Del Gesu Archings

Now the final design stage brings us to the del Gesu archings.

In figuring out his archings, I found that they are done the same way as Montagnanas' were. I had to move the line for the catenary curve in, so it follows about the same as the Montagnana. Del Gesus archings are lower, but the basic geometry is the same, and each would have understood what the other was doing. I found that if you want to have a straight cycloid on the outside, you can't push the cross arches on the inside out to close to the edge in the bouts. It will make a nice full arch, that some models follow, but it won't be the arch that defines del Gesu, or Montagnana.

The arches do rise up on both models quite quickly in the c bouts; that is just the nature of a shorter, taller, cycloid. It isn't just straight up though. The radius at the low point is an important feature. The radius changes all along the edge, and in the bouts it is very flat, especially on the del Gesu. How can we work that in? Maybe having set points, with certain radii, and then blending them in so the change is imperceptible?

Now I did do some changes. I changed the curves into the corners from the upper and lower bouts. Straight radii don't look so good there. The c bouts look fine round. Both models use the same scroll. I think it was the model set out by Andreas CNC shop, tolerances =/- .5mm. I need to make some copies, get some more 1/2" MDF to make the molds, and I need a couple pieces of spruce for bellies, and at least on back and one neck; I think I'll make the del Geus out of some crazy stock I have.

Montagnana Arching

I did some work with the cycloid program. First I made some long arches for the belly that will cross, and create the final long arch. It is a combination of these arches and the width of the cross arches that define it. It seems like the result will be almost exactly a circle. Cool. I did the same with the back, but for that there are two aches that don't make it the entire length. These I scaled at 270 long, so they come out to the sine of 51.8 degrees, another golden number. (273 works too, using the mold length and not the length from block to block, another golden number)

For some reason Dominico shifted the thick point quite high on the back, yet the long arch still appears to be a circle. If we make the top arching .3-.4 shallower, and make the top thicker and the bottom thinner, we get the results we want. Maybe he was trying to loosen up the bottom, maybe he was trying to stiffen the top. Whatever the reason the middle is thick, but not the thickest area.

Checking the cross arches I found that the line I was using for the cross arch width was off. Making the line where I had it, the wide thin area in the bouts around the edges could not be that thin. I had to re-draw it in red. The belly arches from the poster match the cycloid ones I drew up, (well the computer did), and I marked out the inflection line, where the arch will change from convex to concave. The back arches match quite well also, except for the one on the lower bout, were it seems it could have been arched too widely on the inside, and ended up a little fuller than the cycloid came out. The archings are quite thin in many places, and I don't think I went that thin on my other one. I really need to take notes.

I was going to make it with 19.5mm and 16mm arches, then I thought to make them original 19.9mm and 15.6mm.
Now I've decided to use 19.5mm and 15.75mm. Why? They come out at a ratio of .809, so why not? I'm also making the mold the same length as the del Gesu, because the lengths were given over the arching, so 352 long is more likely.

String angles, Please tell me if I'm wrong

I forgot to put this in, so I'm scrambling.

String angles are like a holy grail to some. I've read people who swear by 159 degrees for violins; certainly not less than 158 degrees. But in drawing out violins with higher arches, especially if they are shorter besides, even 157 degrees is a bit of a stretch. It is purely a geometric impossibility. I've tried to draw out 159 degrees, and it never works out. The overstand is too high, or the saddle is too high, or the bridge is too short. The point is, I don't even know why the angle is important.

I've read people talking about bows, and how as the angle is increased, so does the pressure. That just isn't the case on a violin string. The pressure is the same for a given string diameter and pitch, regardless if the string angle was 159 degrees, or 152 degrees. It is purely a physical function; tension times diameter at a set length, equals pitch. So what is it that they are after? I don't know. If you know, please tell us.

