For Peter KG, Don Noon, and others interested in engineering.

[Don Noon]

OK, curved surfaces, inflection points and all that stuff definitely influence apparent local normal stiffness and therefore mode frequencies and shapes, and therefore sound. No argument there.

The difficulty comes in practical application, as I see it. Since I am narrowly focused on practical knowledge as it applies to violin acoustics, I see the shorter path to enlightenment as looking at the actual mode shapes and frequencies of a violin, and trial-and-error experiments based on that. Even that simple-sounding path has not seemed to yield much in the way of obvious success for the several folks I know who are doing that kind of thing, myself included... but I still hold out hope for minor improvements. The mathematical analysis route appears far too complex to me to yield any better results, and academic exercises are not my thing.

[Carl Stross]

My point being (and to Don also)  Get your minds out of the gutter.  Talk vibrations,  forget violins.  To discuss varnish generally, perhaps forget violins.   Don't go to a Violin University.   Go to a university.

 

The point is this:  vibrations in curved shells have extra stuff over vibrations in rigid flat plates.  You should know this.  And what is the need for 8th order differential wave equations?  Well,  there are those coupling cross terms in the solutions.

 

The violin is a good application,  but not the only one............ BUT  think about the inflection,  that certainly should be of interest.   Isn't that about the place where makers graduate the thinnest ?  Sounds reasonable to me.

 

You seem erratic.  Reminds me of the one who's name we do not speak.   And telling us "Get your minds out of the gutter" is not the way to make friends.

What is the point you are trying to make ???  Is it some novel idea about how to make a better violin ? Could you elaborate on THAT ?

[John Masters]

You seem erratic.  Reminds me of the one who's name we do not speak.   And telling us "Get your minds out of the gutter" is not the way to make friends.

What is the point you are trying to make ???  Is it some novel idea about how to make a better violin ? Could you elaborate on THAT ?

I said precisely what I intended to say.  You are asking what I said......  OK:  If there is a bump in a stiff (not perfectly rigid)  plate,  and you want the bump to move up and down,  it will exert tension on the web surrounding the bump...........  Will you agree to that?

 

If you don't agree,  tell me what is wrong.  If this tension seems reasonable,  perhaps a violin plate would have these inplane tensions that vary with the vibration normal to the bumps  (which is what radiates.) 

 

That is,  there is a coupling between inplane tension and bump movingupanddown-ing.  There is vibratory tension in the plate.

 

That is interesting.  My first post was to simply point this out.   At this point,  do you agree that this happens?

 

I don't thing that is erratic thinking.  My various responses were to people with variations on how to look at this....

 

Getting one's mind out of the gutter...... a sarcastic joke against those who think that violins are unique.  Anything a violin does is going to be seen in many situations,  or mental experiments.   Do agree to THAT?   Goes double for varnish discussions except for color.

 

NOW:  if there is vibratory inplane stretching,   might that relate to certain kinds of damping in the wood,  perhaps a discussion of the viscoelastic losses in wood is in order.  Especially wood soaked with varnish in a way that hurts a violin.   Might that be due to viscoelastic losses?   Or do you have another opinion?

 

Naturally,  I could not speak of all the implications of the effect.  I only wanted to present the effect to see if it could be understood.  IS it understood by you at this point?   Or do you disagree with the GENERAL proposition (with your head out of the gutter).   That is in the general case of a non-flat stiff plate.

[John Masters]

But it is.

I see we're diving head on into Hausdorff Topological Spaces. A meaty subject, worth at least 20 pages.

 

By the way : ever heard of developable surfaces ?

Considering a single plate,  I do not see a Hausdorff space.  The entire body has nearly discontinuous (but not totally) disjoint surfaces.  The entire surface of a violin does not seem to me a Hausdorff space.   And why bring it up in the first place?  Does it apply to the dynamics of the given (bumpy plate) in the example ?

 

You keep your background a secret..  You may be a mathematician.  If so,  explain why your posting is relevant.

[John Masters]

But it is.

I see we're diving head on into Hausdorff Topological Spaces. A meaty subject, worth at least 20 pages.

 

By the way : ever heard of developable surfaces ?

Yes it is a 2D Euclidean surface embedded in a 3D space.  I should have said that it is not a Euclidean plane as one discusses in 2D plane geometry.  Sorry for the confusion.  And one needs the 2D surface embedded in the 3D space to make my picture.

[Evan Smith]

.  But there is an important line of points at the inflection.  A small sample of wood here is curved in only one direction,  like a cylinder. It could be flattened here.

