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#241 Johnmasters

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Posted 14 April 2010 - 03:15 AM

Maybe comparing many curves in a sort of statistical manner could give some clues? The archings may have been corrected some times, but nontheless it would give a collection of data to extract best fitted curves from, e.g. similar to Johns simple geometrical functions, or more complex ones like splines, which are used in 3D modeling for their conveniece and efficienecy for that.

Dammit ..... They may be simple geometrical functions, but I am sure it would have been a LONG time before they were seen had I not proposed them... And how many people would have guessed the analogy which led to them...? All of the forum folks must be exceedingly modest to not have proposed them. There are a few people here with math ability. But they did not use it.

Splines say nothing at all.** They are just best-fit polynomials. There is no unusual property of indefinite differentiation etc.

The simple functions all have the general properties desired. As a class, they are a matched set in this regard.

** I suppose you could specify a set of perhaps 10 points along each half-arch and see how those points fluctuate in the different examples. Certainly, one would need to scale the heights to be equal. Or at least the average heights to be equal. It is very likely that shape and height scaling are not related. I think that should be assumed if you are going to do this statistical exercise. Don't ask me how I know, it is just obvious to me.

#242 Johnmasters

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Posted 14 April 2010 - 03:38 AM

Anders,

Don't hardangers have very long flat lengths of arch plus rapid dives at each end?

Are there inflections in these dives? (Bet a dollar there are not)

Because of the extreme curvatures at the end (if they are like I recall) then why not do your statistics on good hardangers? Do you have access to several really good ones ?

#243 Johnmasters

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Posted 14 April 2010 - 05:35 AM

Bruce,

Do you have a "most ideal" longitudinal arch in a photo? Perhaps Strad is better because he was the most meticulous and may show more of any principal that may lie behind the arch. (I can download the picture and print out a full-size version on paper. Actually, scale is not so important.)

If so, Could you post it? I have an idea to try. I think it can be done with one violin if you can answer the following.

1.) Is the curved part the same at both ends in spite of the fact that the two ends of the outline are not the same? If so, is this generally the case, or is there some consistent difference in length of the "most curved part" or any other thing in one end vs the other?

2.) If you think they are usually the same, just post a photo that has at least one end close to "perfect" and best case.

Don't worry about center distortion. One can take nearly any point near the center of the violin to be the center of the arch, if my ideas are right.

Hopefully, it would be a dead-on side view with the rib-joint-line straight.

Thanks, John

#244 yapkv

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Posted 14 April 2010 - 01:47 PM

I am in the midst of making my no 7... just finished with the purfling.

Right now I am in the middle of finishing the arching while following this thread and trying to figure out how to form the arch correctly.

I've just re-read Juliet Barker's book.

At chapter 5 page 40 she suggested the making a cylindrical shape between the F-holes, whereas the highest point of the back can be found by "drawing lines diagonally from corner to corner and draw an ellipse that extends about 5mm on each side of this point and 20mm up and down".

With that it is quite easy to get the flat plateau effect as seen at most violin tops. spruce has quite a strong long-grain properties but quite a weak cross-grain. I guess having a cylindrical shape area between the F-holes strengthen this area since a round shape is the strongest shape. That's also why most tin can has a cylindrical shape.

However this makes me wonder, some violins I saw has a relatively flat area between the F-holes, some having more "acute" area. I guess that's why they sound differently.

Now having the cylindrical shape between the F-holes, one can then decide how it raised from the neck-joint and saddle area... How these curves raise (whether quickly or slowly) would also somehow determine how the cross arch looks. A fast rising long arch may also cause the cross arch to raise rapidly, making the plate more rigid, hence better high-frequency response. A slow rising long arch would cause the cross arch to raise slowly, making the plate more flexible, hence better low-frequency response.... I guess that's how a maker could have done to compensate the strength of the top given different qualities of spruce.

