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Violin sound - basic questions....


EternalStudent

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I have not played a mute violin nor do I have feelings about its response.

Yes, the bridge impedance problem is of interest to me, or compliance as one wishes to call it. NO, I do not think that fine adjustments of post etc need enter into a discussion of good vs bad violins. OK, here it is,, the transverse and vertical compliance of a bridge/plucked string need not be the same. This is the origin of the analogy with the two strings of the piano tuner. It is also a sufficient model to understand the lack of sustain of a plucked violin note. Now, what can you make of that ?

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The answer is no......... The standard linear harmonic oscillator is a model for instructional purposes. It has an ideal spring (massless) and a connected mass (completely rigid.) There are two quantities in the equation of motion, the stiffness of the spring and the mass of the ...... mass. These two things are kept distinct as ideal quantities.

One can go on and take a large but finite number of ideal masses and springs and hook them all up togeather. The number of degrees of freedom is the number of masses. A langrangian solution will give that same number of independent normal modes. One advantage of the Lagrangian solution is that it is not dependent on choices of coordinant systems. This is the insight that Einstein pushed through to get himelf famous in 1905. From there, one makes a continuous transistion to media with distributed mass and springiness. In fact, this is tough in practice. Finite element analysis software takes the continuous system back to a very large number of discrete modules. They design cars and airplanes etc with this sort of software nowadays.

Each mode of a continuous sytem (infinite number of degrees of freedom, by the way) can be approximated by a single harmonic oscillator, perhaps, and for some purposes. But it is only a model. One never knows what is being thrown away in such an approximation. And one may lose the essence of one's question if too much is simplified or discarded.

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I am sure if the response of any excited body has a sine wave returned for any excitation of a sinewave (same frequency) than you have a linear system. That may or may not obtain for a violin. But for any system, I believe that the assumption is that it will be linear for sufficiently SMALL inputs and outputs.

I would not overlook the fact that a violin is prestressed either. Leave the strings on perhaps, if you wish to look at reponse mechanisms.

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I have been following this thread with a lot of interest. This type of analysis is what I do for a living with complex micro/millimeterwave electronic communication systems.(i.e. 54 Globalstar satellites in orbit) The computerized tools that I use perform taylor series expansion, fourier analysis, finite element analysis and method of moments analysis to evaluate systems. The level of complexity of the violin as a system for scientific analysis/simulation is comparable to that of an RF transmitter operating in a nonlinear region of the power curve.

The string is the oscillator generating a rounded sawtooth wave form. The signal passes into higher impedance of the bridge. This impedance mismatch reflects a portion of the incident wave that excite odd modes within the string to dampen the string and blur the fundamental. The bridge/tail filters the fundamental input and is the nonlinear impedance match between the string and the higher impedance of the top. The bridge/tail vibration transmits the fundamental at different phases for the different path lengths into the top which now acts as a nonlinear amplifier. Odd modes harmonics and intermodulation distortions are all produced. The higher impedance of the top reflects a portion of the power into the bridge thus effecting that system to produce further harmonics etc. the top nonlinearly amplifies the sound and transmits it into the lower impedance of the surrounding air. The sound post and ribs acting as separate paths that go thru the same effects as the bridge excite the back at different phases and impedances.

To isolate the string from the body from a practical sense would change the effective impedance that the string and bridge sees and alter the dynamic between the body and the string giving a false result. To sense acoustical vibrations produced by such a system and to accurately make a comparison that deembeds the body from the string is next to impossible with todays technology. A passive sense of the string would not have enough signal to noise to accurately compare the string to a body excitation as the body is providing significantly more gain in the system equation.

I will not go on as this could take years to write.

Now throw wood thickness, density, sound velocity in different wood, the curtate cycloid of the curvature of the wood, the cosine squared curvature of the the wood, the vibration of the neck imparting a feedback oscillation into the string, the effects of different size shaped cavities and the dynamic of F hole size and position on sound transmission. Reference work by Dr Hutchins and Chladni et al. If somebody had $9-10 milion I could probably get a team of 20 started on it and get back with some results in about 10 years.