 

The inflection has never been addressed here in any kind of sensible way.  I think that one could learn a lot by learning to place it in a certain region.   The curtate cycloid does this.  But there is more than one way to use CC.  One can make them transverse the entire length,  or possibly radially from ywo points in the upper and lower bouts. .

 

 

I see this thinking exhibited strongly in strad arching,,,

not so much in other makers,

 

If the inflections are positioned in the right places, the instrument will have a higher sensitivity to the attack of the bow.

 

And the domed arching with all the bumps jumping around should determine the Hz. of the response.

[curious1]

The line of points where the inflection is zero depends on where you draw the CC.  If they go the entire distance from one end to the other,   the line is guitar-shaped and goes to the endpoints.  (there is no recurve at the ends of the plates.   However, there is enough wood to make a small cosmetic one.)

 

If there is a large longitudinal inflection,  here the end compressions cause a dip to be pushed in near the ends.  The area is small but I did not like it..  I found that in FEA.   I decided to not use the arching where a point is chosen in the bouts and the CC are drawn radially from here to the edges.

I cant speak in mathematical or engineering terms but my own observations, of fine Cremonese instruments, over 25 years as a restorer would agree with you. There is no recurve at the end of plates.

In my own work it is something that I have been giving a lot of thought to lately. I don't use CCs but instead I've been attempting to plot key points in the arching based on other types of geometry. This I hope helps me to build arches and, for the sake of structural and tonal comparison, quantify those shapes in simple but useful ways.

[John Masters]

I cant speak in mathematical or engineering terms but my own observations, of fine Cremonese instruments, over 25 years as a restorer would agree with you. There is no recurve at the end of plates.

In my own work it is something that I have been giving a lot of thought to lately. I don't use CCs but instead I've been attempting to plot key points in the arching based on other types of geometry. This I hope helps me to build arches and, for the sake of structural and tonal comparison, quantify those shapes in simple but useful ways.

Thanks for the verification.  I have seen many photos,  plus don't see a purpose for a recurve at the ends.  Do you intend to thin at the inflection?  It seems there is not much bending near there.

[Peter K-G]

Maybe this can add something, balance between the place where you get straight lines:

 

Back_arch_tuned_StraightTangentLine_Correct.jpg

 

 

John,

 

The tuning of the arch do in practice what you are saying! If you look at the area between the straight lines, in upper and lower part of the plate, there's where I remove wood (and maybee slightly move the inflation point) until the frequency stops rising.

 

If the wood is very good (high speed of sound) less wood is removed there and the arch height can be lower.

On the sides of the plate,between the straight lines, you can remove wood to get the volume down, without lowering the frequency too much.

 

It might be possible to find an equation/formula to calculate the height at the center from speed of sound, cut out the straight lines and calculate the longitudinal curve.

 

I have no need for that because tuning does the maths for me.

 

Peter

[curious1]

Thanks for the verification.  I have seen many photos,  plus don't see a purpose for a recurve at the ends.  Do you intend to thin at the inflection?  It seems there is not much bending near there.

I would say generally speaking I leave it thick there, maybe too thick. I certainly don't try to get it thin.

These are shots of a recent violin to give you an idea of what I try to do. I am dissatisfied with copying Cremonese arching and with carving it until it looks right. I would like to find a way to define the arching in an architectural/geometric way without using templates. I think it is important to think about where it is bending.

I am a decent violinist and the thing I'm most interested in is not tone so much as functionality. What happens when the bow touches string and the behavior of the string.

[Michael_Molnar]

curious1,

 

Could you give us a little more info on that top plate and the method of creating the shadows. Very cool, indeed.  

[curious1]

curious1,

 

Could you give us a little more info on that top plate and the method of creating the shadows. Very cool, indeed.  

Venetian blinds and strong morning sun.

[GlennYorkPA]

I cant speak in mathematical or engineering terms but my own observations, of fine Cremonese instruments, over 25 years as a restorer would agree with you. There is no recurve at the end of plates.

 

 

Curious1

I'm following this discussion with great interest but don't have the mathematical background to follow John's thoughts in detail.

However, I'm struck by your comment about the lack of recurve on Cremonese plates. By 'recurve', you are referring to to the dip on, or inside, the purling, correct? So, are you saying the groove is deeper at the C bouts and not so pronounced at the top and bottom of the plates? (It seems that way from your Venetian blind pics).

