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Dennis J

Arching Templates

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This is the latest version of my arching experiments.

I've decided that making the arcs tangent to the DSL lines is not a good idea.

I've concluded that it is best to keep the DSL lines at a fixed distance from the centreline, about 49 mm as shown in the pic. That will result in verticals made between the upper and lower bouts going through or just behind the longitudinal centre of this violin pattern.

And the arcs intersect the lower bout cross-arch line 80 mm from the centreline  and extend to within 39 mm of the centreline as well.

With these settings I had no trouble making test drawings on paper using a set of french curves, using an arc elevation of 6 degrees. I've also done a set of test drawings of the back arching using exactly the same geometry but with an arc elevation of 5 degrees without any problems.

If you wanted to use this system to make templates with a higher arch, say 16 mm or more as opposed to 15 mm here, you might have to increase to the arc's elevation a little. And if you wanted an arching shape with a narrower arching and a wider recurve component you would need to set an arc extending further towards the centreline of the pattern. There is no right or wrong setting. If you can use french curves to smoothly combine the upper convex and lower concave arching figure you must have the inflection point's position about right.

One thing I've known but haven't worried about is that the inflection point's height calculation based on the circular arc is to some extent incompatible with the long arch's flattened curve, especially the top.

So, when making the arching templates, I cut below the marked inflection points of the two centre arches by about .5 mm or so.

And at the corner arches I've cut above the marked inflection points by a similar amount. It helps facilitate a smooth transition from the upper convex arch line and the lower concave recurve line. This shows that small differences of the inflection point's height can significantly alter the arching profile's shape.

Probably the most important arch is at the centre bout. I've put one at the narrowest part of the Cs. I've found that the arc which fixes the position of the inflection point on the horizontal axis needs to be about 17 mm from the plate's edge. This gives enough room for a recurve scoop of reasonable width while allowing for a reasonably wide convex central arch.

Where the arc crosses the lower bout cross-arch line is also important as to its proximity to the plate edge. It's about 21 mm on this plan and I think it looks good. Of course when those positions are fixed all of the cross-arch positions are locked in, so it's important to get it how you want it.

Just added a pic showing the position and path of french curves used to draw the arches through the inflection points. This shows how the upper convex curves are positioned with the longest radius of curvature at the top of the arch in such a way as to blend smoothly with the other side of the arch.

I've found the height of the inflection points using a 6 degree calculation to be a very good fit for this particular arc arrangement. I'm in the process of finishing back templates using a 5 degree calculation, using exactly the same arc arrangement of course.

I've included a pic of the top and back long arches to show how the inflection points, connected by the blue lines, rise above edge height. I've only done it with the top long arch but the back is done in exactly the same way.  So, using the red lines shown in the main layout as a baseline for a right angle triangle calculation at 6 deg., the upper corner inflection point height above the edge works out to be 2.06 mm based on the 19.6 mm long baseline, the waist 3.34/31.8, the bridge 3.34/31.8 also, the lower corner 2.74/26.1.

At 5 degrees the back calculations work out at 1.71, 2.78, 2.78, 2.28. These measurements are added to a nominal edge height of 4.5 mm to give a total inflection point above the base of the plate.

I used a large french curve to draw the long arches similar to an example based on Stradivari arching shown in Sergei Muratov's book. Done the same way as the cross arches, the curves meeting at the centre.

There seems to be a lot of controversy about using french curves in violin design and I just do not understand why that is the case. They are clearly an integral part of violin design. The fact is that without using them, doing what I have shown here, is simply unachievable. 

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Thanks Michael. To a certain extent I'm in uncharted territory regarding plate arching. I put on hold violin making about five years ago, mainly because I wasn't sure about arching matters. I knew at the time what I wanted but I ended up with something looking like a mass produced Chinese job. Now that I've got templates that I'm happy with I'll have to deal with the practicality of using them.

My understanding of the C bout area is that fluting should be sub arching profile. But just what goes on regarding plate thickness or arching figure there with some violins is a mystery to me.

 

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David, I can assure you that the arching profiles I've shown match very closely Cremonese examples. I really don't understand the controversy there seems to be regarding arching.

I think that the arching profile is one composed of two back-to-back spiral forms touching at an inflection point. I know that if I can draw the arching with french curves I have got the geometric settings of the system I use right.

 

 

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8 hours ago, Dennis J said:

David, I can assure you that the arching profiles I've shown match very closely Cremonese examples. I really don't understand the controversy there seems to be regarding arching.

