Arching criteria

[Arsalan]

 

I appreciate it if experienced people answer to this question… 

 

Most of the experienced violin makers, agree that arching has the biggest impact on production of a good violin… 

 

Considering there are excellent violins with a range of different arching styles… 

I conclude , there must be some factors in arching design that if followed and mastered properly, then you can make low , high , full and … arching but still good instrument ? 

 

What are those factors ? 

I hope I will get a straight answer to this question 

 

Thank you 

[Dennis J]

Believing experienced makers would know a lot about all aspects of violin arching seems to be a reasonable assumption to make. However I think many use a working method that produces the shape they like, based perhaps on some predetermined heights along the length of the violin.

Descriptions like low, high and full could mean different things to different makers. Starting with the top long arch you could have a low flat arch, or a low more rounded arch (which would make heights at the upper and lower bout very low). A high arch could also vary the same way, although a very high arch would probably not work with a flat profile, it would just be too bulky. How full an arch is depends on the ratio of positive to negative components existing on cross-arch profiles, which can vary quite a bit.

That is arching reality. The arches that you can have complete control over are the front and back long ones. So you can decide on heights for upper and lower bouts as well corner and centre bout ones. Along with the position of the highest point (centre or otherwise), they will determine the arch shape. That shape can be established very early in the arching process.

So all of those factors can be controlled. How you or anyone else goes about it is another thing. Predicting outcomes from all of that, with any approach, is something else also.

[Torbjörn Zethelius]

On 12/17/2023 at 1:51 AM, Arsalan said:

 

I appreciate it if experienced people answer to this question… 

 

Most of the experienced violin makers, agree that arching has the biggest impact on production of a good violin… 

 

Considering there are excellent violins with a range of different arching styles… 

I conclude , there must be some factors in arching design that if followed and mastered properly, then you can make low , high , full and … arching but still good instrument ? 

 

What are those factors ? 

I hope I will get a straight answer to this question 

 

Thank you 

Consider that the air inside the violin vibrates when played and the vibrations are projected out through the F-holes. Mastering how these vibrations behave determines the quality. Thicknesses of the plates is also a contributing factor but less so than the shape of the arching.

[Don Noon]

On 12/16/2023 at 4:51 PM, Arsalan said:

I hope I will get a straight answer to this question 

If you do get a straight answer, ignore it.  

Pay attention to the arching of instruments whose tone you want to emulate.  Keep track of what you do as best you can, noting height, recurve locations, and where the arching is tightly curved and where it is not.  Radius templates will help quantify the curves.  

Try variations, and migrate your arching depending on how things turn out and what you like.

[Arsalan]

55 minutes ago, Don Noon said:

If you do get a straight answer, ignore it.  

Pay attention to the arching of instruments whose tone you want to emulate.  Keep track of what you do as best you can, noting height, recurve locations, and where the arching is tightly curved and where it is not.  Radius templates will help quantify the curves.  

Try variations, and migrate your arching depending on how things turn out and what you like.

Got it thank you very much 

[Shunyata]

5 hours ago, Torbjörn Zethelius said:

Mastering how these vibrations behave determines the quality. Thicknesses of the plates is also a contributing factor but less so than the shape of the arching.

Can’t agree. Arching and graduation are a pairing.  Poor graduation is disasterous.  Even the reasonable range of good arching yields different tonal character.

[Christopher Jacoby]

Yeah, it's part of a tripod. Arching shape and height/density and stiffness of the wood/graduation.

A soft, light back needs a higher, stronger arch. A strong arch with less recurve needs to be worked thinner along the edge, etc...

[Torbjörn Zethelius]

1 hour ago, Shunyata said:

Can’t agree. Arching and graduation are a pairing.  Poor graduation is disasterous.  Even the reasonable range of good arching yields different tonal character.

I didn't say poor graduation. But you are right, poor graduation is disastrous.