Neck angles I can see will make a difference in the way they feel when played. If one violin has a neck set at 8 degrees, and another is set at 4 degrees, a player would notice the difference. But what would it be? The left arm might have to be held higher, or lower, the instrument tilted differently, but they both could be played. After a while on either instrument, playing the other would seem strange, until you got used to that one.

Or is there a holy grail there too?

How about bridge heights? If you use 26mm as an average fingerboard projection, a bridge will be about 31mm or so tall. With a higher arch that may even be too high. But something is even more important there. I drew the Strad up with a 32mm bridge and a 16mm arch; a 2:1 ratio. That is the leverage that is forced on the body by the strings. If the arch was only 14mm, the leverage goes up 14% to 2.28:1. If the arch is 18.25mm the leverage goes down 14% to 1.75:1. I'm guessing that would have more effect on the sound and the way the instrument plays than the string angle. Would the higher leverage make the instrument louder? Easy to get moving, but hard to play softer? Am I wrong? Please tell me.

So on to the way I have the string angles figured out for these two:

The problem I see is that when you make the neck flatter, and increase the overstand, it makes it possible to even out the string angles at the bridge. But you can only go so high. It is easier to lower the saddle to even things out, but that makes the included angel tighter. Doesn't it? It seems like everything is conspiring to make the angle more acute, not flatter. Please tell me if I'm wrong.

String Angle Tutorial

This is something that is never covered. I've never seen it anywhere, but still string angles are given for each instrument, along with string lengths, afterlengths, saddle heights, projections, and overstand. I think drawings work best, so that is what I will use. Here it is with a basic Stradivarius, the only one where the "rules" easily work.

There is a lot of stuff there.

There is a side view that I use to find what works. Things will only work within a small range. The saddle has a range. The bridge has a range. The overstand has a range. The nut location has a range. Finding a place where everything is in range when the "givens" are plugged in is the goal.

The givens on a standard Strad might be something like this:
357 long
195 stop
130 neck
158 degree included string angle

I added a 32mm bridge which gives a 2:1 bridge:arch height ratio, and a 26.9 projection. Maybe the projection is a little high. Before we do anything we need some corrections. The radius on the top of the fingerboard gives us one correction. The radius is the same, but the width is different. Use Pathagorus, and we get .8 degrees. Same goes for the string clearance, I settled on .9 degrees. Add them up and it is 1.7 degrees.

Do the saddle end first, then subtract the rest of the included angle. Here, 22 minus 14.1 equals 7.9 on the string side. With that we can figure out the top of the nut. And then we calculate the bottom of the nut by subtracting 7.6 from it, the height of the nut. From there subtract the 1.7 from the strings (7.9) to get the neck angle (6.2); and from there we can figure out the overstand (6.0). I just say the belly is 4mm. It may seem complicated at first, but I'm sure you could do it in high school geometry class.

Many instruments drop the ribs from the top corner to the neck. This will increase the overstand by whatever the drop was. It will also make the nut "seem" like it is a little more than twice that drop higher. I believe the nut should be around zero. So plus on the top, and minus on the bottom is great.

Now we have the neck angle and mortice. I always cringe when people ask what angle to cut the end of the neck at. It depends. How are you cutting the mortise? I use a system that Michael Darnton recommended, with my own stuff (my wife says I can't leave anything alone). He cuts the bottom of the mortise the same depth as the overhang. I use the overhang plus the ribs. At the top I make my neck half the length of the fingerboard. So on this one it is 135mm. If the ribs and overhang are 3.5mm, I figure I need to go .75mm into the block on the top. Doing some calculations the angle of the mortice will be a little over 5 degrees, and the neck has to be cut about 1.15 degrees short of 90 degrees.

The last thing I look for is a 2:1 ratio of the strings to the other end. Then I want a 2:1 ratio there between the tailpiece and the afterlength. I think that may create a rocking couple that may make the strings more active. Maybe it doesn't, but I'll try that first.

Next what happens with the small del Gesu.

