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Paper: A Data-Driven Approach to Violin Making


tsuresuregusa
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Hi

This is my first post so I'll do a bit of introduction too. My name is Sebastian Gonzalez and I'm a researcher at the Museo del Violino in Cremona. I did my phd in physics in Holland where I met my ex wife, whose family makes violins in Germany since 1700 or so. Fast forward a few years, and I moved to Cremona to simulate, and soon hopefully also experiment with, violins. (I just finished building my first one while in lockdown here in Italy.) Maybe some of you saw my talk in Claudia Fritz's conference last year. 

We just have submitted our second article (the first one will be soon published in JASA) but I feel this one could be more interesting for luthiers as it shows some general correlations between the eigenfrequencies of the top plate and the outline, thickness and material parameters of the violin. And interestingly, shows that the outline is far more important in determining the vibrational behaviour than the thickness of the plates.

We also use artificial intelligence to predict the modes from the shape/material parameters which is kind of cool. I'd be really glad to discuss our results and answer your questions if you have any. (You can think of it as open source peer review B)

This is link for the pre-print https://arxiv.org/abs/2102.04254

This is an ongoing project, so any input could turn into actual research. We are currently studying the FRF of the free plates and in the next months we are going to simulate the acoustic response of fully assembled violins, it is just more time consuming than free plates so we wanted to be sure the methodology was working before embarking in the real project. 

Cheers

Sebastian

 

 

 

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Hi Sebastian,

I did see your talk at Claudia Fritz's video conference last year.  But I think it was given at about 3:00 in the morning here and it may have been remembered as a dream.

The understanding of violin mechanics is progressing very quickly from the kind of work you and others are doing.  But what has surprised me is all the scatter of player's and listener's preferences which makes it difficult to see if any experimental construction change (plate thickness, arch shape, wood properties etc.) is giving any significant improvement.  There are several problems:   How big does the change happen to be in order to be detected?  Is making the change preferred over the original? , and if so how big should the change be and is there an optimum where further change in that direction is detrimental?

The Bilbao project (also reported on) is an example of a seemingly simple experiment of changing top and back plate thickness where everything else is kept as constant as possible.  This was an amazingly massive effort and it was eventually learned that thinner tops and backs were helpful.  But there wasn't complete agreement will all participants and you really have to use good statistical analysis with many participants to show valid trends like in Claudia did.

So I think the great scatter in personal taste likes and dislikes is what has caused violin improvements so difficult to make in the past and now.  

 

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Hi Televet, thanks for resuscitating the post ;)

 

Marty, indeed we are not interested yet with the perceptual aspects of the violin for as you well say it's extremely complex. We are after something much simpler which is how to make "equivalent" violin tops from different materials. This equivalence is for the moment studied only in the vibrational domain since sounds is a function of the eigen-frequencies and the shape of the violin. If we are able to "copy" a violin in this way only then we are going to deal with the perceptual problems associated to defining what's better/worse, and for that we would probably need to go far beyond self-reporting into neuroscience and such... it's part of our long terms goals though. 

A point that you mention regarding the "directions of change" is something our study sheds light on. The directions of change are not trivial superpositions of variables, and for example, according to our results is the ratio of the stiffness to density (sound speed) that has more impact on the vibrational behaviour than either of the material parameters alone so matching only density or only stiffness could in some cases be "worse" if you want to keep your results stables. For the case of the geometry it gets even more complicated and the use of PCA is very helpful here, since the "geometric directions" are not as simple as "wider", "shorter" or whatever.   

 

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Thank you, Sebastian for sharing your work with us.  Televet: I think the reason there are so few responses is that the paper is highly technical.  I have read it and confess I can get the general idea but I can't understand all of the methods.  If I have the overall picture, the authors have used an artificial intelligence learning program to analyze and predict the vibration of the top of violins, sans bass bar, with respect to material characteristics, shape and thickness.  They conclude that you can't reproduce a master instrument's sound with simple geometric copying because the wood may be different.  They have not yet addressed arching variables or the inclusion of a bass bar.  They hope to be able to use this method to direct design based on material characteristics.  For me, mystery of violin sound quality remains;  what if any are the most useful surrogate markers for competed instrument sound quality that a luthier can use along the way?  

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It was an interesting read. Thanks for sharing. I do have some questions about the relevance of this study to actual violin making, but perhaps that is a topic that needs to be addressed by a further study. Here are some observations you might consider...

