraphing of the preference “scores”

While one might be able to see a weak correlation in favor of new over old—a correlation that only grows weaker once outliers are removed—one would be hard pressed to pronounce a clear preference for one set over the other. But even here it is important to remember that this type of conclusion cannot be generalized beyond these specific instruments and soloists. Making suggestions in that direction only confuses the matter. This is not because of fundamentally flawed methodology, as some have suggested, but because of the type of data the study was set up to collect.

All of this might seem like mere semantics. But, since this study, by its own admission, is motivated more by the desire to combat myths than to generate new insight it is precisely on this semantic level that we should care about how the results are portrayed. I believe the impact of the study would have been more powerful if it had been more careful in how it presented its findings. For all of its shortcomings I do think that the Paris Experiments were very valuable in lending strong credence to the notion that musicians should stop caring so much about whether instruments are old or new, which is almost—but not quite—the same as saying that no clear preference between the two can be found.

Taking a slight tangent from the main thrust of the paper, the sentence that most caught my eye was:

Individual violins may or may not have been recognized or remembered across the sessions, so the extent to which Session 2 ratings are affected by those made in Session 1 is not known.”

As a maker the question of how self consistent musicians are when trying instruments sounds far more interesting than average preference between old and new instruments. In fact, I wish I could have been in the room with the soloists while they tried the various instruments to see what types of things they paid attention to and cared about. I realize it’s silly to wish that a study focused on one question had asked something entirely different, but in this case it feels like a missed opportunity. And actually, I don’t think it’s that different of a question. Describing how top musicians go about evaluating an instrument and what they pay attention to when they do—i.e. the type of thick description the study was well set up for—would have revealed how little musicians care about old versus new, while also avoiding the shortcoming of trying to get qualitative data to speak with quantitative rigor.

I think part of the frustration and difficulty of responding to this study—which is also reflected in the mess of widely varying responses that came out after its publication—is that it was constructed in response to a pervasive but not entirely well defined myth. Any attempt to grapple with vagueries ultimately leaves one sounding a bit vague oneself. To my mind the strangest aspect of the entire old vs. new instrument debate is that so very few musicians will ever be able to play, let alone afford to buy, a classic Italian instrument that for most people it really doesn’t matter if a Strad is “objectively” “better” because it’s not a realistic option anyway. And at the same time, even those of us who advocate most strongly for modern instruments, continue to make instruments that are close copies of historical instruments. So hopefully this study can allow us all to collectively move on and start using science to address new, and more interesting, violin related questions in the future.

The original two new sciences.

References & Notes

References & Notes
1 With heavy caveats.
2 Note that this purposefully ignores their size
3 Note: this is not the same LD1 from the first part of the study.
4 Perhaps the tidbit that the Deganis are a notable exception to the overall trend, is worth following up on, but I don’t know what to make of it in isolation.
5 With the notable exception of late del Gesu violins, which are outliers in so many way.

Lessons from Designing a Viola

Monday, April 3rd, 2017

Violin making is a conservative discipline. The vast majority of instruments are copies of previous instruments. When it comes to violins the first place we look is usually the work of Antonio Stradivari. While Strad did make a few violas, common wisdom does not regarded them as well as his violins. So when I was sat down to make a viola I found my options had narrowed down to everything else.

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The first choice I had to make was size. Most violins are about the same length. It’s a size that works. Violas, however, don’t work. Violas are made in a range of lengths, roughly from 15 to 17 inches. There are two things going on here: First, each model is an attempted compromise between sound and playability. A larger instrument can give a fuller and, importantly, louder sound. Part of the reason that viola concertos are rarer than violin concertos is that the violin is able to project over the orchestra in a way that the viola has trouble with. I swear there is no anti-viola conspiracy at work here; it’s just physics. Basically, the viola is tuned a fifth lower than the violin but is not scaled up proportionally to be a fifth larger.

Tuning of the violin vs. viola

The strings on a violin and viola.