Design Aspects, Montagnana

Now that you know how I draw things up, this one will be easy. He used .618 for the base, as del Gesu did. Where the mold for the del Gesu is only 344 long, this one is 347 long. Wider overhangs will make it 5mm longer. The apex is 2.75 up. the lower bout is .809 down, lower corner .6 down, upper corner cos 54 degrees of that (another.809 number) and the upper bout is half of that down. The c bout is 3/8 between as the del Gesu was, which happens to be, in a roundabout way, another.809 number.

The width of the lower bout is given by the corner triangle. The upper bout is, you guessed it, .809 of the lower. And the center bout is about 1/2 of the lower. The triangle for the f holes is built the same as the del Gesu. The lower eyes are set lower, using the .63 number instead of .618. The upper eyes are set quite close.

The bass bars on both seem to be 1/5th of the bouts to the outer edge. Works great for the del Gesu; this one would need a 39mm or so wide bridge at the feet. The C bouts are almost identical. I drew the Montagnana on the right side of the del Gesu, and you can see that it is just shorter.

The big difference is in the corners. Del Gesu pulled his bout outlines out at the corners, and used a larger radius. Montagnana curved his bouts in, and used a small radius. The result is monster corners, the likes of which Roger Hargrave would post a picture of and caption it: "Ponder that for a while."

The f holes on the Montagnana I drew up may be too long. But they look cool enough, and match my criteria, if not the intended one. They look the same as the del Gesu ones. It must be just the shape that I like. I drew them on the same piece of Bristol paper, so you can see how similar they are with the light box.

You can see the line where the cross arches end, and a flat platform stays. Later that area will be made convex, after the outside has the recurve put in. I have the del Gesu one penciled in on this one to show that they are almost the same. I have the notches for the blocks figured out, and the location of the holes to use in gluing the ribs on.

You can see how the template for the catenary curve ties in with the upper f hole. Even a cello I drew up is like that. I don't know that it means anything, but they do.

Design Aspects, del Gesu

Now I hope that apart from the differences, notably the corners, you can see the striking similarities in the outline of the two instruments. The Montagnana is about 5mm longer than the del Gesu, but the proportions are almost identical. The biggest difference is that the del Gesu is a little wider across the c-bouts. The upper corners are also located higher up on the violin.

I base all my violin drawings on the mold length. Add the rib thickness, and the overhang, and multiply by 2 and you have the lengths and widths. I can't imagine that they ever drew it up from the outside edge. That just happens, and can be adjusted later if you have to. First the del Gesu:

It is a small instrument, and the small overhangs, and thin edges make it seem smaller. No, I haven't ever seen it. I've never seen anything. In contrast to other del Gesus, the edgework is not dug in. He decided to leave the whole edge a mm or so thinner, and then he didn't have to dig it in. Makes sense to me. I always see del Gesu instruments as having a lot of recurve. They certainly don't have the straight to the edge arch like a Guadagnini does. Taking the cross arch templates you can figure out where the catenary curve that forms the framework for the arching starts. Put a few dots on the drawing and blend them in. That's where it all starts.

The long arch for the back is simple enough. Two arches from each end that don't make it to the other end. This leaves an area that gradually gets shallower to the middle. That is how the center of the back gets thicker. The belly long arch is different. I can be a straight catenary, a cross catenary, or made similar to the back, with the center deepened. Guadagnini used the straight catenary. Stradivarius a cross catenary, and del Gesu looks to me like he used the third method. The problem with that one, is that relatively long, slightly curved center area is weaker from the thinning, than a thicker back would be; the full length long arch is not there. There again, the weaker arch lets the belly move more easily, for more sound. It can be made thicker, and still get movement, but make it too thin and it will warp. That area is basically supported by the bass bar and sound post.

