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Violin sound - basic questions....


EternalStudent

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Hi, all,

reading through this really interesting "break in" thread, I noticed that in general there is no consens about what makes the sound of a violin "good" or "poor", except of some very rough and obvious distinction. (I had once the opportunity to play the "Seefried" and the "San Lorenzo" Strads and they were different like day and night, but both beautiful) I also have not heard about any systematic research in this area. S I'd like to publish some questions here alog with possible experiments to (probably) answer them.

Quote jmasters from "Why new Instrument sounds better after play?? "

"In other words, the best science is the science with the best questions, not the best answers."

First, and most basic:

What is the difference in the overtone spectrum between a ringing string (without any resonance body) and that of the whole violin? IOW what kind of "distortion" does the body of a violin do to the spectrum of the string alone.

-The experiment should not be too difficult, but time consuming: The string(s) could be placed on sort of a silent violin with a heavy frame, "played" with sort of a "soft" capodastro instead of human fingers and electromagnets instead of the bow and the frequency spectrum sensed electronically. The same string(s) can then be placed on real violins, the same "playing technique" used and the sound recorded with a top quality mike. Analysis of the spectrum about frequencies and phase can then be done with a computer, which can as well search for common parameters.

Second:

What is the difference between "good" and "bad" violin sounds?

-Using the "playing technique" suggested above "known good" and "known bad" instruments can be recorded and their spectrum analyzed and searched for common "domains" and their relative intensity and phase. In parallel the electronically sensed, artificially distorted and amplified sound of the abovementioned silent violin can be compared to the sound of real violins, good and bad. There are of course several things to watch - the acoustic response of the room for example. (My violin exhibits a bad wolf note at G sharp, but it is very strong just in one of my rooms, in the others it is nearly gone and in a church where I play frequently it seems to disappear totally)

Third:

Now, with the abovementioned analysis at hand, we can do some "Chladni plates" analysis again using the same setup and "playing technique as above. Of course we can hardly use dust particles as indicator, and that makes the experiment complicated and costly. Actually I am thinking of some laser sampling of the surface of the plates, in an equipment similar to a computer tomograph.

This could give us some idea how top and back behave at different frequencies. Again we'd have to search for "common domains".

Then we come to ask: What causes the difference in the frequency response of the plates?

Instruments "in the white" with different arching and very thick plates at the beginning, where we gradually remove material and make the above measurement, might give some answers here. NC - controlled tools spring into mind here.

No answers, just questions.

If we could answer all of them we might have some additional hint how to (reproduceable) build good sounding instruments (maybe), but anyway, the research could be fun

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""""""""" What is the difference in the overtone spectrum between a ringing string (without any resonance body) and that of the whole violin? IOW what kind of "distortion" does the body of a violin do to the spectrum of the string alone. """"""""

The violin body will favor some frequencies over others. This means that the string on the violin may have some overtones accentuated more than others. (Alternate description is that the compliance of the bridge is frequency-dependent.) A string fixed ridgidly at both ends also has a finite diameter and some stiffness. These add corrections to the simple string model you get in physics 101. By the way, read the new thread I introduced. Some things here are related.

I am sure that the string designers modify construction based on the mysteries of what is going on. They must do it empirically and by evolution. I am pretty certain that they do not have a working theory, except that they would know the corrections to the string problem caused by stiffness and finite diameter.

""""" The experiment should not be too difficult, but time consuming: The string(s) could be placed on sort of a silent violin with a heavy frame, "played" with sort of a "soft" capodastro instead of human fingers and electromagnets instead of the bow and the frequency spectrum sensed electronically. The same string(s) can then be placed on real violins, the same "playing technique" used and the sound recorded with a top quality mike. Analysis of the spectrum about frequencies and phase can then be done with a computer, which can as well search for common parameters. """""

I have asked others about the response of electric violins with solid bodies. I still don't know how they feel about "tone" in this comparison. Also, if the electric violin comes with some kind of filter to approximate a real violin sound. If so, there is an electrical engineer out there that I wish were on the forum. If not, it just goes to show that any bowed string is fairly close to a violin sound.