As for the back, I always wonder how a flat-back violin would sound. We can see from other discussion that a flat-back bass is more "punchy" while an arched back bass has more depth.

is there anyone who can explain how different arches of the back affects the sound of the violin?

On page 47 of Juliet's book, "On the back look for a continuous curve swooping down to the purfling. On the front let the arching spring a little more quickly from the purfling and keep the central cylinder". I guess this explain why the top arch and the back arch looks differently.

Looking at the picture of an early violin, we can see the consistency since 1560. :)

side view of Andrea Amati c1560:-
http://orgs.usd.edu/...sSidewaysLG.jpg

more photos of the Andrea Amati c1560 violin
http://orgs.usd.edu/...iolinIndex.html


sorry if there's any grammatical mistake.

#245 Bruce Carlson

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Posted 14 April 2010 - 02:46 PM

Bruce,

Do you have a "most ideal" longitudinal arch in a photo? Perhaps Strad is better because he was the most meticulous and may show more of any principal that may lie behind the arch. (I can download the picture and print out a full-size version on paper. Actually, scale is not so important.)

Hopefully, it would be a dead-on side view with the rib-joint-line straight.

Thanks, John


Hi John,

I'll look and get back to you.

Bruce

#246 Bruce Carlson

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Posted 14 April 2010 - 02:51 PM

In the meantime here are two more long arches. Stradivari 1724-25 and Stradivari 1727.

Bruce

AS1724_25_long_arch.jpg AS_1727_long_arch.jpg

#247 Anders Buen

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Posted 14 April 2010 - 03:34 PM

Anders,

Don't hardangers have very long flat lengths of arch plus rapid dives at each end?

Are there inflections in these dives? (Bet a dollar there are not)

Because of the extreme curvatures at the end (if they are like I recall) then why not do your statistics on good hardangers? Do you have access to several really good ones ?

I have not studied them in detail, but I would guess that they are not very differnt in the long arch as compared to violins. One of the best hardanger makers also made violins and repaired violins, Gunnar Røstad. The differnces are more clear in the cross arches where the central region is flatter and the curve can have more rapid dives at each side, especially north of the f-holes.

Yes I guess I can get access to really good ones. Not my fathers, but my uncles and other players instruments I know. They do not come to me for their repairs, so I would have to meet them. A friend of mine have a Røstad with a very deformed top, saddle type much like your FEA calculation, but the fiddle is exceptionally good. So the arch does not need to look good for the fiddle to sound good.

My own hardanger, the biggish one with the Ole Bull f-holes, is in tonal class with the best hardangers. The arch is more violin-ish. It is built more solid than the Røstad I referred to, at least in the top. The Røstad fiddle have regions at 1,4mm in the top "lungs". It belonged to one of the greatest players in the last century.
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#248 Anders Buen

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Posted 14 April 2010 - 03:36 PM

Splines say nothing at all.** They are just best-fit polynomials. There is no unusual property of indefinite differentiation etc.

A best fitted line is what is needed. If you want to do maths on a polynomial, example giving finding where the double derivative turns sign, that is basically a "piece of cake".
"If the facts don't fit the theory, change the facts". A Einstein

#249 Michael_Molnar

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Posted 14 April 2010 - 03:52 PM

Can we agree on a process to select a model arch to digitize for analysis? This would become The Standard Model.

Mike

Stay tuned.


#250 Michael_Molnar

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Posted 14 April 2010 - 04:00 PM

A best fitted line is what is needed. If you want to do maths on a plolynomial, example giving finding where the double derivative turns sign, that is basically a "piece of cake".


Anders, my friend. Splines are not what we need in order to understand the science of what is happening. John's method allows us to identify the concepts underlying the masters' ideas. For example, a spline will not tell me if I am dealing with a combination of a curtate cycloid and an ellipse. I have done a lot of non-linear regression analysis (complex curve fitting) to know what I am talking about. John is trying to identify the simple functions that combine to make up the complex long arch. This is mathematical science at its finest.