[martin swan]

With regard to the high arching in the OP example, of course there are many fabulous historic violins with similar arching.

But modern makers don’t seem  to want to work with this kind of arching and therefore have no experience of it or any notion of how to make it work.

 

[Andreas Preuss]

There is no straight answer. 
 

If you single out one aspect, let it be the aspect you think is the most important, and try to solve the ‘sound problem’ , you can maybe avoid the worst.

My general idea on arching is that it needs to be adjusted to the material and is more important for the top than the back. 

I would add to the most important sound factors also wood treatment and setup (especially bridge height, bridge weight and string angle). 

[GoPractice]

Generalizations help. They are the bumpers that let kids knock down pins at the bowling alley.

Makers need to commit, perhaps against there wills, papa, against there will, towards the traditional, especially for violins.

I would disagree as to so many exceptions to the current viola and cello making. Not just the archings... 

There are so many different needs. There is a violist who plays a significantly smaller instrument than what I play, but his role in as a section player is different, and he is eight+ inches taller. His physique produces different results. As I play Paganini on violin, he does on viola. Easily.

Patterns alter arching. So there might be a target longitudinal arching, the cross arching might become organic, or could follow the established makers. I hope it is a bit too early to make such major generalizations.

Several of my favorite Strad patterns had very different archings.

Maestro Preuss points are so important as there is variety of sound profiles? tonal ranges? that are necessary for player needs. Many makers also accommodate for players needs in set up.

[fscotte]

My thought is that starting the upward curve of the arch too far from the edge, creates a plate that is less stiff than one where the arch starts earlier from the edge, provided the thicknesses being the same for both plates.

 

[Marty Kasprzyk]

A wide nearly flat rim on an arched plate actually makes it stiffer.  

Consider pressing down on a rimless arched plate resting on a flat table.  The plate will spreadout sideways.  If the arched plate has a wide flat rim this rim can  not stretch much in the hoop direction which will make plate much stiffer and more resisitant to downward forces.

Rather than wrecking violin plates I suggest doing the above experiment with two ordinary paper bowls with one of them with its rim cut off.   Paper plates are designed to have a high stiffness while using a minimum weight of paper to reduce cost. Arched violin plates are sort of similar--they're designed to have a high stiffness while using a minimum weight of wood to increase sound output.

Paper bowls have flat bottoms so they don't tip over and spill things.

 

[Dennis J]

I find it hard to imagine how a plate which is glued to the rib structure can "spread out". Distort or change shape in some way perhaps.

There is limited room for a wide scoop and recurve at the centre bout. But there is plenty of room to vary an arching at the upper bout and particularly the lower bout. And I suspect a wide, convex arching with an inflection point perhaps about 1.5 cm from the edge at edge height as opposed to one with a narrow convex centre possibly with a wide, shallow recurve down to the edge, might have different tonal outcomes.

[Marty Kasprzyk]

The downward deformation from a bridge force is called "out of plane" or OP deformation.  For a violin top plate this causes a big volume change and produces a lot of sound.

The sideways spreading out is called "in plane" or IP deformation and this produces little volume change so it produces only a small amount of sound. The widening of the top plate causes the entire violin body to bend producing the B1- and B1+ resonance modes.

The B1- and B1+ modes do produce a lot of sound but the sound is generated by the volume change giving air movement through the f holes  rather than the body bending movement.

The sideways spreading out IP deformation is reduced by the ribs, liners, and blocks as well as by the rim area I had mentioned.  So the stiffnesses of all of these affect the frequency and amplitudes of the violin resonances all of which affect the sound character.

The violin's curved outline shape also has an effect.  The deep curves of the C bouts makes the ribs quite stiff.

deformed arch ◊ Layer-1 ◊ 1 _ 1.pdf

[fscotte]

I can't wrap my head around the scenario that you're suggesting above, that the plate pushes outward.  Doesn't the rim prevent the plate from pushing outward? Isn't that kind of the purpose of the rim?