""""Second:

What is the difference between "good" and "bad" violin sounds?

-Using the "playing technique" suggested above "known good" and "known bad" instruments can be recorded and their spectrum analyzed and searched for common "domains" and their relative intensity and phase. In parallel the electronically sensed, artificially distorted and amplified sound of the abovementioned silent violin can be compared to the sound of real violins, good and bad. There are of course several things to watch - the acoustic response of the room for example. (My violin exhibits a bad wolf note at G sharp, but it is very strong just in one of my rooms, in the others it is nearly gone and in a church where I play frequently it seems to disappear totally)""""

I agree that one needs a large statistical database of what players think is good and bad. It would be nice to find the common denominators and try to see what they are, physically. Everyone likes response, body, and evenness. Volume too. I would add another. What is it that causes a violin to "saturate" ? That is, diminished returns after a certain effort to play very loudly with a good sound.

""""Third:

Now, with the abovementioned analysis at hand, we can do some "Chladni plates" analysis again using the same setup and "playing technique as above. Of course we can hardly use dust particles as indicator, and that makes the experiment complicated and costly. Actually I am thinking of some laser sampling of the surface of the plates, in an equipment similar to a computer tomograph.

This could give us some idea how top and back behave at different frequencies. Again we'd have to search for "common domains".

Then we come to ask: What causes the difference in the frequency response of the plates?

Instruments "in the white" with different arching and very thick plates at the beginning, where we gradually remove material and make the above measurement, might give some answers here. NC - controlled tools spring into mind here. """"

Yes, I like the idea of laser pickup. One can buy chips with combined laser diode and photocell pickup. They are not expensive. Digikey sells them.

Also, there are a lot of cheap software spectrum analysers out there. They give an FFT (fast fourier-transform, in real time) of the signal. They are power spectra, and leave out relative phases of the component frequencies. I don't know how this would effect any conclusions.

"""""No answers, just questions.

If we could answer all of them we might have some additional hint how to (reproduceable) build good sounding instruments (maybe), but anyway, the research could be fun """"

Now that is the spirit !!

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"An engineer is someone who can do for a dollar what any dam' fool can do for two." (Thomas Edison?)

So in a spirit of parsimony, feeling the breeze with a wet (index!) finger, I offer the following:

Solid-body electrics, the small set I've seen, pretty well approximate rigid support at both "ends" of the string. Chunky bridge with piezo pickups: not much flex or compliance there, especially compared to a fine bridge on an acoustic instrument. Some piezo bridges are cut with heart and kidneys, but their overall thickness makes me suspect that only bats, not dogs, could hear the effect. I could be wrong about that. Helicores are pretty floppy, so for now let's ignore end stiffness effects. Longitudinal stretch probably comes into play in the form of frquency doubling (whoops, there goes the linear model.) Fore- and after-length tuning might matter, or may well be hidden down in the short grass.

High-end instruments (again, my small familiar set) don't do any on-board filtering or equalization, just present the string signal as convolved with transducer response. From the size of the elements, I don't expect high-frequency rolloff to be an issue; I don't know where their low-frequency cutoff would be, but experience suggests it is well below the fundamental of a viola C. Flat response in the mid-band? I don't know, but I bet any anomalous dips and spikes or phase wierdnesses lie well outside the conventional 20Hz-20kHz area of interest.

Tone? That's what the preamp and effects pedal are for. I don't mind the sound of a naked pickup, but also like a hint of reverb.