It’s not all bad, though, because this is exactly why the viola sounds the way it does. The unique, and desirable, timbre of the viola—which is often described as “dark” or even “growly”—seems to be the trade-off for a somewhat less powerful instrument. Which isn’t to say that no one has built a violin scaled up to viola tuning, but that’s not a viola.

Building a larger viola can often get you more oomph, but at some point you make it difficult to play for those of us without extra long arms. Trying to play a too big instrument isn’t just uncomfortable (though, who wants to practice hour after hour on a painful instrument?) but can make more virtuosic passages nigh impossible or even lead to injury. Because there is no single good compromise between tone, volume, and playability we instead continue to build a range of violas to suit different players and different needs.

The second thing going on is that there used to be two kinds of violas: tenor and alto1Riley, Maurice W. The History of the Viola. Ann Arbor, MI: Braun-Brumfield, 1980. 12. The larger, tenor, viola has largely fallen out of fashion. There is no clear cut single reason for this. Part of the story is undoubtedly that they are just too big to play comfortably2One could speculate about alternative performance practices such as playing on the arm or even on the lap like a cello, but that doesn’t help the modern violist playing modern repertoire.. Part of the story might also be changes in musical style and needs. But, the details are difficult to trace, in large part because of terminology-confusion, so I’ll leave that for a future post.

As a quick aside I should mention that there are some wacky (esp. non symmetrical) violas designs out there which have been offered over the years as creative solutions. Some of them might even work. I don’t know and that’s all I can say on that topic. On a similar note, while we often talk about viola sizes in terms of back lengths, obviously that’s not the whole story because it’s really about vibrating string length, internal air volume, plate surface area and curvature, and more—all of which generally scale with back length but not necessarily or directly3Which is to say: Dear violists, please don’t focus so much on back length when searching for a new viola. Thank you..

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For this instrument I—arbitrarily—chose to make something on the smaller end of things. I had access to a technical poster of a G. B. Guadagnini viola with a back length of about 400 mm (~15 ¾″). Ideally one would always chose a model based either on the past experience of having built a number of them, or at least from having heard the original. Unfortunately we often have nothing more than recordings and the traditional knowledge of the violin making community to go off of and are limited by what instruments, posters, and books we have access to.

I had some confidence in this model because Mr. Guadagnini made a bunch of them. In addition to the example from the poster I found two more in the Guadagnini Book, and a fourth online, which seemed enough to establish that this was not a one-off design. Furthermore, they are all from late in his career when he lived in Turin. Guadagnini employed a variety of viola models over the course of his life. These changes might not mean anything. We can never know for certain why a maker made the design changes and choices they did. Today we are driven, mostly, by a desire to optimize certain tonal properties. Of course folks in the 17th and 18th century cared about sound4e.g. Prizer, William F.  “Isabella d’Este and Lorenzo da Pavia, ‘Master Instrument-Maker’.” Early Music History 2 (1982):87-118+120-127, but projecting our desires and mindset onto past makers may or may not always be accurate. For example, we can’t know what kind of influence Guadagnini’s patron at the time, Count Ignazio Alessandro Cozio di Salabue, might have had. And lastly, even if the Old Makers were designing in the service of sound, we should still be cautious about the conclusions we draw because of differences in historical set-up, playing style, and possibly acoustical aesthetics. But still, given that Guad kept making this particular model right up to the end of his career I am inclined to believe that he considered them “successful”, whatever that might have meant to him. Hopefully it meant, at least in part, “great sounding”5I doubt it meant “great looking” because these violas are squat and a bit awkward visually. But, here again, aesthetics change over time so we have to be careful..

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Now that I knew what I was going to copy I had to figure out how to copy it.

Many violin makers pride themselves on making close copies of historical instruments. That does not, however, mean that we all have the same approach in mind. Ask two makers to use the same model as reference and you might end up with three or four very different instruments. Just saying “copy everything, and get it as close as possible to the original” is far too broad to be useful as a guiding principle. To help me narrow it down a bit I use the following sensitizing concepts when thinking about how to approach a copy6None of which are unique, or even original, to me..

My underlying axiom is that I care about sound. I believe that the impetus for using old instruments as the basis for my models is to capture their sound profile. Therefore, what I am trying to copy are all the things related to how they sound.

