Paper: A Data-Driven Approach to Violin Making


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20 hours ago, ctanzio said:

If one starts with a set of mode frequencies one wishes to obtain, then certainly a mold, arching shape and plate thickness plan can all be newly designed to achieve the desired results by applying the results of your study.

Unfortunately, one typically starts with a mold and arching shape based on other factors, like visual effect or a desire to match a classic violin shape. Material properties are only somewhat under the control of the maker.

That leaves plate thickness as the primary tool for adjusting the violin plate. So any quantifiable insight your study can give on where to adjust thickness to affect plate modes would be welcomed.

>

If you had a set of mode frequencies you wished to obtain then it might be helpful to pick your wood, model and arching shape that best helps achieve them.  

 

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On 2/19/2021 at 2:54 PM, Marty Kasprzyk said:

If you had a set of mode frequencies you wished to obtain then it might be helpful to pick your wood, model and arching shape that best helps achieve them.  

Even if it resulted in a violin that was ugly, difficult to play in higher positions and awkward to hold on the shoulder?

The point was that there are constraints on violin geometry and available wood properties unrelated to mode frequencies, as well as on the motivation of a maker to frequently redesign molds.

In light of these constraints, wouldn't it be nice if a scientific study gave some quantitative insight on how to adjust violin performance by scraping the inside of the plate?

 

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17 minutes ago, ctanzio said:

Even if it resulted in a violin that was ugly, difficult to play in higher positions and awkward to hold on the shoulder?

I think that's a bit of a stretch. The results we present show variations of around 5% in the area of the outline for a 10% variation in the sound speed of the wood. Probably the area variation will be way smaller when we consider varying arching. 

On the other hand, I think we will be able to provide precisely such a tool in the near future. And hopefully with an easy interphase where you input images of the arching and outline, material parameters, and desired frequency output. 

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Just to illustrate the point. In magenta you can see the starting outline for a material with rho = 400 kg/m^3 and E = 10.8 GPa and in black the optimised shape to reproduce the eigenfrequencies of the initial top with the materials parameters that the figure shows. 

 

image.thumb.png.65348288a28583100e9f09c1a4cfb370.png

 

So unless you are working with extremely stiff balsa wood the optimised outline does look like a violin. 

Note that these results are only for the optimisation of the outline, when you also include the thickness optimisation my impression is that the outline changes even less. Tomorrow I try to get the data from my student, we didn't think of plotting things like this in the paper but I'm finding it really useful to visualise the variations. 

Now, if one is already using AI to make shape optimisation I think the least one should do is CNC the mould, to keep it period correct that is :P

 

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2 hours ago, ctanzio said:

Even if it resulted in a violin that was ugly, difficult to play in higher positions and awkward to hold on the shoulder?

The point was that there are constraints on violin geometry and available wood properties unrelated to mode frequencies, as well as on the motivation of a maker to frequently redesign molds.

In light of these constraints, wouldn't it be nice if a scientific study gave some quantitative insight on how to adjust violin performance by scraping the inside of the plate?

 

 

The Spanish "Bilbao project" is exploring what happens when the plates are thinned from the inside while keeping everything else constant.

https://www.bele.es/en/bilbao-project-progression/

Music tastes change over time, humans have gotten bigger, string materials have improved yet we believe classic violin shape and size is still best?  Player injuries are a problem nobody seems to want to address.

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16 hours ago, tsuresuregusa said:

Just to illustrate the point. In magenta you can see the starting outline for a material with rho = 400 kg/m^3 and E = 10.8 GPa and in black the optimised shape to reproduce the eigenfrequencies of the initial top with the materials parameters that the figure shows. 

 

image.thumb.png.65348288a28583100e9f09c1a4cfb370.png

 

So unless you are working with extremely stiff balsa wood the optimised outline does look like a violin. 

Note that these results are only for the optimisation of the outline, when you also include the thickness optimisation my impression is that the outline changes even less. Tomorrow I try to get the data from my student, we didn't think of plotting things like this in the paper but I'm finding it really useful to visualise the variations. 

Now, if one is already using AI to make shape optimisation I think the least one should do is CNC the mould, to keep it period correct that is :P

 

This is fun stuff! 

It would be really interesting to see how the shape changes when just the cross grain stiffness is varied with a typical density spruce wood.  I have often thought that plywood top instruments should be made narrower.  Maybe plywood has gotten a bad rap because the shape wasn't adjusted so they didn't sound right.