Taking your example that a wider flatter edge is stiffer to the extremes, why not just make a nearly flat plate with a little arch in the middle where the bridge is?  A nearly flat plate will deflect more than an arched one, and thus this is why they are heavier and thicker than an arched plate.

I'm assuming that the flat area without any arch, is what would cause the plate to be less stiff.

[LCF]

On 12/21/2023 at 5:59 PM, Dennis J said:

I find it hard to imagine how a plate which is glued to the rib structure can "spread out". Distort or change shape in some way perhaps.

There is limited room for a wide scoop and recurve at the centre bout. But there is plenty of room to vary an arching at the upper bout and particularly the lower bout. And I suspect a wide, convex arching with an inflection point perhaps about 1.5 cm from the edge at edge height as opposed to one with a narrow convex centre possibly with a wide, shallow recurve down to the edge, might have different tonal outcomes.

 

I think we always need to bear in mind the distinction between gross physical moves due to static stress loads versus the very small amplitudes of  displacement due to oscillating forces ie "vibrations" vs the standing wave patterns of those vibrations at different frequencies. The business of how both types of forces couple between plates and ribs is deeply interesting.  I think the sideways (ip) displacements of the top plate edges are converted into inwards and outwards bendings of the ribs which then couple to the back plate similarly. Perhaps any OP motions at the edges are transmitted direct from top to back and vice-versa since ribs are very rigid in that direction. 

For my own curiousity I grabbed a dismantled junk-usual off the shelves and pushed and twisted bits of it.  Pushing down in the centre of the free plate as shown it is easy to feel the C bouts getting wider. The plate feels less yielding in the centre of the upper and lower bouts but some effect is still detectable. No bass bar btw.

Supporting the back and rib assembly underneath and pulling outwards with thumbs  you get a sense of how easy it is to bend the ribs in situ in different locations . Easiest in the upper and lower, harder in the C bouts and almost impossible where the ribs curve in  near the blocks. 

[fscotte]

Ok so I have to visualize this because it doesnt make sense that a wider channel around the outside perimeter would make for a stiffer plate than one with a more narrow channel.  Sorry for the crappy 'mouse' drawing on my computer.  The top image would be a plate with a narrow channel before the arch begins to rise, the second drawing would be one with a wider channel,  and the third would be taking it to the extremes -  the extremes being that a wider channel creates a stiffer plate, and thus the third drawing would be a very wide channel and small arch.

 

So again, the 2nd drawing would yield a stiffer and lighter plate than the first drawing?

[Don Noon]

While I am not yet convinced of this stiffening effect, I am certain that the effects of the far-more-important higher frequencies will be affected in some unpredictable way.  The only way to see the full effects is to try it... if you are the experimenter type.

[fscotte]

3 hours ago, Don Noon said:

While I am not yet convinced of this stiffening effect, I am certain that the effects of the far-more-important higher frequencies will be affected in some unpredictable way.  The only way to see the full effects is to try it... if you are the experimenter type.

I tend to make the channel around the perimeter of my plates a little wider than normal, on mandolins that I've built, and now the last two violins as well.  I've always had trouble getting plate that taps a higher note than others.  So I'm wondering if my channel is too wide.

[LCF]

3 hours ago, Don Noon said:

While I am not yet convinced of this stiffening effect, I am certain that the effects of the far-more-important higher frequencies will be affected in some unpredictable way.  The only way to see the full effects is to try it... if you are the experimenter type.

There are so many variables in a violin arch shape that it would be difficult to test them all. The history of violin making is doing that for us I suppose. There are no paper bowls to hand atm so I can't do Marty's experiment but thinking about the cross section of the one in the photo there are two areas of very high curvature and the wall of the bowl is abruptly steep so it would have high rigidity in a vertical direction. 

Confounders!