The chief difficulties in isolating "string sound" from acoustic bridge and body effects will be excitation and pickup. Magnetic drive only works on steel strings. Even so, some steel alloys are practically non-magnetic, as in "undetectable by a reasonably sensitive fluxgate magnetometer." Eddy-current hysteresis will vary with winding material and dimension, adding to the chore of calibrating the drive force. Meaningful results would call for a transverse drive at a variable sounding point, causing string excursion amplitude comparable to what you get from a bow. On an acoustic instrument, I believe this means that the pole pieces of your driver must fit between the strings somewhere between the bridge and the fingerboard, with enough wiggle room to vary the sounding point.

I don't know what to do with trying to compare: 1.) projected sound from an acoustic instrument with 2.) whatever, from the rigid-support fixture. In either case, for the same drive signal (sinewave? white noise? swept sawtooth? impulses?) you will likely find a difference in string movement signature, but the only thing you will hear on the rigid fixture is the string itself.

Sorry if I haven't answered any of your questions.

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"" The chief difficulties in isolating "string sound" from acoustic bridge and body effects will be excitation and pickup. Magnetic drive only works on steel strings. Even so, some steel alloys are practically non-magnetic, as in "undetectable by a reasonably sensitive fluxgate magnetometer." Eddy-current hysteresis will vary with winding material and dimension, adding to the chore of calibrating the drive force. Meaningful results would call for a transverse drive at a variable sounding point, causing string excursion amplitude comparable to what you get from a bow. ""

How about bowing the string and picking up the signal in the two degrees of freedom? I would probably send a current in the string and use insensitive magnetic pickups. Then perhaps one could ignore eddies in the metal string or string wrapping. It would be an interesting expeiment.

I would prefer to bow for a first experiment, because one does not know how to simulate the stick/slip bow mechanism which would seem to have a high level of chaos. Of course, later a simple sawtooth could be compared, but driving the string is a problem. Hard to know how to insert enough power magnetically. At least to initiate the effect due to string stretching.

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"How about bowing the string and picking up the signal in the two degrees of freedom? I would probably send a current in the string and use insensitive magnetic pickups. Then perhaps one could ignore eddies in the metal string or string wrapping. It would be an interesting experiment"

Indeed it would, although that seems more like an electric guitar geometry. You could put an array of pickups halfway up the string and sense the overtone mix spatially. Once you run a currrent through the string it will go a smidge flat as it warms, but that should be no problem.

I was thinking of the eddies more as an uncontrolled energy sink in a magnetic excitation system, but they could easily be small enough to ignore. Some strings appear to have an insulating layer between the rope core and the winding, for whatever difference that might make. Of course, with gut or perlon, all magnetic bets are off, regarding either sense or drive.

A bow or rosined wheel is what strings see in actual service, but as the rosining changed I wonder what variable you would control...

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good idea....... I once heard about a juke-box affair that played a real violin this way. Do you know who got his career started making violins for such a device? I have heard it was Carl Becker's grandfather. I may be mistaken (sorry for that Mr. Becker) or maybe even his father.

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Quote:

good idea....... I once heard about a juke-box affair that played a real violin this way. Do you know who got his career started making violins for such a device? I have heard it was Carl Becker's grandfather. I may be mistaken (sorry for that Mr. Becker) or maybe even his father.


The technical museum in vienna has a mechanical violin/piano duet (actually four violins, one for each string). The violins are mounted back to back and the "bow" rotates outside around them. For every note there is a metal "finger" with a felt pad over the string, and if a note is to be played on a string, this "finger" comes down (pneumatic, I think, the whole thing is controlled by a punched paper strip) and the violin for that string is moved a little outwards, so that the string touches the bow. I heard it once in action, it was not so bad

http://www.tmw.ac.at/default.asp?id=482&al=Deutsch

has a picture of that instrument and a short description

As for the magnetic activation of the string: I had not in mind to activate the string directly, my idea was to have a piece if magnetic material attached to the bridge and use feedback for the frequency control. Long time ago I made some measurements on violins together with a friend violin maker, where I used a small metal piece attached to the bridge (clamped under D nd A string) as the magnetic "actuator", but we worked with a series of fixed frequencies, so no feedback.