The first assumption that I make is that instruments are very complicated. Because of this we have to further assume that every minute aspect has the potential to be important for the final sound. Of course, I can use what I have learned—which includes the craft knowledge passed down to me by my teacher, the experiential knowledge from my making, and the scientific knowledge that acoustician and other have produced—to make informed guesses and decisions about what aspects of the instrument are more or less sensitive to being changed. But, I have to be careful because I don’t know everything, I could be wrong, and there could be complex and subtle interactions and knock on effects7There is an even more fundamental assumption at work here, namely that the sound of an instrument is entirely a product of its materiality. Which seems fine to me, but there are ongoing debates in the violin making world about such things as the role of playing-in instruments as well as more esoteric theories about the “magic” of Strad..

My second assumption is that instruments are a product of craft, which is to say that to fully understand them one should look at the process by which, and context in which, they were produced. I believe that it follows that emulating, to the extent practical, the working method of the original maker will help me more accurately capture his end product. First, because by using historical methods and tools I will copy not only the macro features of the instruments but also those micro-features which are “accidental” side effects of particular techniques. And second, because this approach helps me understand the mindset and perspective of the original maker, which in turn helps inform decisions about the model I am trying to copy. The work of people such as Maestro Sacconi, Roger Hargrave, and others—who have not only written extensively about old instruments but also studied the surviving tools of Stradivari and sought to understand how they relate to his making and his instruments—has been invaluable to the violin making community on this front.

And lastly, an important caveat. While I am trying to make a copy, I am not making an identical instrument. I am working with a different piece of wood that has different physical properties (density, stiffness, etc.). Modern set-up is different from historical baroque set-up in ways both small and large (neck set, strings, etc.). The context in which my instrument will live is different (repertoire, performance practice, etc.). And, of course, I am not Mr. Stradivari, or even Guadagnini, but myself. All of which is to say that some deviation from a strict copy will be appropriate and even necessary.

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Enough theory, here’s how I went about getting ready to make this viola.

I started with figuring out the outline, both because it’s the most obvious feature of what makes a given model that model and because it’s closely tied to where we start when building an instrument. Violins, violas, and cellos are built by bending the ribs around a form, that we call a mold8There are other ways to build a rib structure, but for this post we’re confining ourselves to the Classic Cremonese Working Method [CCWM] since that’s what Guad used [WWGD?].. The outline of the top and back plates will then be based on the resulting rib structure.

Stradivari viola mold, image from The Secrets of Stradivari by Sacconi.

That’s a photo of one of the molds that Mr. Stradivari himself used. Unfortunately, the mold that Guadagnini used for the viola I wanted to copy has not survived. So in order to reconstruct the mold I have to work backwards from the rib-structure.  I just want to underline that my interest in the rib-structure here, which is really an interest in the mold that produced it, is a product of my two assumptions from above, and especially of what is known about the Classic Cremonese Working Method [CCWM]; for example, if I thought of copying as primarily a visual endeavor my starting point might be the outline of the plates.

Most of the time we can’t pop the top off a 3– 400 year old instrument and merrily trace the inside of its rib-structure. Usually all we have to work off of are some nice 1:1 photographs, which show the shape of the plates but not the rib-structure since that’s hidden by the overhang.

Overhang is the part of the plate that extends past (i.e. hangs over) the rib structure.

To get at the rib-structure we have a few options. First, we can work off of the plate outline and subtract the overhang + the thickness of the ribs—remember we want the inside of the rib-structure because we are actually after the mold that produced it9Did the CCWM prize the inside mold because they cared about the connection between air-volume and sound? I don’t know, but it’s possible.. Unless we have the instrument in front of us, it’s unlikely that we have that data for every point of the outline. At best we have a few measurements and the hope that there isn’t too much variance—which is more likely to be true of some makers, like Nicolo Amati, than others, like my Guadagnini. Sometimes all we can do is guess based on general knowledge of what kind of measurements that particular maker tended to prefer. Second, we can look at the purfling, which often—but far from always—closely matches the rib-structure. Third, for a select few instruments we have been given the wonderful gift of CT scans. Fourth, for the work of Stradivari, as I mentioned above, we have many of his original molds.

