Wood, Knife, & Sound

Notes from the workshop of Jedidjah de Vries.

Afterlengths: two myths and a “truth”.

November 17th, 2021 by Jedidjah de Vries

The process of building an instrument doesn’t end when it’s strung up to play for the first time. I will spend days, and often longer, making adjustments. It’s impossible to change the fundamental voice of an instrument. But, with patient work and care, it is possible to bring out the best version of an instrument.

So what does that work look like? There are few different ways I can intervene. The three that probably come to mind first are: the choice of strings; the bridge, which can be carved and adjusted; and the sound post, whose exact position and tension can be tweaked.

Slightly less obvious is the afterlength. The afterlength is that bit of the string that is between the bridge and the tailpiece. Its length can be changed by changing the length of the tailgut—the loop of material (usually not gut anymore) that connects the tailpiece to the endbutton. If you make the tailgut longer, the tailpiece will move closer to the bridge, and the afterlength will get shorter. If you make the tailgut shorter, the tailpiece will be further from the bridge, and the afterlength will be longer.

But why bother? To answer I first have to first dispel two pervasive myths about the afterlength.


Myth #1: Longer Afterlength = Higher Tension

The idea that lengthening the afterlength means an increase in string tension follows from our intuition that when you pull back on a string you increase the tension on it, which is true. That’s exactly what you are doing when you turn the pegs to tune your violin up to the proper pitch. And that seems exactly like what is happening when you move the tailpiece back to lengthen the afterlength. I’m grabbing the tailpiece and moving it back, right? Well… no.

Remember, changing the tension is how you tune your violin. If you increase the tension on a string you will also raise the pitch of that string. And we know that’s not the case here! The A string will still be an A string, tuned to 440 Hz (or whatever you’re using), no matter what the afterlength is.

What you have to keep in mind is that the vibrating string length—the distance between the bridge and the nut—does not change. So that distance (L) is fixed. The frequency (f_0) the string needs to play is also fixed. We’re not changing the string itself so its density (\mu) is also still the same. And it turns out that the string tension (F) is strictly set by those three things, and those three things alone. There is even a formula for it that was worked out by a fellow named Marin Mersenne in 1636, which looks like this:

    \[ f_0=\frac{1}{2L}\sqrt{\frac{F}{\mu}} \]

Don’t worry about the math. All that matters is that if you have a specific string, with a specific playing length, and it’s tuned to a specific note then you can calculate the tension on that string exactly. So the physics tells us that changing the afterlength isn’t changing the string tension. But then what about our initial intuition about pulling back on a string? How does that square with the physics and the math?

Imagine I could pull back on the tailpiece (i.e. increase the afterlength) while the violin was strung up and in tune. I would indeed have increased the tension of the string…but, now my violin would be out of tune! It would be tuned too high. So I would use the pegs to detune the strings back to their correct pitch, and—what the formula tells me is that—I will always arrive at the exact same tension that I started at.

It’s almost as if I had two tuning pegs: my regular tuning peg by the scroll, and then another peg behind the tailpiece. I can turn the “peg” by the tailpiece to move the tailpiece back and lengthen the afterlength, except instead of turning a peg I change the length of the tailgut. But then I have to turn the peg by the scroll by the same amount to keep the string at the same pitch. You can think of it a bit like an old school reel-to-reel tape machine, unspooling at one end and picking up at the other. The result is that the tailpiece can move closer or further from the bridge, but nothing about the string, its pitch, playing length, or tension will change.


Myth #2: The magic ratio is 1 to 6

You will often find the advice that the afterlength should be exactly ⅙ of the vibrating string length. From a practical perspective what this means is that if you pluck the afterlength it will produce a tone exactly a fifth and two octaves higher the note of that string. So if you were to pluck the afterlength of the A (440.0 Hz) string you will hear an E (2640.0 Hz) two octaves below the E string of the violin (659.2 Hz). For the luthier setting up the instrument that’s very convenient. It’s a quick and easy way to check whether the length is “correct,” just pluck and listen. This is also often pointed to as the explanation for why the after length should be one sixth the string length.