Stay tuned.
Mike

Stay tuned.


#251 Anders Buen

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Posted 14 April 2010 - 04:05 PM

Can we agree on a process to select a model arch to digitize for analysis? This would become The Standard Model.

Mike

Those with CT scans may have a benefit in this respect. We saw a report from a museum here some months ago. Maybe we may see these models available digitalized for anyone? Maybe the laser photo method used by stradofear can be used for digitizing arches too.
"If the facts don't fit the theory, change the facts". A Einstein

#252 Anders Buen

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Posted 14 April 2010 - 04:18 PM

Anders, my friend. Splines are not what we need in order to understand the science of what is happening. John's method allows us to identify the concepts underlying the masters' ideas. For example, a spline will not tell me if I am dealing with a combination of a curtate cycloid and an ellipse. I have done a lot of non-linear regression analysis (complex curve fitting) to know what I am talking about. John is trying to identify the simple functions that combine to make up the complex long arch. This is mathematical science at its finest.

Stay tuned.
Mike

This kind of "fine mathematical art" is not going to work so nicely for an ortotropic material like wood. It will work nicely for homogeneus materials like plastic. I think the important things happen in the middle of the plate where the bridge is and not in the ends. And we will have to include the effect of creep and swelling from the varying moisture content of wood, in order to understand what is happening with the plates over time. I know it is possible to model this using FEA, but it takes the effort to combine the methodes and models from different groups and works to do it.

Being able to make the models is of course an important step and useful in the process. But there is a long white board to fill in before these modes work similar to what a real violin plate will.

How much do we think that an arch changes with the natural variations in MC (or RH) in the environment the instruments are subjected to?

And how do this variation affect the wooden creep?

What does the resulting deformation look like when these effects are included?

Here is an article on how MC in wood can be dealt with in Abaqus: http://www.vtt.fi/in...s/2008/P687.pdf
And then we have the PhD David Burgess referred to regarding creep in wood, also done in Abaqus: http://scholar.lib.v...3097520/etd.pdf

Which reference situation would you start with? The arch shape you have when you make your fiddle in your shop? Or the average indoor RH in Cremona at a given time of year if you knew when the fiddle you model was made? Or if you knew where the fiddle was fixed the last time, the relative RH of that workshop? Maybe 'medium range' RH would do?

Wood swell differently in different directions. How does this property of wood affect the aching?
"If the facts don't fit the theory, change the facts". A Einstein

#253 Janito

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Posted 14 April 2010 - 06:06 PM

I've just re-read Juliet Barker's book. .....


As Juliet has been mentioned, let me add a little more of her method.

She would rock a pencil along the centre line of the top. The rocking would need to be smooth, with no breaks.

This produces a shallow curve, and not a true flat surface.

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#254 David Burgess

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Posted 14 April 2010 - 06:49 PM

Can we agree on a process to select a model arch to digitize for analysis? This would become The Standard Model.

Mike

It's a worthy goal, but I'm not sure how to accomplish it. Longitudinal back arches get more pointy with time, and top arches get flatter. Add all the "arching corrections" by restorers, and it's hard to know what's what.

Maybe pick the archings off the "best sounding" fiddle? Well, we've been arguing about a process for selecting the best sounding fiddles for years, so that's probably not gonna work.

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#255 skiingfiddler

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Posted 14 April 2010 - 07:54 PM

Maybe it takes a true naif, like me, to have learned anything from this thread. For me, it's been very illuminating. I've learned:

1. It's possible that top and back arches were, originally, very similar in classic Italian violins, and plate distortion over time may be the biggest factor in their differing appearances, today. At least one classic Italian, the Ole Bull, seems to have retained the near identity of top and back arches.

2. If, as a modern maker, you choose to have similar, maybe even identical archings, top and back, you can produce tonally acceptable fiddles. David Burgess's violins and the Ole Bull attest to that.