In the simpler forms, neural nets are linear predictors of behavior. Inputs are multiplied by weighting factors (linear coefficients), and then the differences between the predictions and the observed results ("errors") are used to adjust ("train") the weighting factors.

If you are varying the inputs of your experiments by "small" amounts (the geometry), resulting in "small" changes in the results (the mode frequencies), you will frequently find yourself in a region of behavior that is accurately predicted by a linear model. Thus you got good correlation with both the neural net and its linear weighting factors, and a simple linear equation regression.

One of the advantages of a neural net approach is that linear "layers" can be cascaded, one after the other, to form a predictor to complex behavior. It doesn't seem necessary for the geometry changes you considered in your paper.

What would be interesting to see is which geometric parameters had a significant effect on the frequencies. In your paper I believe you considered 20 parameters, but found only 7 had any real effect on the results.

The experiments with thickness were perhaps unremarkable. If you published the shapes of the first 5 modes, I would wager you could predict where a thickness change would affect each mode. What might be of interest is multiple simulations of thickness changes in small regions, and then maybe a color coded plot for each mode displaying the relative effect of each thickness change on the mode frequency. For makers interested in plate tuning, this could give some guidance on how to thin plates.

There is a research paper circulating about that connects free plate modes to fixed plate modes. If I can dig it up I will post a link. It might give some insight into which free plate modes should be the focus of future studies.

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Thanks for the comments ctanzio.

The variation in geometric parameters is quite small and therefore the linear regime is quite accurate, but the examples of violin shapes we obtain are far from "small changes", they go from really skinny fiddles to "fat", almost gamba looking ones (we are planning on releasing the dataset together with the paper for people to see). We needed to cap the distribution of values to keep the things looking like violins. So it's not that we are limiting ourself to small variations but that the parametrisation is really "good". If you use other descriptors (width at the bouts, distance between corners) the prediction is not as good, since there is a strongly non-linear relation between the parameters of the model and the more "normal" descriptors.

 

We have just uploaded this other paper (also under review) that looks precisely to how each frequency is modified by which change on the outline:  https://arxiv.org/abs/2102.07133

 

As you well say, the cool thing of the neural networks is that can be layered, going from frequency to spatial behaviour, and from there to sound field. This is a test case if you want, what's the simplest thing we can predict of the violin that it actually works. And it does so we are happy with it and keep on extending it. 

Quote

The experiments with thickness were perhaps unremarkable. If you published the shapes of the first 5 modes, I would wager you could predict where a thickness change would affect each mode. What might be of interest is multiple simulations of thickness changes in small regions, and then maybe a color coded plot for each mode displaying the relative effect of each thickness change on the mode frequency. For makers interested in plate tuning, this could give some guidance on how to thin plates.

 

I don't understand how is that different to what we have done, except for having more and smaller regions? We actually could do that quite easily, but my impression is that the smaller the region you modify the less correlation there is. And it depends on what model you are using, this plot is for varying only the thickness profile, when you start varying the material the correlation goes to a max of .5 which is rather low. Maybe I understand now, do you mean that beside of the correlation coefficient I plot the slope of the relation between thickness variation and mode frequency? If that's what you mean I can do it easily.

 

image.thumb.png.f9354c725e1e474e11aa3ed9f6e3852b.png 

 

Concerning the bass bar... We are using Comsol for our simulations but the creation of the dataset is done in Matlab and we are having a bit of a hard time joining different meshes. The varying arching is already coded, at least for the transversal arching. We could also vary the longitudinal arching since we use a polynomial fit to a Strad but each parameter we add implies lots of more analysis so we are trying to go step by step. 

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If I understood you correctly, here's the % change in frequency for the first 5 modes. Colour is the amount of variation per mm of thickness variation and opacity is the correlation coefficient from the previous plot. The frequency that varies the most is the second one and depends mostly on the centre. It's also the one that has the most correlation so one could say to lower f2 make it thinner. 

I think we could have easily 18 regions but more than that is a bit complicated since we need to ensure the inside is continuous and nicely varying from point to point. 

image.png.f178377fe51bef549e96c78a3cbc7e9d.png

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Looks cool. I've mentioned these math and computing methods waiting to be used few times before and now it's taking shape...