These four approaches don’t exist independently of each other. Each can help inform and refine the others. For example, when scans of the particular instrument we’re after aren’t available, other scans—especially when from the same maker—can help us double check and calibrate our other methods. And looking at the purfling can be an important supplement in areas where the overhang is very worn or erratic. For me, the exact blend of methods I end up relying on is largely driven by what data is available to me.

However, no matter what you do all of these methods run up against some basic limitations. The instruments we are looking at tend to be 3– 400 years old. Any wooden object that old will display, sometimes significant, wear and distortion, especially one that has been prized primarily for its use-value and not just art-value. Even an instrument in pristine condition could be misleading. These are handcrafted objects so human variance always plays a role. The mold does not completely constrain the shape of the rib-structure, and once the rib-structure is removed from the mold further variance is possible. You might say who cares, if you’re making a copy you should copy it warts and all. But, molds were rarely one off designs10Though, it is notable that Stradivari seems to have experimented with different molds more than most. so unless I have strong reason to believe that one specific instrument is significantly more successful than others made off of that mold, it’s probably the maker’s intention, as embodied by the mold, that I am after. Moreover, I too am human and am likely to introduce some variance. If I add my “error” on top of that of Mr. Guadagnini I will likely be even further from my intended goal.

Are we then stuck with an imperfect outline? Not necessarily. Wear, distortion, and human variance don’t happen randomly; each has its own pattern. By studying old instruments we can build a mental model of how instruments tend to change over time and use that—plus our knowledge of the types of shapes and design decisions particular makers tended to make—to make informed decisions about how we might work backwards from what’s in front of us. For example, we can decide that the outline we have is good enough, or that there isn’t enough information or reason to change it one way vs. another, and just go with it. We might conclude that one side of the instrument is more pristine than the other and make a half template, that we then flip to get both sides, thus yielding a symmetric outline. We might chose to make “corrections” to the outline by hand, or with the aid of a compass or french curves. Or we might do what I did for this particular viola: a geometric construction.

But, before I get into what the heck that means two important caveats. One, while I am spending a lot of time in the post on the outline, outline ≠ destiny. There is a lot more to a model than just the rib-structure, such as rib height, ff-hole placement, stop length/vibrating string length, and arching. The outline influences all of these, but it does not completely determine them. And two, at the end of the day the model is only a third of the instrument’s destiny. Instruments are the product of design + material + construction11Which includes set-up!. This post only covers the journey.

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At its most basic geometric construction is drawing shapes using just a compass and straight edge. These days we mostly think of it as an academic exercise with an interesting history (think Euclid), and some abstract mathematical applications, none of which explains why I would want to use it to generate the outline of my viola. Going off what I’ve written up to now you might expect me to whip out some evidence that Mr. Stradivari sat around in the evening with his trusty compass and doodled new violin designs. No such evidence exists. In fact, there is no direct historical evidence that these techniques were used as part of the classic Cremonese working method.

What we do know is that—as has been demonstrated by the important work of François Denis in his groundbreaking book Traité de Lutherie—one can successfully draw a wide variety of classic Cremonese models using the techniques of geometric construction. Furthermore Stradivari—and presumably others—owned a compass and straight edge12In fact, we have technical drawings in Stradivari’s hand that use compass arcs to locate where the ff-holes on an instrument should go., so at the very least it’s possible that geometric construction was part of their repertoire. Also, there is some evidence that geometric construction was used to design other instruments such as lutes and harpsichords, most notably a 15th century manuscript left to us by Henri Arnaut de Zwolle, inching us from possible towards plausible.

Geometric construction of a lute from de Zwolle’s 15th century manuscript.