 

Original examples, or examples which have been re-shaped a few times?

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It seems to me that apart from the fact there seems to have been a certain mastery of arching by early Cremonese makers I haven't seen any rational explanation of what so called Cremonese arching is.

But I do know that one of Michael Darnton's laser line pics closely matches a set of archings I recently made. I simply held up each arch template to the screen at the respective arching position to verify that.

Most of the scans that David Beard posted also closely match french curves, I checked.

 

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57 minutes ago, Dennis J said:

It seems to me that apart from the fact there seems to have been a certain mastery of arching by early Cremonese makers I haven't seen any rational explanation of what so called Cremonese arching is.

 

I would describe it as an arching which tends toward more of a barrel shape, than a figure-eight shape.  This would be accomplished by moving the inflection points of the upper and lower bouts more inward.

But I have no problem with you doing whatever makes you happy. :)

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Now I see what you mean by figure-eight shape. Yes, moving the upper and lower inflection points closer to the centre line would result in a larger recurve width, especially above and below the corners. But there are plenty of Cremona examples where the upper and lower bout arches are wide and full with the inflection point at least as close to the plate edge as the ones I've just shown.

Just by changing the arc's radius by a few mm the arching shape can be manipulated quite a lot. I think it's a matter of balance between the convex upper section and lower scoop widths.

 

 

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You need to be careful about the distinction between generating a curve and tracing a curve 

French curves will trace ANY smooth shape.  But they generate no shape. Testing that you can fit French curves to something only means it's a smooth shape.

How is the shape controlled?  That's the significant question.

 

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20 hours ago, Dennis J said:

Now I see what you mean by figure-eight shape. Yes, moving the upper and lower inflection points closer to the centre line would result in a larger recurve width, especially above and below the corners. But there are plenty of Cremona examples where the upper and lower bout arches are wide and full with the inflection point at least as close to the plate edge as the ones I've just shown.

Indeed there are. How much investigation have you done into archings which are largely original, versus those which have suffered the ravages of time, or suffered the ravages of multiple "re-archings"?

In the early days of plaster molds, it was much less time consuming to remove material from the mold, than add, and it still is. The outcome has been that many Cremonese instruments are much more bulbous than they once were.

 

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7 hours ago, David Beard said:

You need to be careful about the distinction between generating a curve and tracing a curve 

French curves will trace ANY smooth shape.  But they generate no shape. Testing that you can fit French curves to something only means it's a smooth shape.

How is the shape controlled?  That's the significant question.

 

I really think that you are missing the point. The inflection point that is. The purpose of the geometry I've laid out is to locate the position of the inflection point at each cross-arch position on an arc, both on the horizontal and vertical axis. Along with the long arch height, the bottom of the scoop and the end of the arch at the edge crest, the inflection point will define/control the arch shape.

Of course, using those points you could use french curves to create any sort of odd compound curve. But the obvious requirement of the arching shape is as smooth an integration of the upper convex and scoop curve as is possible. And the position of the inflection point is of paramount importance in achieving that aim.

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1 hour ago, Dennis J said:

I really think that you are missing the point. The inflection point that is. The purpose of the geometry I've laid out is to locate the position of the inflection point at each cross-arch position on an arc, both on the horizontal and vertical axis. Along with the long arch height, the bottom of the scoop and the end of the arch at the edge crest, the inflection point will define/control the arch shape.

Of course, using those points you could use french curves to create any sort of odd compound curve. But the obvious requirement of the arching shape is as smooth an integration of the upper convex and scoop curve as is possible. And the position of the inflection point is of paramount importance in achieving that aim.

Ok.  So you're system produces one control point giving a cross arch's inflection point.  And, of course the crest of the cross arch is already given by the long arch along the center line.

But this is not enough well determined points.  What other controled points does your system generate.

Yes. French curves are a fine way to run a smooth curve through some set of controlled points.  But they are worthless when then aren't enough well determined points to establish the shape.

Note that the simple notion of a bent spline is the idea behind French curve shapes.  And the older notion of 'smooth' for the boat builder, architect, and artisan.

