Parameter Overload

(Caution: this turned into a long-winded think-out-loud essay on the finer points of guitar design. TLDR: Experts disagree on some key geometries; rather than blindly pick an expert to model, I need to bring my own – albeit amateur – woodworking experience to bear in the decision.)

I’ve been making myself slightly crazy by diving into texts and plans written by a variety of classical guitar builders. While the general parameters of a classical guitar are fairly settled (scale length, length and width of body), there are lots and lots of details with the potential to significantly affect the quality of the sound and playability. 

I’m a science guy, and I like mathematical models. It turns out that a few hard core acoustic scientists have tried to model the parameters that affect the quality of a guitar’s sound, but most professional builders have concluded that their information does not provide great guidance. In order to assess the effect of, say, the bracing pattern under the top, all other parameters (shape, thickness, overall manifold topology) have to be held constant. But if you go and then alter one of those other crucial parameters, the information gleaned about bracing patterns goes out the window. There are too many parameters to model.

When I have a statistical model with lots of parameters, I use computer algorithms to “hill climb” to an optimal solution for my problem. There might be hundreds of parameters to tweak – all the computer needs to know is that tweaking one parameter in a particular direction results in a better or worse fit to my desired outcome. The computer algorithm tries to efficiently simultaneously adjust everything at once in order to arrive at an optimal solution.

There are at least two reasons that approach won’t work for a builder. First, the sense of an “optimal” sound and playability is not static; every player wants something a little different in terms of sound color and string action. Some professionals have a quiver of instruments, each selected for playing a particular genre of music. So optimizing design parameters is not a one-off challenge; one has to understand how all of those might change depending on how one wants to color the sound. And the “color” of sound is itself a complicated quality to describe – another multi-parameter space. 

The second problem is that incremental iterations toward an ideal sound happen one instrument build at a time. Even professionals working full time can at best turn out one instrument a week, and that’s with many of the processes automated. It takes years of iteration to gain an intuition of how altering a particular parameter set influences the final product. 

Of course, I want to hit as close to a target of “good sound” as I can for guitar #002. One approach is to stand on the shoulders of giants – to pick a set of plans that have been evolved by an expert builder over decades, and use that as a model. After all, the expert has already gone through dozens if not hundreds of tweaks to his/her design in order to arrive at a good baseline. This is what I set out to do, basing my guitar on a design by J. S. Bogdanovich and published in his classical guitar making book. To triangulate against his designs, I’ve also been scrutinizing the text by Cumpiano and Natelson, as well as revisiting the guide I used for guitar #001, the classic text by Irving Sloane.

I’ve got an overall outline and bracing pattern (straight out of Bogdanovich), and many of the other parameters (top thickness, etc) are given in his book and are in accordance with other sources. There is just one place where all three texts disagree – somewhat radically – and it has major implications for the build. This is the geometry (or is it topology?) of the top and its relation to the neck angle.

The simplest approach is that of Sloane – the top face of the neck (before the fingerboard is glued on) should be completely coplanar with the entire top, which itself is a simple plane. Now, it’s known that once the guitar is finished and the strings are tuned up, the tension on the top face (transmitted through the bridge) can tend to distort the top over time, pulling it up (bulging) behind the bridge and depressing it slightly in front (under the strings). If this distortion is severe it can affect the playability of the instrument, and then some replaceable pieces (namely, the nut and saddle) may have to be re-shaped.

There is one camp of builders that pre-stress the top by pressing it into a gentle curve and holding that shape with curved internal braces. Both Bogdanovich  and Cumpiano & Natelson use curved tops. But now that I thought I had my parameter explosion under control, again I see subtle distinctions.  Bogdanovich both curves the top and tilts the lower bout (the fat part of the body) back at an angle; essentially this compensates for the increased height of the bridge produced by the curve. Push the top out, tip it back, and in theory the bridge ends up in the same spot it would have been in an unstring, planar guitar. Cumpiano & Natelson curve the top but don’t perform any sort of tilting compensation. Then, just to make it really interesting, I’ve come across builders who curve the top but tilt the upper (smaller) bout of the guitar back, to change the overall angle at which the string intersects the top. This is the so-called elevated fingerboard design (this page by Howard Klepper describes his particular approach).

Here’s the last issue – some of these top geometries are much hard to execute than others for an amateur builder. Obviously, the flat plane is easiest. Next easiest would be the overall dome of Cumpiano & Natelson – the standard solution is to create a dished out work board that the top is pressed into when braces are glued on the underside. I’ve already taken the plunge and ordered two pre-made work boards with different degrees of curvature. My big problem is Bogdanovich’s approach – the combination of a curve and a tilt means that one has to (pretty laboriously) hand-shape some of the work board, and there’s an aspect of his neck angle that still doesn’t make 100% sense to me.

And that’s the final rub, my lightbulb moment – whatever I choose for a plan going forward, it has to make sense to me as a builder. I clearly don’t have all the answers, but I’m not a completely blank slate, either. To my eye, there are just too many tweaks that Bogdanovich has to make to his components (shaving a bit under the fingerboard, etc.). So I’m inclined to either go with the general curve of Cumpiano & Natelson (not compounded with a tilt), or punt entirely and use a purely planar design. Maybe someday I’ll come to understand the advantages of Bogdanovich’s lower bout tilt (which is exactly the opposite of the elevated fingerboard approach used by Klepper and others).

At this point I’ve reduced my parameter space to a single binary choice – planar or generally curved. I think I can live with that and move forward, holding the other parameters constant.


One thought on “Parameter Overload

  1. Pingback: Mental Health Days | The Learning Curve

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