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The cross grain stiffness is not really important, the two most important parameters are density and longitudinal stiffness. We are actually varying all the material parameters in the figure above, just didn't write them down. We could do a cross grain only variation but my student is super busy at the moment so would have to wait a bit. Do you have values for the density and longitudinal stiffness for plywood?

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5 hours ago, tsuresuregusa said:

The cross grain stiffness is not really important, the two most important parameters are density and longitudinal stiffness. We are actually varying all the material parameters in the figure above, just didn't write them down. We could do a cross grain only variation but my student is super busy at the moment so would have to wait a bit. Do you have values for the density and longitudinal stiffness for plywood?

Colin Gough (1) did a finite element analysis of a fixed shape top plate having spruce wood with length to cross grain elastic modulus ratios anisotropy from 1 to 25 and found the mode 1 frequency changes very little but the modes 2 and 5 did as shown in his below graph.

It would be interesting to see how the shape of the top should change to maintain a fixed mode frequency with different anisotropy ratio woods.  

 

I wouldn't bother considering modeling the effects of plywood because even it could be made to work well nobody would use it anyway.

 

1.   Violin plate modes, j. Acoust. Soc. A., Vol. 137, January 2015, pages 139-153, http:dx.doi.org/10.1121/1.4904544

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One needs to note that the scale of the anisotropy here is for extremely different materials:

image.png.23e476801e181e744c2613b0bac39790.png

So his results are coherent with ours. Even if you would find a wood that only changes on the cross grain, the effect would be minor. As I said the before, the most material important parameters are density and longitudinal stiffness, so when changing the wood those are the ones that will dominate, not the cross grain stiffness. 

 

 

 

 

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One of the limitations of Colin's approach is that he is varying one parameter at the time in ranges that don't make much physical sense. Does it make sense to have a maple top plate? I don't think so. Secondly, this way of studying things "keeping everything else constant" hides any non-linearity between the parameters. And that's why our approach is more complete/realistic. I doubt you can find two pieces of wood that only vary on one parameter, let alone a whole set for doing the kind of experiments Colin does with his simulations. I don't want to boast but I really think it's time to start thinking in terms of statistics, and our research is the first going in that direction. 

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I finally got around to skimming thru the paper...

On 2/9/2021 at 11:56 AM, tsuresuregusa said:

And interestingly, shows that the outline is far more important in determining the vibrational behaviour than the thickness of the plates.

For a simple beam, frequency will vary directly with the thickness and with the inverse square of the length... so length is a variable with higher influence.

Also, if the arching causes linear stretching of the material to be a large factor, thickness becomes even less important, dropping to zero influence in the pure stretching condition.

 

On 2/17/2021 at 7:42 AM, tsuresuregusa said:

Damping: extremely interesting. This two works do not consider damping for it's just the eigenfrequency study. We are computing the frequency response function of the top plates now, and we still don't understand how to correctly include the damping.

The problem I have as a maker with these rather academic exercises in frequency predictions is that even with minimal investigation, you find:

1) Violins that are considered great do not all have similar body modes... they vary quite a lot.

2) Really crappy violins can have body frequencies that are perfectly normal, or can be identical to great violins.

So the logical conclusion is that frequencies are not the answer to making a great violin.  Damping could well be strongly involved, as well as a pile of other variables that are not that easy to measure, much less analyze or simulate.  And the full set of variables is actually infinite.

But this is not to say this type of research should stop; I'm happy that folks are able to put time and effort into such things, and you never know where it will end up or what will come of it.  I just don't see any immediately useful results I can use in my shop, at least for a very long time.

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16 minutes ago, Don Noon said:

For a simple beam, frequency will vary directly with the thickness and with the inverse square of the length... so length is a variable with higher influence.

Probably, but for the sake of simplicity we decided to use fixed length violin bodies. It seems to us that this is the common practice nowadays, we can easily re-run the simulations and the analysis if it's not the case (or luthiers would be interested in seeing those results).

If you had the data of the really crappy violins which have identical frequencies of great violins we would love to see it. We have yet to find two violins with the same FRF. 

The sound produced by a loudspeaker is a function of its geometry and their frequency response, in which the damping has indeed a great influence. I don't follow your reasoning with "infinite set of variables". However, as far as I know that was never an impediment to define temperature, so even if that's the case one probably can define averages or order parameters that help understand how the system works. 