3. Del Gesu seems to be one of the classic Italian makers that tried a number of different archings, perhaps more so than the other classic Italians.

4. All the Stradivari (and all were post 1700) images of long arches were quite consistent; if Stradivari experimented, he did so more subtly than did del Gesu.

5. A simple 2 dimensional view of the long arch ( a curve showing height and length) can be deceiving in its simplicity. Bruce's pairing of a Strad and a Maggini doesn't produce striking differences in long arch. The Maggini may be slightly higher, but just slightly. I suspect the differences start to show up in the cross archings. Similarly, Jim Murphy's image of the long arches in an Andrea Guarneri (a good stand in for Nicolo Amati) doesn't show a striking difference from the long arches of Stradivari. I suspect that the Andrea Guarneri, in its cross arch, would show more of the semi-cylindrical hump in the middle than the more gradual rise from the edge that Strad might show. But both may attain the same height, or nearly so, and thus the similarity in long arches.

Even if my generalizations are not yet on the mark, at least ideas have been planted that can be tweaked or discarded entirely with more future information. "The only things you can learn are the things you almost already know."
Caveat lector!

#256 Johnmasters

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Posted 14 April 2010 - 07:58 PM

Hi John,

I'll look and get back to you.

Bruce

Thanks, I have been running various trials on a series of arches. I think I know in advance that either a pure cosine or a parabola is strongest in compression. But that is not necessarily what makes the best violins. I don't for a minute think that the beautifully uniform tops with barrel arches and rounded end archings were distorted from back-like archings. You have been very polite in not raging against this hypothesis.

#257 Johnmasters

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Posted 14 April 2010 - 08:00 PM

In the meantime here are two more long arches. Stradivari 1724-25 and Stradivari 1727.

Bruce

I like the one on the right better. But either is sufficient for now. Thanks (The one on the left may have a slight inflection at the neck, but can see it past the raised edge.)

#258 Johnmasters

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Posted 14 April 2010 - 08:04 PM

A best fitted line is what is needed. If you want to do maths on a polynomial, example giving finding where the double derivative turns sign, that is basically a "piece of cake".

Yes, to copy. That is not my interest. I want a set of curves that ALL obey certain conditions that the arches themselves obey. Then take combinations of these, not combinations of x^n which is all a spline is.

I want a best fit while never leaving the intitial restraints. If that can be done, it may SAY what the restraints are. Now doesn't that seem to make sense? I don't want to copy, I want to discover what if anything is universal in these arches.

#259 Johnmasters

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Posted 14 April 2010 - 08:08 PM

A best fitted line is what is needed. If you want to do maths on a polynomial, example giving finding where the double derivative turns sign, that is basically a "piece of cake".

Piece of cake, of course. I know how to do derivatives, and my 10-year-old son is getting some skill himself. Polynomials are not infinitely differentiable, or at least not that gives a non-zero result. (I did not need to tell you that, I am telling the others.)

In practice, likely more than third derivative does not mean much for stress distribution. But I am curious to find out just the same.

I have not studied them in detail, but I would guess that they are not very differnt in the long arch as compared to violins.

I think I had a false memory because of the oddish flat center.

#260 Johnmasters

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Posted 14 April 2010 - 08:13 PM

Anders, my friend. Splines are not what we need in order to understand the science of what is happening. John's method allows us to identify the concepts underlying the masters' ideas. For example, a spline will not tell me if I am dealing with a combination of a curtate cycloid and an ellipse. I have done a lot of non-linear regression analysis (complex curve fitting) to know what I am talking about. John is trying to identify the simple functions that combine to make up the complex long arch. This is mathematical science at its finest.

Stay tuned.
Mike

Gosh...... well, thanks. But I do think that if one is going to take linear combinations of functions to make up a Cremonese arch, finding a set that has all the important ideas in each function will do it well.

Furthermore, if a set can be found, then the intrinsic properties of those components will BE what we are looking for.




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