I haven't read the article yet (just peeked inside) and I still don't see the most important point of all - connecting the data with actual sound of instrument. You can predict frequencies of plates or determine which piece of wood will get you there etc. but that still is not approaching the practical outcome of violinmaking. It's hard (or close to impossible) to quantify quality of violin sound without pretty heavy research of it's own and even with that there will always be some folks disagreeing with whatever you find out because you have to do some statistical methods to get some usable data. I wonder what you plan to do next...

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I need to justify my position for at least 3 more years so cannot answer all the questions in our first paper :P

Quote

 It's hard (or close to impossible) to quantify quality of violin sound 

Agreed, and we are not even thinking of that for the moment. Our question is much more simple and and concerns how to modify the shape of an instrument so it sounds like another one. (Think of making acoustic copies of a given instrument.) We have demonstrated in our second article that you can compensate for material variations with variations of the outline, making two different pieces of wood to vibrate the same under free boundary conditions. 

Now, the sound pressure is a function of the volume and the square of the frequency (under certain assumptions) so I expect the frequencies to be the determining factor in making acoustic copies, and that our optimisation algorithm work as well to "copy" a given acoustic response. 

Regardless of the feasibility of that, the approach of creating thousands of examples and computing from that what are the most important parameters is something for me particularly interesting. There is post now asking about the influence of the outline on the sound. Since I haven't done the simulations I don't know, but I have numbers to show that statistically the outline is much more important than the thickness profile in determining the eigenfrequencies of the plate.

My plans for the futures is the simulation of the complete violin, then some CNC carving to show we can make acoustic copies with different materials, then, if that works, think about relating perceptual descriptors with structural properties and pivot the whole methodology and apply it to winemaking. 

 

 

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On 2/9/2021 at 8:56 PM, tsuresuregusa said:

I'd be really glad to discuss our results and answer your questions if you have any. (You can think of it as open source peer review B)

Hi Sebastian,

nice to see you here. I appreciate your will to publicly share your work to expose it to criticism, it is not something that is easily encountered among researchers. There are somewhat complex aspects for an "ordinary" luthier, but I believe that here you can find some opinions from some "out of the ordinary" ones.:)

Good luck with your research!

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Hi Sebastian,

Violin researchers have often focussed on the various mode frequencies of free plates (typically mode 1, 2, 5) and the assembled instruments, (often the signature modes A0, B1-, B1+) with the idea that controlling these frequencies will somehow help makers produce a desirable violin.  

However, as I mentioned earlier, player and listener tastes in sound character vary greatly. So now I'm trying to explore other violin qualities that are more universally appreciated by players.  I believe playability issues as note evenness, dynamic range, absence of bad wolf notes, ability to shape the sound, and loudness are some of the most important things

One of the most unintended and exquisite insults I've ever received happened when Itzhak Perlman played one of my violins for me after our concert master Michael Ludwig had earlier tried it. It was a wonderful wonderful experience to hear it played so beautifully.   

But then Ludwig said  "Wow--You can make anything sound like a Strad! 

 

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I think this is a difficult task because there are so many factors in good violin design.

1. Sound quality; Baroque violins sound better than modern, viola da gamba is better accompaniment than a cello, and I prefer the harpsichord to a piano.   Also Vivaldi was best composer ever.  How do you put numbers on this?

2. Sound volume; Modern orchestra needs 32 violins. If they were baroque violins you would need 64 to produce the same volume.  A voila da gamba has a hard time standing up to even a baroque violin in a duet.  Harpsichord has no volume control at all.  A country fiddle has to be LOUD so that single fiddle can stand up against all the other instruments in the band.  Composite monstrosities work great for country.

3. Playability; C bouts are as much about allowing bow angle as shaping the plate for achieving some sound quality. Old vielle didn't have c bouts, but they also had a fairly flat bridge and it was impossible to play only one string at a time.  Why do modern basses still have a notch back and tapered neck like an old viola da gamba?  Sounds better?  Nah.  It's just more comfortable on such a large instrument to not have those sharp corners digging into your ribs.  Lots about the shape makes the instrument easier to play.  Why does a cello have much thicker ribs than a violin?  Because it can.  If a violin was that thick, you couldn't stick it under your chin comfortably.

4. Constructablity; Violins are "easy" to build, at least in comparison to older instruments. Do modern shapes with corners sound better than older "smooth" figure 8 shapes?  Probably not.  Corners are simply an artifact of how they are made, starting off gluing corners onto the mold.  Guitars don't need them, but they are also built differently and need a larger negative mold and bending the ribs is more complex.  Why do violins have complex 6 order curve shapes on the arching of their plates?  Because to guide the carving the profiles were drilled out to 6 different depths.  Why 6? Maybe 7 takes more time to drill out and doesn't help make the arch smoother, while if you only use 5 distances too great between profiles and the curve gets sloppy.