 

Glenn

[Don Noon]

I don't have the 25 years of restoring experience, but the lack of recurve at the endblocks is quite apparent in the Strad3D CT scans. By "recurve", I think that means where the inflection point is between convex and concave arching. At the endbocks, it appears to be convex very close to the purfling. Crossarching can inflect much farther in.

A possible exception might be the ex-Jackson Strad, which I recently tried to copy. There does appear to be a significant recurve at the neck block; but that might be due to distortion raising up the long arch under the fingerboard, thus creating the recurve effect at the block, where the plate is thicker and not as distorted.

[curious1]

Curious1

I'm following this discussion with great interest but don't have the mathematical background to follow John's thoughts in detail.

However, I'm struck by your comment about the lack of recurve on Cremonese plates. By 'recurve', you are referring to to the dip on, or inside, the purling, correct? So, are you saying the groove is deeper at the C bouts and not so pronounced at the top and bottom of the plates? (It seems that way from your Venetian blind pics).

 

Glenn

Yes, there does seem to be a difference to me. And yes i think we are talking about the area just inside the purfling. More broadly I think John is talking about the point where the arch changes direction from convex to concave.

I hesitate to write for fear of revealing my ignorance but here goes.

With the work of del Gesu, which I think I'm more familiar with, I get the sense that the arch rises in a straight line out of the channel. The arching looks like it is neither concave or convex. There must some way to categorize this slope. Obviously at the the top it rounds over and forms the top of the arch or in the longitudinal direction changes from slope to the "flat" part of the arch (belly). In the c bout there is more channel but still a tendency to rise in a straight line (unlike Strad who seems fuller and more rounded).

But I don't want to just copy these arches. I want to understand their fundamental geometry. Im sure im not alone in this. How do they carry the load, how do they bend/stretch.

Trouble is I'm not a mathematician, engineer, or physicist. But I'm sure these problems have already been solved.

I don't think correct geometry will make my violins great any more than playing in tune makes great music but it is a concrete place to start.

[curious1]

I don't have the 25 years of restoring experience, but the lack of recurve at the endblocks is quite apparent in the Strad3D CT scans. By "recurve", I think that means where the inflection point is between convex and concave arching. At the endbocks, it appears to be convex very close to the purfling. Crossarching can inflect much farther in.A possible exception might be the ex-Jackson Strad, which I recently tried to copy. There does appear to be a significant recurve at the neck block; but that might be due to distortion raising up the long arch under the fingerboard, thus creating the recurve effect at the block, where the plate is thicker and not as distorted.

Yes, I too think cross arching can inflect farther in. This always bothered me when making contours. I'd make an arch and it would be fuller longitudinally and I would think I was making a mistake. Don't worry about that so much anymore.

[Don Noon]

Trouble is I'm not a mathematician, engineer, or physicist. But I'm sure these problems have already been solved.

It is quite apparent you are not an engineer... otherwise, you would know that NOTHING has been solved

[curious1]

It is quite apparent you are not an engineer... otherwise, you would know that NOTHING has been solved

Nice to know I'm not alone.

[John Masters]

I would say generally speaking I leave it thick there, maybe too thick. I certainly don't try to get it thin.

These are shots of a recent violin to give you an idea of what I try to do. I am dissatisfied with copying Cremonese arching and with carving it until it looks right. I would like to find a way to define the arching in an architectural/geometric way without using templates. I think it is important to think about where it is bending.

I am a decent violinist and the thing I'm most interested in is not tone so much as functionality. What happens when the bow touches string and the behavior of the string.

I am at least curious,  as you are. 

 

John,

 

The tuning of the arch do in practice what you are saying! If you look at the area between the straight lines, in upper and lower part of the plate, there's where I remove wood (and maybee slightly move the inflation point) until the frequency stops rising.

 

If the wood is very good (high speed of sound) less wood is removed there and the arch height can be lower.

On the sides of the plate,between the straight lines, you can remove wood to get the volume down, without lowering the frequency too much.

 

It might be possible to find an equation/formula to calculate the height at the center from speed of sound, cut out the straight lines and calculate the longitudinal curve.

 

I have no need for that because tuning does the maths for me.

 

Peter

That sounds like an excellent idea.  I need to listen to myself more !   As to calculations,  I don't do them with the math,  I was using the form of the math to make conclusions.  I,  for example,  do not know the relative magnitudes of an in-plane stretch as opposed to stress changes in a vibrating bump. 