More concretely, we know that it was widely used in the fields of architecture and cabinet & furniture making, which may seem like a long way off from violins but this passage from the Roman era Vitruvius’13He’s also the guy behind that famous Da Vinci drawing of a guy inside a circle and a square. 1st century BCE book On Architecture—which was well known and regarded from the 16th century onward, especially in renaissance Italy—will give you an idea of the type of thinking we are about to follow:

On this account the ancient architects, following nature as their guide, and reflecting on the properties of the voice, regulated the true ascent of steps in a theater, and contrived, by musical proportions and mathematical rules, whatever its effect might be on the stage (scena), to make it fall on the ears of the audience in a clear and agreeable manner. Since in brazen or horn wind instruments, by a regulation of the genus, their tones are rendered as clear as those of stringed instruments, so by the application of the laws of harmony, the ancient discovered a method of increasing the power of the voice in a theater.14De architectura, V3§8.

And a little bit later on he write:

For nature has made the divisions of tones, semitones, and tetrachords, and has established those proportions of the intervals, by which workmen are guided in making and assigning their just proportions to instruments.15De architectura, V4§4.

And then he goes on to take a lengthy detour from architecture into music theory, and all the different kinds of chords and scales there are. The key word that shows up in both of these passages is proportion. While the tools of geometric construction may be the compass and straight edge, the real engine is ratios. These days, when we sit down to design something we think in terms of measurements. This needs to be x inches long or y millimeters thick. It’s a system that works particularly well when everything is standardized, e.g. dimensional lumber or screw sizes, like we have been doing since the industrial revolution. But, with geometric construction you start from one measurement—which you can think of more as setting the scale for the whole project—and everything else emerges from that using a system of ratios. These ratios are more than just a cheat sheet to quickly generate a series of measurements. The ways in which the ratios repeat, reappear, and relate to each other is the at the heart of what ultimately produces the design. This idea is behind a lot of classical and baroque architecture. And of course, as Vitruvius alludes, it’s also how music works, which speaks more to a shared theoretical approach than some kind of grand acoustical convergence. Though, that kind of grand convergence is exactly what folks at the time had in mind when they talked about the music of the spheres.

From the Cyclopedia Of Architecture, Carpentry And Building

The take aways here is not that using geometric construction and ratios will magically produce a better designed or sounding violin, but that using these techniques can help us see shapes, and understand the ideas & relationships behind them, in a new way—one that is likely closer to the mentality of the pre-industrial revolution artisans we are trying to copy than our more modern digital caliper approach. One way in which this becomes particularly useful is when studying old instruments and the way that makers built off of and adapted the work of those who went before them. This video from the wonderful maker Kevin Kelly does a great job of that. Be sure to check out all of his other videos about geometric construction, they are a fabulous resource and will give you a good start towards helping you understand how to go about doing a geometric construction of a violin.

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Armed with all of the above I turned to my viola. As I mentioned above, I worked off of 4 different instruments that I believed to have been constructed on the same mold. First I measured everything I could think of, and—essentially working backwards—tried to uncover the underlying ratios at play. For example I would measure the width of the lower bout and the width of the upper bout and then divide one by the other, hoping that the result came out close to a whole number ratio. Then I would check it on the other three instruments to make sure it wasn’t a fluke.

I want to make a quick aside here about the golden ratio. There is a lot of mysticism caught up with the golden ratio and sacred geometry and how it shows up in nature16That link is to a really awesome video that is really worth watching. that tends to sneak in when one starts down the road of geometric construction. Also, the fact that it happens to create aesthetically pleasing rectangles is nice but not actually the point. So let’s clarify what the golden ratio is. It is the ratio such that a:b = b:(a+b). When using numerals the golden ratio looks pretty hary, 1:1.68033987..., which makes it seem like any appearance of it must have required great effort. But, when thinking in terms of geometry it’s place becomes simpler and more clear.

A big part of what makes the golden ratio so powerful is the way that it builds on itself. Once it’s part of your scheme it will keep cropping up by itself. See how once you have one rectangle whose sides are related to each other by the golden ratio it becomes trivial to construct a second. These types of self perpetuating ratios are precisely the types of interrelated relationships that make geometric construction tick.