[Don Noon]

28 minutes ago, LCF said:

 thinking about the cross section of the one in the photo there are two areas of very high curvature and the wall of the bowl is abruptly steep so it would have high rigidity in a vertical direction. 

Confounders!

And then there's the extreme loss of stiffness (for spruce) when there's significant off-quarter, which there would be with a steep slope.  Confounders^2.

[Dennis J]

22 hours ago, LCF said:

 

I think we always need to bear in mind the distinction between gross physical moves due to static stress loads versus the very small amplitudes of  displacement due to oscillating forces ie "vibrations" vs the standing wave patterns of those vibrations at different frequencies. The business of how both types of forces couple between plates and ribs is deeply interesting.  I think the sideways (ip) displacements of the top plate edges are converted into inwards and outwards bendings of the ribs which then couple to the back plate similarly. Perhaps any OP motions at the edges are transmitted direct from top to back and vice-versa since ribs are very rigid in that direction. 

 

I get the idea from this discussion that people believe gross dynamic physical changes occur while the instrument is being played, which affect tonal outcomes. Perhaps they do to some minor extent. I'm fully on board with the very small vibrational  dynamic.

I see the lower bout with its relatively wide profile, as well as the upper bout, as being areas which have the potential to flap around a lot. As you say the centre bout ribs are very rigid in the vertical direction. But surely the central rib assembly along with the sound post and narrow arch and thick back are also quite rigid in all directions.

It's all a bit beyond me. I just see the arching as being a functional aspect of violin design. There is really not a lot of variation possible. Fairly small variations in the width of recurves, perhaps 1 cm at the upper and lower corners will change the arching profile, or how it looks, quite dramatically. Really wide recurves there will result in wide recurves at the upper and lower bouts. So that might be where tonal characteristics are involved. However a very wide recurve at the lower bout will lead to a peaked convexity at the centre along with very flat areas down to inflection points near the edge. Ditto with the upper bout.

[Dr. Mark]

We can make some generalizations about those curves that may give some insight.  Say we deform similar curves by a small amount by applying a vertical force adiabatically (i.e. just very, very slowly) at the center/apex.  Let the illustrated curves be the resulting equilibrium curves.  Two things are evident: the sum of all of the forces in each direction is zero, and the sum of the torques (forces x moment arms) is zero.  If we draw a horizontal line through any of the figures, i.e. perpendicular to the applied force, then if we sum  the forces at these intersections its equal to zero so the two vertical forces at these points caused by deformation are equal and opposite to the applied force.  The sum of the two horizontal forces is zero.

The two way that wood can resist these forces is through compression and tension.  The component of the applied force that's tangent to the curve causes compression in this case, and the component that's normal to the surface causes bending, so with our applied force, it's initially all bending.   But internal to a thick curve, bending causes tension tangent to the curve on the 'outer' side of the bend and compression on the 'inner' side.  There's also shear, and I'm considering the shear modulus to be very high so we're essentially rigid in shear.  What weak shear would do is allow the curve to deform or fracture directly under the applied load with perhaps more vertical tensile forces, or no forces (if it plasticly deforms or ruptures) at the interface with adjacent segments of the curve.

So these reactive forces at the point of the applied force are passed back and forth along the curve until equilibrium is reached.  At equilibrium the forces along the curve and normal to it at every point are equal.  Where the curve is steeper, the component of force tangent to the plate curve is larger, so less bending occurs because the component normal to the curve is smaller, and v.v.

Hmmmmmm - not sure if that's all correct or if it clarifies anything even if so... a spur of the moment ramble before watching a movie with the girls.

Mr. Noon - hope the tweaking went well and all is good.

 

[Dennis J]

Here's a photo of a top showing profiles drawn with arching templates I made.

Moving inflection points at edge height on the upper and lower bouts closer to the centre line by about a cm would result in peaked, flat sided arches. I don't like that look. They look quite low but are based on a preliminary overly thick edge height. Lower one is 12.5 upper 12.