[John Masters]

I don't have the 25 years of restoring experience, but the lack of recurve at the endblocks is quite apparent in the Strad3D CT scans. By "recurve", I think that means where the inflection point is between convex and concave arching. At the endbocks, it appears to be convex very close to the purfling. Crossarching can inflect much farther in.

A possible exception might be the ex-Jackson Strad, which I recently tried to copy. There does appear to be a significant recurve at the neck block; but that might be due to distortion raising up the long arch under the fingerboard, thus creating the recurve effect at the block, where the plate is thicker and not as distorted.

Yes,  that is what I was thinking of.  If you are using CC transverse arches,  they perhaps should go the full length.  The small recurve at the end blocks was the cosmetic one I mentioned.  The wood is thick here for about an inch outward.   I did my FEA with constant thickness.   Did not have enough elements to simulate the extra wood at the edges.

[John Masters]

Yes, there does seem to be a difference to me. And yes i think we are talking about the area just inside the purfling. More broadly I think John is talking about the point where the arch changes direction from convex to concave.

I hesitate to write for fear of revealing my ignorance but here goes.

With the work of del Gesu, which I think I'm more familiar with, I get the sense that the arch rises in a straight line out of the channel. The arching looks like it is neither concave or convex. There must some way to categorize this slope. Obviously at the the top it rounds over and forms the top of the arch or in the longitudinal direction changes from slope to the "flat" part of the arch (belly). In the c bout there is more channel but still a tendency to rise in a straight line (unlike Strad who seems fuller and more rounded).

But I don't want to just copy these arches. I want to understand their fundamental geometry. Im sure im not alone in this. How do they carry the load, how do they bend/stretch.

Trouble is I'm not a mathematician, engineer, or physicist. But I'm sure these problems have already been solved.

I don't think correct geometry will make my violins great any more than playing in tune makes great music but it is a concrete place to start.

I used to calculate transverse arches from parabolas.  It worked OK,  but I kept the edges thin.   I have mixed results.  Now that I can calculate an arch (using the CNC),  I am interested to get back to work on this.  After two years,  I have made only one violin with the CNC,  and it is full of mistakes from inexperience [with the CNC]. 

[John Masters]

It is quite apparent you are not an engineer... otherwise, you would know that NOTHING has been solved

Solutions to the violin in particular are iffy.  I wanted to back up and see if the geometry itself could suggest something.  I hope the others forgive me for not giving a definitive strategy to improve violins themselves.

 

I was not trying to solve anything myself.  And sorry to tell you to get your head out of the gutter.  I just wanted to point out a possible thing of interst that comes out of the form of the math.  I will be the first to admit that I do not actually solve these equations.  My FEA has only 1000 nodes,  and I have played with circles with bumps,  like a .......nipple.  I learned a little bit, but it is hard to come to conclusions.   And I did not even learn the time-dependent FEA.  If I had time and ambition,  I would do more.  At this time,  it is an interest in grounds. 

[curious1]

John,

 

The tuning of the arch do in practice what you are saying! If you look at the area between the straight lines, in upper and lower part of the plate, there's where I remove wood (and maybee slightly move the inflation point) until the frequency stops rising.

 

If the wood is very good (high speed of sound) less wood is removed there and the arch height can be lower.

On the sides of the plate,between the straight lines, you can remove wood to get the volume down, without lowering the frequency too much.

 

It might be possible to find an equation/formula to calculate the height at the center from speed of sound, cut out the straight lines and calculate the longitudinal curve.

 

I have no need for that because tuning does the maths for me.

 

Peter

I assume that this is to make the plate as light as possible for a given stiffness.. But what does this do for the sound? And if you have to distort the arching to maximize stiffness/mass how does this affect bending in general especially in the finished instrument?

[Peter K-G]

I assume that this is to make the plate as light as possible for a given stiffness.. But what does this do for the sound? And if you have to distort the arching to maximize stiffness/mass how does this affect bending in general especially in the finished instrument?

 

Well,  you can try to go as light as you can for a specific M5, for example 345 Hz. 65 g for top and 95 g for back is quite optimal.

 

No distort! The contrary actually, tuned top:

 

 

[Melvin Goldsmith]

Well,  you can try to go as light as you can for a specific M5, for example 345 Hz. 65 g for top and 95 g for back is quite optimal.

 

No distort! The contrary actually, tuned top:

 

Top_arch_tuned1.jpg Top_arch_tuned2.jpg

It is great that this scheme works for you but if you handle a lot of instruments I know you will find many that break the rules..