And getting it to show up the first time is easier than you may think too. First, this concept of building on itself may remind you of the Fibonacci series, which would not be a coincidence. It turns out that the ratio between any two successive numbers in the series will approximate the golden ratio, getting closer as the numbers get bigger. Thus using whole number ratios like 3:5 or 5:8 or even 5:13 will give surprisingly close approximation of the golden ratio, especially at the scale of a violin. Second, while calculating the golden ratio requires taking the square root of five and yields a gnarly irrational number, it’s actually very easy to draw through geometric construction, for example:

But back to the viola: Once I had amassed a mini-library of ratios the real work began. I had to figure out how these various ratios related to each other and how they might emerge organically from my geometric construction scheme. Mostly this involved drawing outlines over and over trying to get closer and closer to the instruments I was trying to copy. Sometimes I would get something that fit one of them really well but was very off for the others. Then I had to think about what parts of each I trusted the most and why, and where I wanted to try to compromise between them. You can think of it as a sort of forensic reconstruction. The instruments were my crime scene, and I had to come up with a plausible Colonel Mustard with the candlestick. Being slightly to the inside of one of them might be fine if I was still to the outside of another, but clearly being outside of all of them was highly unlikely to be correct. I want to emphasize that this was not just a roundabout way to come up with an average of the four outline, but the application of a technique17As in the greek τέχνη. to see the underlying shapes and harmonies of those outlines.

But, if one thing was off I couldn’t just fix that one thing. Inherent in this technique is that everything affects everything else. Changing one step in the construction leads to a knock on effect that changes every step after it. At one point I thought I had it. I held up my tracing paper to the poster and felt pretty good, went and ate dinner, came back to the workshop, and looked again. I don’t even remember the set of ratios I used for that outline because they were way off. In the end, this is what I came up with—I promise there is a viola outline in all those circles:

And while I have no direct evidence that this is the same outline Guadagnini was after, I feel confident that it’s close. In the end, this approach helped guide me beyond just my outline. My ff-hole placement, stop length, and vibrating string length were all fixed by the same system of geometry and ratios, and even my arching, rib heights, and scroll were informed by the proportions and shapes I had gotten down and dirty with.

Of course, for all of the exacting geometry that went into this instrument it was still my organic hand that did the actual work. I have no desire to make clinical looking instruments, just ones based in the best of violin making’s nearly 500 years of tradition and knowledge. Using geometric construction as my design technique helps me to get a little bit closer to that.

Viola after Guadagnini mid-construction.

References & Notes

References & Notes
1 Riley, Maurice W. The History of the Viola. Ann Arbor, MI: Braun-Brumfield, 1980. 12
2 One could speculate about alternative performance practices such as playing on the arm or even on the lap like a cello, but that doesn’t help the modern violist playing modern repertoire.
3 Which is to say: Dear violists, please don’t focus so much on back length when searching for a new viola. Thank you.
4 e.g. Prizer, William F.  “Isabella d’Este and Lorenzo da Pavia, ‘Master Instrument-Maker’.” Early Music History 2 (1982):87-118+120-127
5 I doubt it meant “great looking” because these violas are squat and a bit awkward visually. But, here again, aesthetics change over time so we have to be careful.
6 None of which are unique, or even original, to me.
7 There is an even more fundamental assumption at work here, namely that the sound of an instrument is entirely a product of its materiality. Which seems fine to me, but there are ongoing debates in the violin making world about such things as the role of playing-in instruments as well as more esoteric theories about the “magic” of Strad.
8 There are other ways to build a rib structure, but for this post we’re confining ourselves to the Classic Cremonese Working Method [CCWM] since that’s what Guad used [WWGD?].
9 Did the CCWM prize the inside mold because they cared about the connection between air-volume and sound? I don’t know, but it’s possible.
10 Though, it is notable that Stradivari seems to have experimented with different molds more than most.
11 Which includes set-up!
12 In fact, we have technical drawings in Stradivari’s hand that use compass arcs to locate where the ff-holes on an instrument should go.
13 He’s also the guy behind that famous Da Vinci drawing of a guy inside a circle and a square.
14 De architectura, V3§8.
15 De architectura, V4§4.
16 That link is to a really awesome video that is really worth watching.
17 As in the greek τέχνη.