5. Durability. Most amazing thing about a 400 year old Strad is that it's a 400 year old Strad and can still be played. Amazing.  Violins are tough, strong designs.  How I never broke the neck of my cello when I was a kid, I'll never understand.  What's the best profile for a plate?  The lightest, thinnest shape that won't break with daily use for 400 years.

6. Looks; Violins have this classic "perfect" shape, which is kinda like a feminine body.  I've seen 1 million electric guitar shapes, where they are solid bodies and doesn't make a bit of difference to sound.  Each and every one is uglier than a violin.

 

Something I'd like to see which I think would be interesting would be strength testing of different shapes.  How can making small changes to shape of plate effect it's strength:mass ratio?  Also to measure "prettiness" of shape, could you produce some kinda poll where people are given two generated shapes to compare and pick which they like the best?

 

 

 

P.S. Even though no one has figured out how to build a prettier violin than Strad in 400 years, gotta try.  Here's my go.

 

fiddle2.jpg

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

My name is Sebastian Gonzalez and I'm a researcher at the Museo del Violino in Cremona. I

It's an interesting approach.  Who knows what you'll manage to tease.

One challenge question though. Why do you think that diagram is actually Stradivari's work??  That's a tall assumption.

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The additional reference was helpful. You published something in that second reference that might of interest to makers in general, and plate tuners specifically.

To summarize for readers: for any given "reasonable" geometry change (the instrument still looks like a violin), it is possible to adjust the plate thickness to recover the mode frequencies of the original geometry.

Another way of stating it might be that if a maker has a set of mode frequencies that make a "good" violin, then if they decide to change something about the geometry, they should be able to tune the plate to that same set of mode frequencies by adjusting the plate thickness in some way.

It was also interesting that material property changes have a much smaller effect on mode frequencies than geometry and thickness. Many people here tend to obsess over density and sound speed. It might be worthwhile if you could post the range of values of the material properties you analyzed to see if it is in the range of material properties makers encounter with the wood that is available.

Did you consider the effect of internal damping? I did not notice it in the references but I only read them in enough detail to make sure I understood what you were doing. There is some research suggesting that as violins age, the internal damping decreases significantly. It is a motivation for some makers to use heat treated wood to artificially age the wood to a lower state of damping. This might be one of the larger contributors to the power of older violins, but not necessarily beauty of tone >smile<.

When analyzing the effect of vibrational input to structure response, one measure I used extensively was modal participation factor. Frequency of the mode was part of the response problem. But I wanted to know "how much" of the mass was participating in the mode's movement. This is roughly equivalent to how much power a mode can potentially contribute to the sound.

Training neural networks with multiple hidden layers is as much art as it is science. Good for you for taking on the challenge, but personally, it was a source of much angst before I retired from research. Generation of meshes for FE models was another area that caused me much worry. It might be the main reason more researches have not pursued detailed FE analysis of assembled violin structures.

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Sorry for the slow replies but the moderators need to approve my responses so it's taking far too long to reply one by one the comments...

Thanks Davide, I hope we can have another live session soon here in Cremona presenting our last results. 

Concerning previous research... I do think the A0 B+ B- focus of previous research is a bit, how to put it nicely, ungrounded? I don't have a formation in musical acoustics, my PhD is in Physics, so I didn't approach the problem the way the literature has done before. One particular thing we tried to avoid is the "leave all the other parameters constants" approach, and I think we have successfully came up with a way of doing this. Limited but far more complete than the state of the art. 

Concerning the playability issues, those can objectively measured (maybe I'had trouble with "note evenness" and "ability to shape the sound"). Our idea for the future is include these observables in our studies so that one can predict them from either parameters of the violin, or actual measurements of the eigenfrequencies of the free plates. 

About Stradivari's diagram, that's a question for Fausto Cacciatori, the curator of the museum. We are basing our statement on ref. 20 where they write is his. It does perfectly match the Messiah scan that we have though, so I don't really care about its authenticity as long as it's a useful tool for creating violins. I wish I could call it the Gonzalez's method but I literally just copied what is in the diagram, played with the numbers and the results were violins.

