The DNA of design

Discussions of geometry and ratios in violin making are not new to these pages. Over the past ten years I have been asking basic questions about the use of such methods in old Cremonese work. Was geometry used at all? How can we best observe the presence or absence of these things in historical examples?

What sort of geometry was used? How extensive were these methods? What my research uncovered was the use of the kinds of ratios and shapes that can be worked with just simple dividers and a straightedge. ­e shape, size and position of each feature in old Cremonese work show what we might call a ‘recipe’ of geometry and ratio behind it. ­is ‘recipe’ structures the feature, but also presents a number of options or choices, leaving the maker in the driver’s seat. But it seems all the old Cremonese makers were very traditional. We see them sometimes pushing, or even expanding, the boundaries of a feature’s traditional recipe, but never just ignoring or not using the methods. Let’s imagine how those makers might have passed on one of these recipes (see gure 1):

Giovanni Brother, once I have the length for an instrument, how do I settle on the width?

Paolo ­at’s easy. We do as Father and Grandfather did. We walk o. the proportions with our dividers. Today I’ll tell you the recipe for instruments like the violin or lira da braccio, where the shoulders come in straight to the neck. Gamba family instruments are diTherent. We can talk about them tomorrow Giovanni So what proportions do I walk out?

Paolo Just like Father, we make the length to width ‘a part less than double.’ So, if you walk the width in 3 steps of your dividers, double would be 6, but ‘a part less’ makes your length 5 steps.

Giovanni Is that all there is to the recipe?

Paolo Yes. ­at rule of thumb gives us the ratios 9:5, 7:4, 5:3 and 3:2. ­ese are enough to make anything from a skinny violin to a stout lira. Remember, as with all the recipes, you always have your liberty with the margins. So, you’re free to calculate these ratios from the outer edge of the plates, or from the pur.ing line. ­is gives you a bit of freedom to nudge the shape skinnier or fatter.

Giovanni What about special cases like pochettes, which are too skinny?

Paolo Ah. As always, we derive any needed exceptions as directly from the normal recipes as possible. Here, we can just take a normal-recipe width and divide in two.

Now let’s walk through the recipes and choices used to work Cremonese lower-bout shapes. We have already seen how to set the width from the height. For illustration, let’s choose a 4:7 ratio on the outer edges. Now we choose a ‘long arc’ to pass under the bottom of the instrument. €e traditional recipe calls for centring the long arc along the body length. €is radius can be any halves, thirds, or .fths of the body length. For Cremonese violin work, the radius for a bout’s long arc was most commonly 1, 4/5, 2/3, 3/5, ½, 2/5, or 1/3 the body length. A shorter radius choice will leave the lower bout more rounded underneath. Let’s choose a radius that is 4/5 of the body length, for a fashionably .attish bottom ( gure 2).

Next, our recipes call for a pattern of overlapping circles. €is pattern is called a vesica, from the Latin for ‘bladder’: it was once thought to have a bladder-like shape. When the circle centres divide the line through them into equal parts, the pattern is called a vesica piscis. But the old Cremonese violin makers didn’t focus on ‘special’ ratios. Rather, the tradition developed to favour ratios for their practicality in working a feature. €e most common traditional proportions for a violin lower bout shape were 5:4:5, 4:3:4, and 4:4:4. For our example bout shape, let’s choose a 5:4:5 vesica.

First we mark two vertical lines, dividing the bout width into our chosen 5:4:5 vesica proportions ( gure 3a). We know our vesica circle centres will be on these lines. But a little divider work is still needed to locate the centres vertically. We work these centres so our vesica circles will end up sitting smoothly tangent to the long arc underneath (3b). Completing our vesica is simple once the circle centres are located (3c).

Lastly, we set the ‘riser arcs’ (4), which carry the lower bout shape partway towards the corners. The riser ‘recipe’ traditionally calls for simple arcs with their centres placed along the bout line. We can nd the riser centres in any of three ways: on the vesica circle centres themselves; centred in the middle of the bout width; or centred ‘one vesica unit o from the circle centres’. This last makes use of the units of the vesica proportions. For our example lower bouts, let’s use the third option.

ALL THE MANY FEATURES OF AN INSTRUMENT NEED A SHAPE, SIZE, AND POSITION

ALL IMAGES DAVID BEARD

Amazingly, the full range of lower-bout shapes seen in Cremona examples is given merely by varying our choices within these recipe options (see table, right).

Building a full instrument involves many such recipes, but all have the same ‘choose one of these’ structure. An old Cremonese build can thus be ‘encoded’ as.the sequence of all these choices. Repeat the sequence, repeat the design. Vary the sequence, vary the design.

Does any of this matter? We can now ‘read’ the choices behind the making of Cremonese instruments, creating new possibilities for historical research, or for copying instruments. But this rediscovered knowledge also reopens some long-closed doors. A maker today could now decide to work entirely by resuming the old ways.

I have focused on classical Cremona. But these tools could be used to look more broadly. I have traced the way Cremonese choice preferences changed and developed in f-holes, scrolls, and every other aspect of a violin. When I checked a few examples beyond my Cremona focus, I found that the broader strokes of these methods are not unique to Cremona. There is much that others might explore.

Intriguingly, the research suggests a possible explanation for the ascendance of Cremonese and other Italian making. A 2015 MIT paper (bit.ly/33o6azk) points to how the shapes of soundholes changed in northern Italian instrument making from about 1250 to 1750 in a way that looks like evolution. Was I looking at the cultural mechanism for this evolution? Did the sequence of recipe choices used in building an instrument act like a kind of DNA? We can see the old makers mostly worked by repeating their recipe choices from recent instruments, while also tinkering with a few of their choices. Were the great heights of Cremona making reached through design evolution; by simply favouring repetition of choices from their more successful work?