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I've said long arch height, the bottom of the scoop and the end of the arch at the edge crest, not crest as in the high point of the arch. I don't see any need for additional control points. As a matter of fact any additional points would make the use of french curves unworkable. You define the end of the scoop next to the edge crest with a circle, but in the course of finishing the scoop it will end up as a curve with a changing radius. I'm using french curves to construct the whole figure. So it is important to determine the location of the inflection point beforehand. As I have said before, it is not possible to locate all these inflection points' heights exactly using the circular arc's elevation because of the long arch's flattened shape. So they are best used as a guide. Nevertheless  I've found them accurate to less than a millimetre height wise going by eye. But, if the inflection point's height is in an unworkable position you have to alter the arc's degree of elevation. If you get the elevation height right with say the centre arch the rest will also be right.

I know how splines work. Early makers probably used them to generate curves in violin making just as they did in other applications. Anyway they can be generated using a CAD program.

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So you have nothing controlling the amount of curvature from the center to the inflection point.

You need at least one more controlled point.  

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12 minutes ago, David Beard said:

So you have nothing controlling the amount of curvature from the center to the inflection point.

You need at least one more controlled point.  

Well there is actually. When I place the french curve on the centreline to draw one side of the arching I make sure that  it is as close as I can judge at the apex of the curve so that when I complete the other side of the arch the two lines combine smoothly at the same time as connecting with or close to the inflection point. As you can see there is no peaking or flattening of that curve at the top of the arch.

Once the top part of the arch is completed in that way I just find a section of a french curve which will complete the arching profile in the scoop up to the edge crest.

 

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"Some people will never learn anything, for this reason,  because they understand everything too soon." Alexander Pope

 

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15 minutes ago, duane88 said:

"Some people will never learn anything, for this reason,  because they understand everything too soon." Alexander Pope

 

Alexander Pope also wrote: "What can we reason but from what we know?"

 

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42 minutes ago, Dennis J said:

Well there is actually. When I place the french curve on the centreline to draw one side of the arching I make sure that  it is as close as I can judge at the apex of the curve so that when I complete the other side of the arch the two lines combine smoothly at the same time as connecting with or close to the inflection point. As you can see there is no peaking or flattening of that curve at the top of the arch.

Once the top part of the arch is completed in that way I just find a section of a french curve which will complete the arching profile in the scoop up to the edge crest.

 

The requirement of a level slope at the crest still is not enough to settle how fast your curvature will fall to thw inflection point.  You will find that if use different French curves, you've left room for many very different paths from crest to inflection.

You have a system that you have used to make some archings.  But it is still shy of a determinate system for others to use.

Then there is the question of if it has anything at all to do Cremona arching.  I say not generally at all.  

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38 minutes ago, Dennis J said:

Alexander Pope also wrote: "What can we reason but from what we know?"

 

Yes, but what you have "reasoned", relative to Cremona, is flawed.

What you suggest as a method for creating an arch is fine for making a violin, but won't explain or give you something that emulates the Golden Period, as we call it, in Northern Italy.

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4 hours ago, David Beard said:

The requirement of a level slope at the crest still is not enough to settle how fast your curvature will fall to thw inflection point.  You will find that if use different French curves, you've left room for many very different paths from crest to inflection.

You have a system that you have used to make some archings.  But it is still shy of a determinate system for others to use.

Then there is the question of if it has anything at all to do Cremona arching.  I say not generally at all.  

Using the level slope as you call it at the top of the arch absolutely defines the rate of fall to the inflection point when using french curves.

The only way to change that is to use a curve which is not spiral, or employs some sort of distortion.

As I've said before unless you can definitively point out where any of the arching profiles I've posted are not consistent with scans, or laser line images of early Cremonese instruments you don't have a case.

 

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3 hours ago, Dennis J said:

Using the level slope as you call it at the top of the arch absolutely defines the rate of fall to the inflection point when using french curves.

The only way to change that is to use a curve which is not spiral, or employs some sort of distortion.

As I've said before unless you can definitively point out where any of the arching profiles I've posted are not consistent with scans, or laser line images of early Cremonese instruments you don't have a case.

 

You're a tough nut to crack, Mr. J. :D

While a formulaic method may eventually emerge to reproduce the best of the 16th through 18th century Cremonese violins, what I would suggest in the meantime is improving your visual assessment skills. Some of us were immediately able to see that your method is a little off, if your goal is reproducing the archings of such instruments.

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22 hours ago, David Burgess said:

Indeed there are. How much investigation have you done into archings which are largely original, versus those which have suffered the ravages of time, or suffered the ravages of multiple "re-archings"?

 

 

Hi David,   if you don't mind saying,  which old Cremonese violins still retain the most original arching?  I assume the Messiah would be one?  Which others?  How close is the Titian?  Since I have the poster from that one.  

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