We all know the shape, a classic design invented at Martin Guitars around 1916, named after the biggest battleship of the day. Compared to the more tender traditional guitar styles of the time, the Dreadnought guitar was as radical as green eggs and ham when it first appeared, and it was a breakthrough on many levels. First, the relaxed waist created a far more rigid body, capable of handling the greater tension of long-scale steel strings, so the body wouldn’t warp up so quickly over time, and so remain more playable, longer, before needing a neck reset. Second, the longer strings it allowed were LOUDER, which every cowboy wanted in the days before amplification. Third, a more subtle but potent psycho-acoustical transformation was the decrease in the frequency of the lowest body air resonance to roughly G-99Hz, 3^rd fret on the low-E string. Smaller guitar bodies just couldn’t get that low, so they lacked the acoustical ability to provide musical “Oomph” to those low notes that form the anchors of the ever-popular E-chord and G-chord.

The newly-accessible G-99 air resonance also happened to coincide with the voice format of the human male baritone voice. Subliminally, a voice with a formant in this frequency range indicates a “big guy” on the scale of guys, what sociologist might call an “alpha-male”, and what FM radio announcers tend to sound like. We are hardwired to estimate authority, strength and threat indicated in a voice by the depth of its voice formant. If you upset a dog in the dark, and it goes “Yip! Yip! Yip!”, you don’t pay it much mind. However if it gives a loud, deep “Woof! Woof!” your instincts might remind you suddenly of an important appointment you are late for in the next town.

Which brings me to that beautiful Dreadnought shape. Scientists have studied what body shapes humans of one sex finds most attractive in the opposite sex, and for men in every culture around the world the ideal female’s waist-to-hips size ratio is 0.7. I measured the same waist-to-hips ratio of the Dreadnought in the picture above, and the ratio comes out to 0.68. Hmmm…not too shabby. So the Dreadnought design resonates with us on a number of levels, some deeper than others.

Today I was working on creating a CAD model of a Dreadnought guitar body, and for one reason or another I thought I would trace one from an online picture.  So I found the above picture in Google Images, and I copied it onto the surface of large flat rectangle I created for the purpose.

To create smooth curvy shapes in CAD there is a wonderful thing called a “spline curve”. You select this spline tool in a sketch and click along the feature you are interested in, and a beautiful smooth curve is created that passes through each “control point” you created. You can then subtly alter the shape of the curve by moving around the control points pixel-by-pixel.

In this picture is part of the spline curve I created around the Dreadnought body, trying to follow its outline as exactly as possible. The thin blue line is the spline curve, and along it you can see small blue dots which are the control points I created. The spline seems offset from the edge of the guitar, however you can see from the light glint off the outer binding that the binding is mostly invisible, and I have had to estimate its boundary. Alternatively, you can choose to control the curve with “handles” which is a bit more artsy and intuitive than changing pixel coordinates of control points.

Anyway, you create a spline control point about every inch or two around the perimeter, then spend a good bit of time tweaking them at high magnification to match the curvature as exactly as possible. And all those yellow comb-like lines I haven’t said anything about yet? Well, that is where things get very interesting.

The yellow lines are called “curvature combs”. They are displayed perpendicular to the spline at every point, and their length indicates the “rate” of curvature at that point, that is, the degree of deviation from a straight line. In art and guitarmaking you hear a lot about a “fair curve” as being something highly desirable visually over a not-so-fair curve, for example in the design of a guitar body profile. If you feel along the side of a guitar, you can feel how smooth the mold was it was clamped in when it was bent. Subtle ripples indicate a home-made bending form made on a shop band saw, or else free-hand side bending on a hot iron. Companies that can afford it use really precise CNC-made guitar side-bending forms, so when your hand around they feel very smooth and, well, boring (I personally like free-hand side bending, as it is fun, and something that is handmade is more fun to look at. A handmade anything has a general slight crookedness to it compared to a production version that your mind has to work a bit to straighten it out visually, making it shimmer slightly in your mind’s eye. Unless that is if it is really crooked, and your mind gives up and says “Yup, Crooked!”.

Now, I can’t run my hand around this guitar, as all I have is its picture, but the curvature comb of the spline I created shows pretty clearly the deviations of my spline curve from smooth. The curvature comb of a true fair curve would look much smoother. Since I couldn’t see the outer edge of the guitar clearly most of the way around, I had to visually estimate an offset from the herringbone purfling, which I am guessing at high magnification had an accuracy of about 0.020”, and I was really trying to be good. So I think this resulting spline curve pretty well reflects the actual (magnified) smoothness of the side of the guitar. Another hour of tweaking would likely not change it very much.

Then I got to wondering what a Dreadnought shaped from a true fair curve might look like, or if it was even possible. So I began going around this spline curve, control point by control point, handle by handle, tweaking and tweaking and tweaking the curvature comb until I got as close to a fair curve as I could get that still fit around the Dreadnought shape pretty closely. After more than an hour of training to become a Spline Ninja, I ended up with this:

As a fair curve it is not perfectly smooth, as I only worked in whole pixel control-point location increments, but I think that this curvature comb Mohawk is pretty close to what your mind’s eye sees when it looks at a Dreadnaught guitar, which is a slightly hallucinated improvement on the original. So just how different is this hallucinated fair curve ideal from the actual shape in the picture? If we zoom in, there are some definite differences. Here are a couple:

The upper bout has a definite bump to it at about 2 o’clock in the above picture compared to the smooth curve ideal. To the left of the top of the curve you can see a slight flat spot where the gap between the herringbone pattern and the spline curve gets bigger.

At the rear end of the guitar body, the real body profile keeps going up straighter than the fair curve version which bends smoothly to the right. I didn’t take a picture of higher up the side, but you can see that the actual shape would have to swerve-right at some point to catch up with the fair curve. I can’t help but wonder if a Dreadnaught guitar body actually made to a precise fair curve would be visually noticeably different from one that is just close. I am guessing not.

Now, none of this is to suggest that there is anything wrong or inferior about a fair curve that is hallucinated from one that isn’t. The human mind seems to enjoy “fixing” things which are close to ideal but are unavoidably just a bit off. Your mind fills the rather large “blind spot” in your visual field with its best guess of what is there based on what surrounds it. Your mind lets you hear a rich fundamental musical tone when it is really not there, but is instead hallucinated from a series of high-frequency harmonics of the fundamental that are there. A Dreadnaught’s waist-to-hips ratio of 0.68 is pretty close to the universal 0.7 ideal. A hand-made chair from a master craftsman is a delight to look at because it is fun for your mind’s eye to exert itself ever so slightly in straightening out all the slight imperfections in its shape. And anything handmade by a grandchild is the most beautiful of all.