The story is usually fleshed out with appeals to resonance, that by being “in tune” this way the afterlength will resonate sympathetically when you play, which is taken to be a good thing. This can sound plausible. There really is a bit of sympathetic resonance going on between the four strings of the violin when you play, which contributes to that ringingness you get when you play a note in tune. When talking about the afterlength people will often take this further and say or imply that having it set to just the right length will make the whole instrument resonate, or resonate correctly, or resonate more, or something. And, again, more resonance is taken as necessarily better.

It all quickly starts to sound a bit like the classical theory of the harmony of the spheres, in which music, ratios, beauty, and God’s perfect ordering of the world aren’t just metaphors and symbols for each other but manifestations of the same underlying universal truth. I don’t think I have heard anyone explicitly appeal to the harmony of the spheres to explain why the afterlegth should be at a ratio of 1 to 6 with the strings. But, there is a bit of hand-wavy implication that having things be in a whole number ratio with each other, and thus “in resonance” with each other is inherently good acoustically.

Except, it doesn’t actually work that way.

Robert Fludd, De Musica Mundana (1618)

The design of the violin does have a lot of whole number ratios. It’s a product of the era it emerged in, and that includes a bit of harmony of the spheres world view where the perfect ratio of the musical pitches were carried through a design elements with the idea that they represented the perfect merger aesthetics and functionality. That’s just not what’s going on with the afterlength.

This is a good example of how craft knowledge can be true in that it gives good working knowledge and results. And, at the same time, from an empirical science lens be wrong in that the explanations don’t actually make sense. So It is the case that making the afterlength be a sixth of the vibrating string length is how luthiers will often go about setting up an instrument. It’s usually about the right length. But, it’s not because it’s one sixth.

To be very clear: the afterlength does vibrate. The way and frequencies at which it does so matter for the sound of the instrument. But, the afterlength doesn’t vibrate on its own! It’s that whole behind-the-bridge assembly of the tailgut + tailpiece + afterlength. So what does changing the length of the afterlength do? The biggest thing is that you are moving the mass of the tailpiece forwards or backwards, and that changes the mass distribution of that whole behind-the-bridge bit, which in turn changes how it vibrates.

This is the same idea behind those wolf-eliminators, the ones that look like bits of brass stuck to the string behind the bridge, that you’ll sometimes see on cellos. The physics of what’s going on there is a topic for a future blog post but basically that too is about changing the mass distribution, except by adding a moveable mass, instead of moving the tailpiece.

You may have also heard all this stuff come up around the question of whether to add four fine tuners to your tailpiece. Hopefully now you understand that the problem isn’t that it changes the tension on the string. And the problem is not directly that it’s heavy and heavy is bad (else we would all be playing without tailpieces and instead just a loop of metal or something!), though the change in weight is a big part of what changes. The problem really is adding something to a tailpiece that wasn’t designed for it. If you want four fine tuners you are better of using one that was intended to be used that way, like the various models with built in adjusters.

At the end of the day, the physics of why and how all that matters for the sound is a bit more complex than simple sympathetic vibrations. There isn’t a direct linear relationship between making changes in the afterlength and a specific aspect of the instrument’s sound. That’s why having a quick heuristic, like ⅙, is useful to get us in the ball park before starting the lengthy work of listening, adjusting, listening, adjusting… till it’s just right.

 

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Faith & Uncertainty

May 11th, 2020 by Jedidjah de Vries

I remember the first time I had to fit a bass bar. I was certain it was impossible. It took me multiple days and a lot of coaching from my teacher. Now it’s just a morning of concentration from start to finish. When you are first making violins technical tasks—such as fitting two surfaces together or even sharpening your tools—seem by far the most difficult. But eventually you get the hang of them. That doesn’t mean they are actually easy, just that they are a specific kind of hard that takes a certain kind of learning and practice to get better at. Different parts of violin making are hard in different ways. But for all of them learning and practice help face the challenge; there is no magic or innate skill here. And I think all craftworkers would agree that it’s always a continuous process that doesn’t really end.

These days, I would say one of the most difficult steps of making a violin for me is carving the arching of the top and back…specifically: deciding when to stop. In fact, it might be the single most difficult step in making a violin.