Thanks for the summary of the other paper ctanzio. But we actually want to draw the contrary conclusion: plate tuning is worse at compensating than outline variations. It can be also seen from the first paper Fig. 7a where the spread in frequency is half of that the one due to material or outline variation. It also can be seen in figure 3 of paper 2 where plate tuning, where we modify the material and then optimise shape and thickness to recover the original vibrational response

 

image.png.e0f9398221b02128e1fe39809314bea8.png

 

So thickness can reduce the error but the best is to modify outline and thickness together. 

 

About the materials: density ρ = 3600-4400kg/m3 and longitudinal stiffness Ey = 9-11GPa.

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. (Meaning, we did it once and don't understand the results so back to the drawing board.) We have a master student doing the literature review, when we have new results I can tell you more. Seems the models available for the damping are mostly for isotropic materials.

Yes, mesh creation is a pain, we have another paper where we give more details about its creation but it's currently accepted so will give later the official link as soon as it has a doi. 

Thanks for all the feedback!

 

 

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Welcome Sebastian,

this looks pretty braintwisting.

I didn't have time to read the paper but if the goal is the sound replication (or sound cloning?) of existent instruments of proven high performance qualities it is certainly extremely interesting.

A few thoughts on the realistic possibilities to do so:

First, from a pure violin maker point of view everything which belongs to the setup of an instrument, and in particular neck angle and bridge proportions can have a huge influence on playability and sound charactistics for a given instrument and has absolutely nothing to do with the proportions of the plates. 

Secondly, I learned with my super light violin project that the proportions of the ribs can have a destructing effect on the sound. Actually building 'wrong' ribs is a perfect recipe to make an non functioning violin.

Thirdly, material investigations on old Italian violins suggest that the wood has been treated, though it is not entirely clear if this was a voluntary act. Research suggests that this has a measurable influence on the sound.

Last not least we face the problem that old wood as such, even if not treated, transforms over centuries. The best explanation I found on this so far was the crystallization of cellulouse through repeated humidity changes.

In my personal view material proportions are the biggest obstacle. And I don't think it is a good path trying to get same results with different material by changeing other parameters. This means if you take the simplified model of  

1.Arching

2.Thicknesses

3.material constants

as the determining factors for sound and lets say the fiddle you are sound copying has a material constant of X and you try with material constant Y to copy it by changeing Arching patterns and thickness patterns I doubt that you can get close enough to call it a sound clone.

However if you manage in the first place to match the material constants the whole thing gets a lot easier. (Just from a logical standpoint)

-----------------------------------------------------------------------------------------------

On the interaction of player and listener, the experiments by Claudia Fritz at least showed that in the ears of listeners the 'Strad sound' is not necessarily what the audience judges as good or pleasant. From my own experience as a concert goer I have heard at least one world class soloist playing a high end fiddle whose sound I definitely didn't like.

I think the lesson from there is that first of all the opinion on the sound from the standpoint of listeners is secondary. What is most important is how the performer feels about the instrument in extreme performance situations. (This must have been the reason whu this world class player has chosen his instrument) Unfortunetely I didn't participate the Fritz experiments but I think she looked into this aspect as well and again some contemporary makers could beat some instruments of the creme de la creme of old Italians in concert performance situations.  (Tough I am convinced that there are still some instruments from the golden period which are extremely hard to 'beat', if this term applies)

I think historically we stand at break point. Our perception of music in general with other genres of music like pop, rock, jazz etc. has changed. This is right now reflected in an evolutionary process in violin making. 

Nevertheless welcome to MN and looking forward to hear more from your investigations. 


 

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12 hours ago, tsuresuregusa said:

About Stradivari's diagram, that's a question for Fausto Cacciatori, the curator of the museum. We are basing our statement on ref. 20 where they write is his. It does perfectly match the Messiah scan that we have though, so I don't really care about its authenticity as long as it's a useful tool for creating violins. I wish I could call it the Gonzalez's method but I literally just copied what is in the diagram, played with the numbers and the results were

My best guess is that your diagram is a post fact attempt to analyze and example of real classical sides, but several generations after Stradivari's time.  

I would say the analysis was by someone who knew they worked the shapes with circles, but not how, nor at what stages of work.

The sides are assymetric as happens naturally in classical work, but the application of circles is only 'almost'.  And partly that's because the sides are never worked directly as circles.  The mold is worked in circles BEFORE the sides are made.  And the plate outline is worked in circles AFTER the sides are off the mold and have acquired the sort of assymetry seen in your example.  But the sides are never themselves true circle geometey.  The mold is good geometry. And the outlines are more comlicated good geometry adapted to follow and reconcile with the sides.