I guess (note the word "guess" ) that the waveform for the activation is not really important as long as amplitude and frequency can be kept constant during the whole series of measurements. A series of short pulses would activate oscillation in the string pretty mich like the activation of the pendulum in a wall clock, which would mean that the string will be oscillating as free as possible.

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The "juke box" is fabulous, I hope the others see it. The one I saw had a single violin that was rotated, and a rosined wheel of some kind. It could not play chords or double stops, I think. The "finger" mechanism was too compleicated to figure out.

"" A series of short pulses would activate oscillation in the string pretty mich like the activation of the pendulum in a wall clock, which would mean that the string will be oscillating as free as possible. ""

Up to a point, one can consider each mode as a simple harmonic oscilator as is the pendulum, approximately. But it is only a pseudo-harmonic oscillator. I would be worried about exciting higher resonances with any kind of impulse that was not sinusoidal.

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Up to a point, one can consider each mode as a simple harmonic oscilator as is the pendulum, approximately. But it is only a pseudo-harmonic oscillator. I would be worried about exciting higher resonances with any kind of impulse that was not sinusoidal.


Hmmm - what then, if we leave the strings totally out (they must be there an tuned to establish the correct tensions, but can be totally damped), and instead feed a pure sinusodial power into the bridge?

During the measurements I made long ago I had to dampen the strings to get the response of the body - the open strings if not damped produced heavy break ins in the resonance curves.

If we can manage to feed pure sinusodial power into the resonance body we will have a pretty clear situation. No string - dependent complex waveforms on input, all harmonics coming out definitely produced by the resonance body. Or am I missing something?

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Yes, I would kill the obviously large resonance peaks caused by the open strings.

""If we can manage to feed pure sinusodial power into the resonance body we will have a pretty clear situation. No string - dependent complex waveforms on input, all harmonics coming out definitely produced by the resonance body. Or am I missing something? ""

You are not missing anything. But it has been done, ad infinitum. You get a resonse curve. But what does it tell you? Some people say to document violins based on these response curves, but others say they do not comment on many properties of the violin, such as response, and other things I am not privy to.

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You are not missing anything. But it has been done, ad infinitum. You get a resonse curve. But what does it tell you? Some people say to document violins based on these response curves, but others say they do not comment on many properties of the violin, such as response, and other things I am not privy to.


Agreed. What was lost in my article is, that I'd be more interested in the output _waveform_ (amplitude and phase of the harmonics generated by the resonance body) and the areas of top and back of the violin where these harmonics are generated (the laser approach). Given the rather short wavelengths of acoustic waves from about 3m to about 5cm or less for violins the area of the body where the harmonics are oscillating should have considerable influence on the phase of the harmonics, especially as some of the higher frequencies are coming from the back of the body.

Now, if we can find some areas in common for good soundig violins and others for poor ones as well as their relative amplitudes the next step would be to try to find out what properties of top and back are responsible for these oscillation patterns.

State of the art technology should make it possible to follow the progress of oscillations through the different parts of the violin body and even to produce some slowed - down model of the oscillationg resonance body (with the amplitudes exaggerated enough to become visible).

Performing this kind of investigation on a violin "in the white", starting with thick plates and removing material gradually could give us (still a _guess_ ) some useful information about the functionality of a violin.

Also subject to researches would be the influence of soundpost position as well as the exact power transfer from the string through the bridge to the resonance body (the degree of power matching and dampening due to the mass of and elasticity of the bridge). I just guess (everything is a guess before actual experiments have been carried out) that the degree of power matching for various frequencies is one of the main factors for playability and response, however, the power matching is not only a function of the bridge of course, soundpost position and properties of the top plate in the area around the bridge feet must also have some influence I think.