The challenge stems from there not being a clear right or wrong answer. For example, when carving a bridge either the feet fit or they don’t. The arching, however, is a complex three-dimensional shape with a range of plausible answers. Creating those shapes is less about hitting a set goal and more like trying to embody an abstract concept.

That means I don’t have a single ideal arching that I’m trying to duplicate. It’s inherently tricky to see, take-in, and hold in one’s mind the whole complex shape at once. It’s possible to take measurements in a few spots here and there, or to compare some select segments to a template. But that kind of approach that will only ever get you so far. And because it all flows together, changes and corrections in one area necessarily affect the shape in its entirety. Any deviation, even a small one, from your ideal platonic model would require a whole series of adjustments to make everything fit and flow together again so as to end up with a coherent whole.

So instead of a static model of the goal I have a bunch of ideas about how I think the arching should work. All those ideas end up interacting both with each other and with the specific outline, wood, and other details and factors in front of me. To be perfectly honest, it’s a jumbled mix of intuitions, concepts, sense memories, guidelines, images, and also a few stray measurements. Together they help me evaluate whether or not I am on the right path. But, there is no preset end to that path. That’s why knowing when to stop is so difficult. The line between just right and too far is both thin and ill-defined. And, of course, there is no way at this point in the construction to directly evaluate what actual matters: the final sound of the instrument.

At the end of the day, sometimes you just have accept a little bit of uncertainty in life. Luckily for me, this won’t be the last violin I build. My experiences from this instrument will help build and refine my arching concepts for the future. For me, this kind of working out of an abstract concept on and through a physical medium really goes to the essence of what it is to be engaged in a craft.


And the arching isn’t just important for the sound. It’s also important for getting the ff-holes right. Laying out ff-holes can be a trip. You might think it’s a straight forward matter or correctly positioning a template so as to meet a few simple constraints. But no. Really you are projecting a funky two-dimensional shape onto a complex curved three-dimensional surface.

The ff-hole you start with and the ff-hole on the instrument are never actually the same. Making even small adjustments to their location or orientation can alter how it looks and its relation to its surroundings in surprising ways. It’s like walking past a fun house mirror trying to find the sweet spot where everything comes out just so. Plus, it all depends on the underlying arching you carved. Even slight asymmetry, a small dip or wave, or just a different flow from usual can make it very difficult to get the ff-holes to sit well on the plate. Sometimes it feels like a puzzle without a solution. But, once everything falls into place they are deeply satisfying to behold. Then again, once they are laid out, it’s time to actually carve them.

Carving ff-holes takes faith. After the initial rough sawing they look ugly. They look scary. They don’t look like ff-holes. I always have the same thought: what if this time I can’t make them look right? But you have to pick up the knife anyway and carefully and slowly begin to remove a bit of wood here and a bit more wood there. There is no guarantee that you’ll end up with a nice ff-hole and not some molten gaping horror. Can’t let that stop you. Sometimes I have to remind myself that I’ve done it before, and that I’ve sharpened my knife well, and that my hand is following my eye. Can’t stop even if you want to because what use is a top plate with a partially carved ff-hole? So you keep carving and making it look a little bit better and a little bit closer to how you want it.

It can be frustrating. That’s why I have a post-it on my toolbox to remind myself of what to do when it gets overwhelming:

  1. Go have some tea.
  2. Sharpen your tools.
  3. Make a small thing a little bit better.

But then, once you get one ff-hole looking pretty good there is always the second one—and now it has to look not just good, but more or less similar to the first one!

But at least while carving ff-holes you can make nice, more or less linear, progress from not-an-ff-hole towards your goal. Carving scrolls takes a different kind of faith.

Craft is most pleasant when you are able to make steady progress towards your goal. And that works for most things. Not scrolls. Scrolls—at least to my mind—take a detour through an ugly phase. You can layout everything nicely, work everything into a nice initial form, and then…there’s a point when the shapes don’t quite make sense anymore and you have weird extra bits of wood and ragged spots that you will, of course, clean up later but right now it doesn’t make much sense to deal with. It always comes together at the end. But to get there you have to maintain your faith, not in your hand skills and tools like with the ff-holes, but in the steps and process that will get you from A to B, and ultimately to C, a good sounding instrument that a musician will enjoy using to produce music.