You can also see the analysis uses arcs that don't join smoothly (main bass side center bout is shown with conflicting partial arcs).

 

I'd love to hear what your historian says is concretely known about that diagram.

And, thank you for your interesting project.

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Hi Sebastian,

Even with scientific training and having published in the social sciences combined with a casual non-scientific interest in violins, it is hard to read your paper. If you plan to publish it in a peer-reviewed publication, I would urge you to make it more accessible to a more general audience. In its current form, the paper is too technical in its non-technical parts (the abstract and the introduction; it's fine to be technical in the technical parts, but it needs better explanation in the technical parts as well). Most importantly, what I am missing from your paper is the hook. Why should I be reading this?

Thankfully, you are putting this in the Summary/Conclusion. In my reading the two most general and interesting results are: first, you cannot just copy the dorsal shape, you need to copy all its physical properties, including local thickness. Luthiers and specialist know that most Strad copies are bad, so your results might give some hints why some are better than others (this is actually a testable hypothesis: are copies that are closer to your specification more successful than others). Secondly, you do complement this result (which is your last) nicely with the first result showing equifinality (there are different ways to get to the same tonal response. To get to the same result one has to vary interactively/interdependently shape and thickness. I would lead with these two results in the abstract as well, because then people might be more inclined to say: wow, this is interesting. All other results are subordinate to these two in my reading, subordinate meaning they either flow from the first two or are less important.

Daniel

 

Edited by DanM
clarity
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23 hours ago, tsuresuregusa said:

>

Concerning the playability issues, those can objectively measured (maybe I'had trouble with "note evenness" and "ability to shape the sound"). Our idea for the future is include these observables in our studies so that one can predict them from either parameters of the violin, or actual measurements of the eigenfrequencies of the free plates. 

>

 

 

Players like note evenness and it can be determined by playing it or by generating it from its frequency response curve where the loudness of each note is found by summing up the amplitudes of each of the note's harmonics.  This is done for each half note of the violins entire range and plotted.  We already know from the testing of real instruments that a frequency response curve having just a few high resonance peaks with deep valleys which are octave apart produce some notes which are overly loud while some are very weak.   Note evenness can be improved by having many smaller peaks and shallower valleys that are randomly spaced.  

So if you can do computer simulations to predict the shape of frequency response curve you might be able to suggest material properties and geometries to help achieve better note evenness.

 

The "ability to shape the sound" is important for players because it allows for more expressive music.   It is desirable to have a violin that can be played with a very hard bow force to produce a loud bright sound while it is also possible to play lightly and far away from the bridge to produce a soft mellow sound.

In large part these sounds are determined by bow position relative to the bridge--playing close to the bridge brightens the sound and makes it louder.  So it is helpful to be able to bow as close to the bridge and this is determined by the intersection point of line plots of the minimum and maximum bow force vs. bowing position.  These lines are determined by the impedances of the strings and the impedance of the violin body.

So if you can do computer simulations of the violin body's vibration you might be able to predict its impedance which in turn would enable you to predict how close to the bridge the violin can be played so you might also be able to suggest material properties and geometries to help that.

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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.  

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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.

Finite Element programs ignore damping effects for their vibrational computations because it simplifies the equations to a classic eigenvalue problem. The solution also gives a method to invert the matrix equations needed for static load computations, so the authors can kill two birds with one stone, so to speak.

To consider damping in the vibrational computation, one has to consider numerical tools to extract the roots of a determinant consisting of the stiffness, mass and damping matrices. Users of FE programs have ways to apply an undamped solution to systems with small, but important damping factors to get an upper bound on things like earthquake response.

Since you trained your neural network on a undamped model, it might be a challenge to figure out how to adjust the results so they can be practically applied to an actual violin with non-trivial damping. Although a general understanding of how geometry and thickness affect specific and important modes might be good enough for a maker to learn from your studies.

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3 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.

>

You said "Unfortunately..this leaves plate thickness..."    If you didn't protesters at your door what else would you choose to change besides plate thickness?

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13 hours ago, Marty Kasprzyk said:

You said "Unfortunately..this leaves plate thickness..."    If you didn't protesters at your door what else would you choose to change besides plate thickness?

Not what I actually said, but even if I grant your selective editing of my post, unfortunately I do not understand your following comment. 

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