Edited Addition: The exact border of power source and power sink in this area has yet to be defined - IOW the bridge (and it's feet, and probably the soundpost along with the piece of the top between soundpost and bridge) form sort of a power transformer. Of interest is the ratio and quality of this transformer and a definition what belongs to it and what is part of the power source and sink.

We can safely assume, that there is only a really small difference between different strings of the same brand. if a string responds totally different to the same bow strokes on different instruments (and setups), the reason must be the way how the power is taken off the string and how maybe additional power is fed into the oscillating string by resonance.

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"" Now, if we can find some areas in common for good soundig violins and others for poor ones as well as their relative amplitudes the next step would be to try to find out what properties of top and back are responsible for these oscillation patterns. ""

Yes, as I keep saying, a statistical database is badly needed. Also, forget all of this linear analysis, it just ain't there. I may be wrong about that, but I consider the burden of proof to be on others.

""State of the art technology should make it possible to follow the progress of oscillations through the different parts of the violin body and even to produce some slowed - down model of the oscillationg resonance body (with the amplitudes exaggerated enough to become visible).""

What "state of the art" ?? There is none. This paragraph is sheer drivle.

""(still a guess""

Indeed;;;;;;;; hate to sound harsh, but you are just guessing (admit it)

"" I just guess (everything is a guess before actual experiments have been carried out"" This is your best comment. The rest of the paragraph is crap.

Sorry to be so harsh.......... you sound like an engineer trained to reduce everything to the linear (calculable) approximation. There is nothing there. I have a bit of mathematical talent myself..... I feel qualified to say that there is nothing in your posting.

Birth in 1944? me too, birthday May 8............

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"Yes, as I keep saying, a statistical database is badly needed."

Definitely.

"Also, forget all of this linear analysis, it just ain't there. I may be wrong about that, but I consider the burden of proof to be on others."

I am not sure what you mean with linear analysis here, anyway, as you postulate tat it is not there:

It is (at least in theory) easy to proof "there is an A with property B" directly by just showing this special A, while "there is no A with property B" cannot (at least for a very high or infinite number of A's) be proofed directly.

So you are right to put the burden of proof on others

""State of the art technology should make it possible.....""

"What "state of the art" ?? There is none. This paragraph is sheer drivle."

Ah, here you are again in the situation to proof "there is no A with property B", and I as your opponent am in the lucky position to have the possibility of a direct proof:

We feed a constant sinusodial power into the bridge of a properly setup instrument with damped strings and scan the surface of the whole body with a rotating laser device. presently available sensor devices are precise enough to measure the exact time, place and momentary amplitude of the oscillating plates at any point. Feed the results into a computer. As a professional programmer I know, that a program to generate a model of the moving plates from these input data can be written - no need to do everything from scratch, there are a lot of readymade algos available. (But it will still be hard work, of course, and take pretty an amount of time and money). The whole thing would work similar to a computer tomograph.

""(still a guess""

"Indeed;;;;;;;; hate to sound harsh, but you are just guessing (admit it)"

I do. See below.

"" I just guess (everything is a guess before actual experiments have been carried out"" This is your best comment. The rest of the paragraph is crap.

"Sorry to be so harsh.........."

No problem, but see [1]

"you sound like an engineer trained to reduce everything to the linear (calculable) approximation."

Well, I am a programmer, and my trainig is to split a large and difficult to solve problem into smaller and manageable parts. Not totally different, but also not totally the same.

"There is nothing there. I have a bit of mathematical talent myself..... I feel qualified to say that there is nothing in your posting."

This is as likely as the opposite (IMHO) - but as this is just my versus your opinion, only the results of an experiment can decide. I doubt whether a mathematical model which could deliver a definite answer exists or can be created. Maybe to describe the outcome of the experiments.

[1] "Birth in 1944? me too, birthday May 8............"

Ay, young boy birthday feb 16 - more respect for the oldies please

Seriously, as I see it everything is open, can maybe solved (to proof, that it _cannot_ be solved seems pretty hard to me, think of "there is no A with property B").