If you look at the other paper I linked, our aim is to learn how to "copy" a given violin with different materials. We have shown it to work with the eigenfrequencies. Implementing the same algorithm for doing a copy of the body modes is simply a matter of changing the "loss function" to include the complete violin's FRF. We are working on this. 

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13 hours ago, tsuresuregusa said:

If you had the data of the really crappy violins which have identical frequencies of great violins we would love to see it. We have yet to find two violins with the same FRF. ...

 I don't follow your reasoning with "infinite set of variables".

Here's one:

firewood.jpg.2a16e0cdcecc459a2d1de98c49dbcba5.jpg

This is a cheap student VSO where I made a new top out of a piece of firewood purchased from Walmart... as an experiment to see what could be done with bad wood.  The signature modes are easily within the range of the great old ones measured by Curtin in his article on signature modes.  In the article, it is obvious that the mode frequencies range quite a lot, so there is logically no great importance to the exact frequencies.  As to why my "firewood fiddle" was crappy, my conclusion is that the response amplitudes above the signature modes are not good... wild peaks and dips, and overall fairly weak in the higher frequencies.

As to "infinite variables", almost anything will have infinite variables if you look closely enough.  For a violin, I don't think you have to look that close... trees grow differently, carved arches are not exactly the same, etc.  To get anywhere with modelling and analysis, simplifications need to be made, but it is mostly educated guesses as to how to simplify things.  For example, you don't know for sure if the shear damping in crossgrain is a key player or not in defining greatness, but it's really hard to do anything with it analytically, so it is ignored for now.  And there's a whole bunch of annoyingly complex little things like that.  

To me, it is obvious that the low-hanging fruit of the major mode frequencies do not determine much about quality, therefore the real quality is buried in all those annoyingly complex details... which, for now, as a maker, might be more readily attacked by trial-and-error, educated guesses, and experience rather than analysis.

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On 2/18/2021 at 3:39 PM, tsuresuregusa said:

Thanks a lot for your feedback Daniel, you are totally correct. Will change the intro/abstract when it comes back from the reviewers. I really appreciate you took the time to go trough the paper and get the big picture.  

Marty, we actually tried to do something along the "evenness" by optimising the location of the eigenfrequencies so they are equally spaced, ie, equal tempered, but the results were quite bad. Probably a random location of the peaks is easier to obtain. 

Concerning the amplitude of the peaks in the frequency response function (FRF), this is a function of where you put the accelerometer. How are you measuring it? simply at the bridge or several surface measurements and taking the average? 

We are able to simulate the FRF, but the results are highly dependent on the damping model used. Recently Jesus Torres used a variable damping model to fit existing data but this seems a bit too arbitrary for me. We are still thinking what to do. 

Do you have references for the bow force/violin impedance? We are still far from simulating the strings and bow interaction with the violin but to have it on the back of my mind.  

Matthews and Kohut (1) electronically modified the sound frequency response curve of a Stradivari violin that had 17 prominent peaks and they increased the number of peaks to 20, 24, and 37 which is similar to increasing the modal density n.  They concluded that 20 to 30 peaks that were not uniformly spaced but were either randomly or exponentially spaced gave increased brilliance, better note uniformity and vibrato response.  I haven’t seen any later studies which contradict Matthews’ results. 

They also investigated the influences of different damping.

Jim Woodhouse has written many articles addressing the minimum and maximum bow forces and their relationships with the instrument's and string's impedances.  His contact information is on his e-book Euphonis.org website.  

 

1.      M.V. Matthews, J. Kohut, “Electronic simulation of violin resonances”, The Journal of the Acoustical Society of America, Volume 53, Number 6, 1973

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On 2/21/2021 at 11:57 AM, Marty Kasprzyk said:

This is fun stuff! 

It would be really interesting to see how the shape changes when just the cross grain stiffness is varied with a typical density spruce wood.  I have often thought that plywood top instruments should be made narrower.  Maybe plywood has gotten a bad rap because the shape wasn't adjusted so they didn't sound right.

I was wrong.  Plywood tops should be much wider.

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Thanks for the data, if you could share the actual numbers instead of a picture it would be lovely. Is that an acoustic measurement or a bridge admittance? 