I start with a triangle that defines the corners. The base of the triangle is always a ratio of the length. A common one is .618, the golden ratio. That's what this one, and the Montagnana use. Then the apex: this one is 2.25 times the length. Montagnana uses 2.75 times the length. The locations on the centerline for the bout centers and the corners are all ratios as well. This one uses .8 lower bout, .6 lower corner, .333 upper corner, and the c bout is 3/8's down from the upper corner to the lower one. The upper bout is .53 down to the upper bout from the top. The widths are ratios as well. The lower bout is tan 30, the upper .8 of that, and the c bout is about half of the lower.

For the f holes a triangle is built. The base of both of them is the lower bout centerline. The apex of this one I couldn't figure out what it was. I drew it up using the dimensions given. When I drew up the Montagnana I had my answer, it is .63 up from the bottom. That is the sine of the angle that has .809 as its tangent. That is 1/2 of the inverse of .618, and .809 is used on everything on the Montagnana. The lower eyes are set .618 down. The uppers are usually set to be somewhat below the narrow part of the c bouts, and wide enough apart to get the bass bar in the right place. A circle drawn from the lower eye crosses the centerline at the stop, and goes through the upper eye.

It's a working drawing, so it isn't pretty, but it shows me just about everything I need to build the body, at least get me started on a mold. I have to finish up archings, and neck and string angles yet. Next, the Montagnana.

Two Different Violins, Start

Recent posts on Maestronet have me thinking about the Plowden again. It is a great poster. The outline is classic. F holes are a little weird, but that makes it different. I do still believe that the basic architecture of the violin is created on the inside; del Gesu is no exception. In fact, we can see the way he did his long arches from the inside on the poster.

Uh, well maybe. I've been looking at a lot of del Gesu violins lately, and he seems to have changed his belly design, and even back design a few times. The "Ole Bull" has a straight catenary arch for the long arch on the belly, just like Guadagnini did. I just saw the "Terminator" yesterday, http://sparebankstiftelsen.no/Dextra-Musica/Instrumentene/Guarneri-del-Gesu-Guiseppe-Violin and it has a very long flat, and almost a diamond shaped back. What's up with that? The "Cessole, Teja-Ferni" cross arches look like it is almost all recurve, with a little lump in the middle, front and back. Others seem to be the same front and back, just a full radius.

So it seems del Gesu was experimenting all the time. Or maybe it is just that the belly long arches have sunk in from string pressure? The "Cessole" is a lot like the "Plowden" with a higher belly arch that looks like it still has its curve. Maybe that's how it looked originally?

I was looking at the outline of the Montagnana violin. I never made a form for the one I made; built it on the back. It actually looks fairly decent, the varnish job came out nicely. I thought of making another using maple, and a mold. I checked my drawing, and my new ideas on drawing up a violin fit right in on whatever I was using before. The Montagnana c bouts are shaped the same as del Gesus c-bouts are. The only difference is that Dominico made c-bouts shorter, the violin 3mm longer; and it has a longer stop. OH, and the almost 20mm arch.

I was thinking of making two violins based on Gagliano, with a short stop, and high arch, and a long stop and a low arch; but I think I'll do another Montagnana, long stop, high arch, and a del Gesu, short stop and low arch. Just the opposite.

First the outlines. To make a convincing copy, the shape had better be there. All violins are made to a print. Problem is, we don't have it. We have Stradivarius forms in museums, and know what model went on what form. Del Gesu got his form handed down through the family. With the one form, all of the instruments can be made on it, simply by changing the corner block shape, or making the upper, or lower, or both blocks longer.

Let's draw them up. My method is a compilation of ideas. I like Muratov's idea on proportions, and ratios, and getting the corners involved (the corners draw the eye, so they better be in the right place). I'm not so sure about the special curve though, and just use a compass instead. I added my own idea on the base and apex for the corners, and the f hole locations are my idea, with the constrictions that are given.

I base all my ratios off the length of the mold, the rib form, which is basically the prominent line of the purfling that we see on an instrument. The edge just happens. Everything we need will be on the drawing, so that it is all in one place. Here are the posters side by side:

We'll talk about it next.