So why not give it a try?

Besides that, IMHO all these experiments at the end won't give us more than a hint about how to proceed further (or to give up because it is hopeless). But hey, I don't like the idea to give up _before_ I have a definite proof that it _is_ hopeless. I am not mad enough to think, that I can answer even just one of the questions mentioned in this thread. Just finding a new and intelligent question would be enough for me.

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I choose to answer to this paragraph separately, because I'd like to ask you, if possible, to elaborate on this one more detailled.

"Also subject to researches would be the influence of soundpost position as well as the exact power transfer from the string through the bridge to the resonance body (the degree of power matching and dampening due to the mass of and elasticity of the bridge)."

What is your comment here? Power matching through an elastic device which acts as a mechanical transformer is pretty straightforward. And the mass of the bridge _does_ dampen some frequencies, adding some ballast to the bridge _does_ change the sound of an instrument.

"I just guess (everything is a guess before actual experiments have been carried out) that the degree of power matching for various frequencies is one of the main factors for playability and response,"

And here?

Low output impedance (low amplitude, high energy) of the string and high input impedance of the body (low energy needed for a high amplitude) as well as the opposite will cause the string to transfer a small amount of it's power to the body, resulting in less dampening of the string, less resonance feedback and easier response. The more we get near a sqare, the higher the energy exchange between string and body becomes, the more the caracteristics of the body will influence the behavior of the string (by pulling power from the string and by resonance feedback). When you read this, please keep in mind that english is not my first language and I have some difficulties to express what I mean clear enough. Btw, have you ever seen a silent violin, which was _not_ easy to play in all registers?

"however, the power matching is not only a function of the bridge of course, soundpost position and properties of the top plate in the area around the bridge feet must also have some influence I think."

What about this one? Do you think the power matching does not exist? Or do you think things are more complex in that area? I'd fully agree then - as I said (maybe not clear enough) it is just _one_ of the contributing factors, not the holy grail

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Concerning the "ring" and "overtones"...

The "ring" is nothing more than the lack of overtones. The overtones are a result of the rate of decay of the base tone, and which of the frequencies between the base tone and the idle state that the violin presents well.

Concider the E string for example, since it's known for having the nasty ring that so many identify with. Both the functionality of the bridge and the areas around the f-hole will determine the response and decay of the vibration when the string is either plucked or bowed.

Tim

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Quote:

Hmmm - what then, if we leave the strings totally out ... and instead feed a pure sinusodial power into the bridge?...

During the measurements I made long ago....


Perhaps you can answer a very basic and profound question -- whether a violin is a harmonic oscillator. (The same question might be easier to answer with a piece of wood, but a complex shape may be necessary.) I think the essence of a harmonic oscillator is this: If you excite the bridge with a pure sine wave, do you get a pure sine wave with no harmonics? (I will allow you maybe the first harmonic, as you may be inadvertently bending the whole instrument at double the frequency.) If so, you have a harmonic oscillator. If not, I think it is a nonlinear system. Either way, I think the answer can tell you much about a violin.

Direct excitation of the bridge is how Martin Schleske does it, except that he uses microphones to record sound from many directions, I think in addition to studying vibrational modes directly. His method has the advantage that he can generate a fairly complete transfer function for each violin. That's about as close as you can get to complete functional characterization. In view of his results, I have to reneg on my previous, mindless agreement that the scientific approach has not achieved much.

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"Perhaps you can answer a very basic and profound question -- whether a violin is a harmonic oscillator. (The same question might be easier to answer with a piece of wood, but a complex shape may be necessary.) I think the essence of a harmonic oscillator is this: If you excite the bridge with a pure sine wave, do you get a pure sine wave with no harmonics? (I will allow you maybe the first harmonic, as you may be inadvertently bending the whole instrument at double the frequency.) If so, you have a harmonic oscillator. If not, I think it is a nonlinear system. Either way, I think the answer can tell you much about a violin."