But that’s just how craft is: Faith and uncertainty, mediated by hand and tool.

 

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The Mystery and Mystique of Making

April 5th, 2020 by Jedidjah de Vries

Violin makers are obsessed with corners. Those are the pointy bits at the end of the c-bouts that you’ve probably never given a second (or first?) thought to. It’s very easy for the fetishization of tiny details to turn into hipster snobbery, and there is plenty of that in the violin world. But allow me to give three reasons to care about corners anyway.

First, small, seemingly insignificant, features are often key to establishing the overall aesthetic of an instrument. The corners help give the eye context as it takes in the instrument’s outline, and convey much of its character and style; especially since the lines of the purfling highlight their shape.

Second, while the overall shape of the violin may seem arbitrary, it actually has a strong internal logic. At the corners, however, the dictates of that logic tend to be weaker. You could therefore see the corners as space for “creative expression”. But, to me, it actually means that you have to think extra carefully about their shape and how they relate to the rest of the instrument.

Third, obsession is sometimes a useful tool in craft. Even if I don’t care about the corners themselves, picking them out as important focuses my attention in a specific way that helps get the outline as whole just right. A masters of a craft will sometimes give explanations for how or why they do something that, to say an engineer or physicist, does not correspond with reality and yet precisely captures the understanding needed to coordinate the hand, mind, and eye to produce the desired result.

All of which is to say, that—as a violin maker—I think it’s worth my time to endlessly contemplate the infinite mysteries of corners, but you…you shouldn’t feel any obligation give them a second (or first?) glance.

But also, corners, because they stick out, experience a lot of wear. On older instruments they are rarely pristine. In fact, full corners look very odd to some people. Even Strad made corner-less violin once! So while I appreciate a perfect corner, I also try to maintain a bit of perspective. Social media tends to be full of perfect photos of beautifully finished work. I find myself, on other hand, tending to share my messy work-in-progress. Even though it’s not always as flattering, I think it’s often more interesting. I guess that’s why I’m a violin maker and not an online brand influencer person.


But more than that, I’d like to break the mystique of violin making a little. I don’t think we should pretend that what we do is more special than it is. Musicians will respect us without appeals to secret ancient knowledge. My ego will be fine without claims of super human precision. I work with my hands based on principles of sound craft, and I think that’s pretty cool on its own. Yes, making a violin is highly skilled work, but it’s not magic. I would rather keep the door to my workshop (metaphorically) open than find myself hiding behind a veneer of prestige.

In that spirit, I have a confession to make about rib structures: they aren’t my favorite…and that’s ok.

Building a violin takes a range of skills. I realize that sounds strange because it all looks like woodworking. But, bending, carving, shaping, fitting, set-up, and varnishing all require different strengths and mindsets. The diversity, and the challenge of bringing it all together, is a big part of what I love about making violins—even if I don’t enjoy each individual step equally.

Not enjoying your job is, unfortunately, common. There is this notion, however, that jobs of passion are categorically different. It’s not true. Even though I love making violins, there are always ups and downs. But, more than that, it misunderstands the nature of work.

I prefer to see making violins, not as an expression of who I am, but as a contribution I make to music, my community, and the world.

Under capitalism, there is no such thing as a pure work of passion. The economic realities necessarily change how we work and our relation to that work. (Just ask a school teacher!) I don’t just mean that it introduces the need to find balance between speed, quality, and price in an effort to triangulate value. To a certain extent that’s always present in craft. But, because in capitalism that value is determined by a necessarily antagonistic relationship between makers, dealers, and players.

More perniciously, this myth is used as a foil to justify the misery of “regular” jobs. By setting apart a small number of “special” jobs the everyday toil of the rest is framed as just the way it is. The hidden assumption here is that our jobs are fundamental to our identity, especially since most of us rent our very selves out by the hour. In this worldview work becomes utterly fulfilling or utter drudgery, and if it’s the latter it’s your fault and not that of the job itself!

But work doesn’t have to be your very identity or the expression of your self worth as a human. I prefer to see making violins, not as an expression of who I am, but as a contribution I make to music, my community, and the world. For me, that radically changes how understand the ups and downs of my work…and lets me enjoy it even more!

An imperfect work in progress.

 

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