We have another paper (submitted not yet online) where we study ways to quantify the differences between FRF by extracting "features" from the data (amplitude, frequency, damping), and using them to "sort" violins by the distance between the features. As you well say, the frequencies vary quite a lot but your conclusion is not warranted: maybe is some relation between the frequencies that is important rather than their absolute values. But without proper statistical analysis is impossible to quantify that. The use of PCA for example is quite useful here, some violins can have freqs in the same range but vary in different "directions" (say one too low another one too high). 

In this same paper we propose a function for the higher frequency part of the spectrum. Instead of looking to each of the peaks we compute the integral between 0 and f of the spectrum, which is the emitted power fraction at a given frequency f. Interestingly, when we compare modern Cremonese violins, a Strad, and a copy made by a famous american luthier, the behaviour of the Strad was completely different to the to the contemporary violins, despite having the first few peaks in the same range as the other ones. 

Here's the plot: 

 

image.png.392298cace48d9dc3b3b62dbeddec9a5.png 

That's just to say we are trying to study all the complex annoying details in a systematic way, and don't pretend that just by looking at a few freq values can determine a violin. If you go back to the last figure of the first paper for example we are comparing 40 eigenfreq, going up to ca. 900 Hz.

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6 minutes ago, tsuresuregusa said:

Thanks for the data, if you could share the actual numbers instead of a picture it would be lovely. Is that an acoustic measurement or a bridge admittance? 

We have another paper (submitted not yet online) where we study ways to quantify the differences between FRF by extracting "features" from the data (amplitude, frequency, damping), and using them to "sort" violins by the distance between the features. As you well say, the frequencies vary quite a lot but your conclusion is not warranted: maybe is some relation between the frequencies that is important rather than their absolute values. But without proper statistical analysis is impossible to quantify that. The use of PCA for example is quite useful here, some violins can have freqs in the same range but vary in different "directions" (say one too low another one too high). 

In this same paper we propose a function for the higher frequency part of the spectrum. Instead of looking to each of the peaks we compute the integral between 0 and f of the spectrum, which is the emitted power fraction at a given frequency f. Interestingly, when we compare modern Cremonese violins, a Strad, and a copy made by a famous american luthier, the behaviour of the Strad was completely different to the to the contemporary violins, despite having the first few peaks in the same range as the other ones. 

Here's the plot: 

 

image.png.392298cace48d9dc3b3b62dbeddec9a5.png 

That's just to say we are trying to study all the complex annoying details in a systematic way, and don't pretend that just by looking at a few freq values can determine a violin. If you go back to the last figure of the first paper for example we are comparing 40 eigenfreq, going up to ca. 900 Hz.

Do any of these violins sound good?

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Just now, Marty Kasprzyk said:

Do any of these violins sound good?

yes. 

The Strad is from a rather famous professional player, and according to him the copy also sounds quite good. Of the Cremonese makers, they were part of the last Mondo Musica so maybe the recordings are online. I'm not sure I can de-anonymise the data though. 

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1 hour ago, tsuresuregusa said:

In this same paper we propose a function for the higher frequency part of the spectrum. Instead of looking to each of the peaks we compute the integral between 0 and f of the spectrum, which is the emitted power fraction at a given frequency f. Interestingly, when we compare modern Cremonese violins, a Strad, and a copy made by a famous american luthier, the behaviour of the Strad was completely different to the to the contemporary violins, despite having the first few peaks in the same range as the other ones. 

A very interesting plot that I have not seen before.  However, I think it would be even more interesting to have the plot in absolute power, and not normalized to 1 for each instrument.  

The Strad plot illustrates what I have been harping about forever.  If you look at the signature modes and anything below 1 kHz, it is smack in the middle of all the modern instruments in terms of response and mode frequencies.  Only when you get above that, the huge difference is obvious.  And it agrees well with the few Strads I have been able to measure:  abnormally strong response between 1 and 2 kHz, whereas modern ones almost never hit their "bridge hill" stride until much higher frequencies.

As yet, I have no clear explanation for why this glaring difference exists, and have not heard any other explanations that make sense (although I do have some unproven and perhaps unprovable ideas).  If you can come up with analysis that explains it logically, that would be a huge advancement.

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those results are bridge admittance measurements so they are normalised by the impact force of the hammer on the bridge, therefore we cannot compute absolute values of power. Maybe with the simulations is easier to do:

image.png.337b7910eba78bec09a2a860e9a1761d.png

 

that's some different examples for top plates with clamped boundary conditions. Don't ask me why we stopped at 2000hz, it was just a test run and we wanted to have an idea of how many points we would need. We need to re-run the sims and then I can maybe say something about to what variables the onset of the raising is related to. Will take a few days, it takes around a week of computing for the 1000 tops we are using.   