Actually I have no answer yet, but would be surprised if it is not a nonlinear system. I plan to make this measurements in the near future, we will see what comes out..

"Direct excitation of the bridge is how Martin Schleske does it, except that he uses microphones to record sound from many directions, I think in addition to studying vibrational modes directly. His method has the advantage that he can generate a fairly complete transfer function for each violin. That's about as close as you can get to complete functional characterization. In view of his results, I have to reneg on my previous, mindless agreement that the scientific approach has not achieved much."

When I made such measurements long ago (but not with pure sinusodial waves), I used seven microfones mounted on a flat plate and fixed about 3 cm above the bridge. The mikes where placed above the center of the upper and lower left/right side, above the f holes and above the middle between bridge and fingerbord. The resulting respons curves gave some information about the places where certain frequency domains where leaving the top plate, but there was far too much crosstalking to give precise results, and the phase of the oscillating wood could not be determined. This was some 35 years ago and the technical equipment was not very advanced this time. Right now we can do a much better job

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""" It is (at least in theory) easy to proof "there is an A with property B" directly by just showing this special A, while "there is no A with property B" cannot (at least for a very high or infinite number of A's) be proofed directly.

So you are right to put the burden of proof on others

""State of the art technology should make it possible.....""

"What "state of the art" ?? There is none. This paragraph is sheer drivle."

Ah, here you are again in the situation to proof "there is no A with property B", and I as your opponent am in the lucky position to have the possibility of a direct proof: """

You have to exhaust all possibilities "A" to show that it never exists without B. That is, if B is to be shown to be importantly related to A. I agree.

By the way, the different modes of oscillation of a continuous system can be each seen as analogous to a bunch of simple harmonic oscillators. But it requires ignoring a lot of things. And also these are driven oscilators when the bow is involved. (Plucking is a different situation) I am not sure this ought to be done with a violin. the bow stick/slip oscillation is very complicated, and even may be "chaotic" in some sense. I will re-read your next postings to see if there is something to note.

If you have a direct proof of something intersting, lay it on me (please.)

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Taking the points in reverese order, I think you can disregard strings, bass-bar, post and other details of setup if you are going to speak about great violins vs. the ones that do not sell for much. The point is obvious. You cannot make a silk purse from a sow's ear. (I will admit that there is a bit of skullduggery in the violin trade with respect to provenance and authenticity. For the moment, let's assume it is legitimate.)

Mapping out nodal lines and finding normal modes is likely to be a waste of time for anything much over 1000Hz. I may be wrong, but for me, this is a working hypothesis at the time. You may be able to find a "fingerprint" signature for a violin for the purpose of identification, but I doubt you will find a strong correlation that speaks to the quality of the instrument. (Its desire to be owned by a player etc.)

Also, I think it is extreamly unlikely that the geometrical patterns of the nodal lines for a given mode will correlate with anything in a meaningful way. These are just too sensitive to small variables in materials and how they are worked. We would never have had consistently good results from certain makers if this were the case. They had no way to see these things, or even do anything that would have determined these nodal patterns in any kind of predictable way.

Finally, all of the modal considerations, with their nodal shapes and frequencies are still the linear results of the Lagrangian analysis. I expect to find little more here. A lot has to be looked into beyond this to find the subtleties. The first-order and linear models are fine to tell one how a violin should sound. They apply to all violins. The fussy-wussy types that pick and choose amongst violins (to buy) are not looking at these first-order models at all.

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I have a couple good programmers and system analysists in my family. I also feel that the computer and its algorithmes have evolved so as to make solving problems manageable in a step-wise process. But I like your attitude.

One thing that can be done with modules may be FEA, but the only problem is to know what kind of things you are looking for. It is also beyond my budget totally. One salesman returned a call after a request. He said, "for your purposes, you might be looking at $8000 for a package." I could sense right off that he thought a violin was simpler than an airplane.

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