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On 2/21/2021 at 6:30 PM, tsuresuregusa said:

One needs to note that the scale of the anisotropy here is for extremely different materials:

image.png.23e476801e181e744c2613b0bac39790.png

So his results are coherent with ours. Even if you would find a wood that only changes on the cross grain, the effect would be minor. As I said the before, the most material important parameters are density and longitudinal stiffness, so when changing the wood those are the ones that will dominate, not the cross grain stiffness. 

 

 

 

 

I think it is a mistake to ignore the cross grain elastic elastic modulus or its cross grain speed of sound because it does have a large effect. 

Cremer's (1) equation 11.24 seen below used a simple flat rectangular plate to model the mode frequencies of a violin top. If the width Lx of the plate for example is one half the length Ly then, because they are squared, the width direction contribution is four times greater than the long direction.   But the wood's cross grain speed of sound Cx is typically only one fourth of the longitudinal speed of sound Cy so both directions contribute the same amount to the calculated plate frequency.

The speed of sound C equals the square root of the elastic modulus/density ratio.  So the 4 to 1 ratio of their speeds of sound produces a 16 to 1 ratio of their elastic modulus stiffness.  This  anisotropy ratio is in the range of spruce wood.  Cremer's equation shows that it is important to have a high cross grain stiffness because this allows the plate to be made thinner and therefore lighter while still producing the same mode frequency.  This in turn increases the loudness of the violin.

Makers are careful to choose top plate wood which has its growth rings perpendicular to the cross arch surface in order to maximize its cross grain stiffness and speed of sound.  An off-angle reduces the stiffness and therefore the plate has to be made thicker (thus heavier) which reduces the violin's sound output.

We also know the tops of many famous old violins were thinned sometime long after they were made.  Some contemporary makers have also regraduated their own violin's plates several years after they were built.  I assume this was done because they might have eventually sounded too bright or even harsh.  Thinning reduces the frequencies of the resonance peaks across the entire violin's spectrum and Claudia Fritz has shown that it only takes about 1.5 to 5 percent frequency change to be perceived.

Martin Schleske (2) has shown how various kinds of varnish increase the speed of sound in the cross grain direction quite a bit over a nine year period.  I assume this is because the varnish is getting harder and stiffer which may explain why plates were sometimes regraduated.

The attached graph (3) shows how the plate should be made thicker or thinner depending upon its cross grain speed of sound using a wood with a longitudinal speed of sound of 5200m/sec. A nominal 3mm thickness at a 1300m/sec cross grain speed of sound(4 to 1 ratio) is shown by the red lines.  It doesn't take much of an increase in the cross grain speed of sound to require some thinning to maintain the same mode frequency of  1351 radians/sec or 215Hz.

1.  Lothar Cremer, "The Physics of the Violin", The MIT Press, 1984, p291

2. Martin Schleske, On the Acoustical Properties of Violin Varnish, CASJ Vol 3, No 6, November 1998

3. me, right now

 

Cremer.jpg

Screen Shot 2021-02-24 at 2.01.43 PM.png

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12 minutes ago, Marty Kasprzyk said:

I think it is a mistake to ignore the cross grain elastic elastic modulus or its cross grain speed of sound because it does have a large effect. 

Cremer's (1) equation 11.24 seen below used a simple flat rectangular plate to model the mode frequencies of a violin top. If the width Lx of the plate for example is one half the length Ly then, because they are squared, the width direction contribution is four times greater than the long direction.   But the wood's cross grain speed of sound Cx is typically only one fourth of the longitudinal speed of sound Cy so both directions contribute the same amount to the calculated plate frequency.

just to be clear, we are not ignoring the cross grain elastic modulus in our simulations. We vary it as well as the longitudinal stiffness but its effect is negligible. This is a result we obtain from the simulations and not an assumption. 

Maybe the range of variation in natural materials is way larger for the cross grain than for the longitudinal in which case our simulations would not be representative. We don't have data on this so we went for what it seemed a reasonable guess. It may be the case for a rectangular plate but not for the violin plates we simulated, and I trust more our simulations than a 2D approximation. 

The varnish... that's interesting, since it's isotropic it will proportionally increase much more the cross grain direction than the longitudinal which would make the completed violin stiffness way off from what we are simulating. But then again we are not even started with varnish in our model. 

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