Some interesting graphs that I have seen in the past was a broad band comparison of acknowledged great violins played along side that of med and poor violins and there was a noticeable difference. Also don't forget that the ear is a filter. What a microphone picks up and shows on a graph is not filtered and thus different is not always better or worse.

Some things are best understood on the macro level and left to learning from example and experience of an artist.

I will still try to tap tune my plates though. Also don't forget the ear is a filter and the microphone is not. what shows up on graph paper may not be significant in sounding better.

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You imply that you are attempting to save others from false input by correcting whatever appears to be incorrect in what they write. However, I wonder if your brash approach may often have a negative effect. If you just leave what others say alone and give your input (a lot of which I find quite useful and accurate), then people may most likely be able to decide for themselves which is correct or at least believable. Anyone who is really interested in any of this is going to do their own research anyhow, based on the ideas presented.

When criticizing others, you should also give thought to your own approach. Having intellect isn't a matter of rattling off a bunch of stuff that means nothing to those you refer to as "lowly craftsmen" but actually lies in the ability to present your theories and facts in such a way that it can be understood by anybody.

In criticizing your approach, I kind of feel like I may be eating some of my own words, but it's not in hopes of now attempting to save others from you, but in hopes that everyone who attempts to give input remains ambitious enough to do so because I learn a great deal from just about everybody here. Someone may have a great deal of worthwhile information to input in a particular area of conversation and may at times venture into unchartered waters and ramble on about something they only know a little about but sometimes criticizing them too harshly for having done so may embarrass them in such a way that they become less likely to offer their input elsewhere where it can be quite valuable.

Tim

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You are right...... I think I do feel that way. It is completely irrational. I started with what I thought would be a very good thing to think about. It got little meaningful attention. I have to guess that means something about what interests people. Glad to discuss anything by email.

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I think you have accurately summarized the complexity of understanding everything, and the importance of paying attention to the art. I think everyone is agreed on the hopelessness of trying to understand everything, especially given the inhomogeneity and uniqueness of each piece of wood. But do we really need to understand everything to have any useful results? Or is it possible to focus on small problems that really can be answered and that have a likely payoff?

I think we already have some examples of useful results, in spite of rather paltry serious effort. You yourself cited significant differences in the spectra of great and ordinary violins. I suspect that Martin Schleske's results on the transfer functions and modal analysis of great violins are extremely significant even if they are not published. His claims to have made tonal copies* of great violins appears to be credible. Michael also cited some proprietary work on varnish, which may or may not be productive. Barlow's work on varnish is published and provocative. I understand that it has been challenged informally in discussion groups. But are the results right or wrong? This is a question that should be answerable. Finally, we have all the backyard attempts to play in a violin mechanically. I can't see any barrier whatsoever to doing this properly. Joseph Curtin's work on the bridge stands out as a useful mixture of observation and scientific insight.

============

* The fact that neither he nor anyone else can make an exact tonal copy is immaterial. Just making a violin with similar tone and similar quality is all that is required, since there has never been a maker who can even make an exact tonal copy of his own violins.

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I think we strayed a little from the original thread.

I encourage EternalStudent to pursue all endeavors in analysis of the violin. More will be learned in the pursuit than can be imagined, no matter what the outcome.

Q1) difficult to do to the level of acuracy needed to be able to draw conclusions with microphones. Signal to noise of current sensors not up to the task. laser sensors are accurate but lasers are usually limited to a single point. The string alone does not project much sound at all. Kind of like a tuning fork. Quiet until you touch the handle to a table top that amplifies its signal.

Q2) there are several papers published on this subject and much can be learned from listening,seeing,feeling the great instruments and comparing to what one has hand crafted. How about a phased array of microphones that completely surround the violin and measure the phase and amplitude output of the violins.

Q3)From what I have read, Chladni patterns provide some pertinent information but do not give the whole picture. there is still room for work. As was suggested, how about a chladni patterning of the entire instrument using laser tomography/interferometry. Sounds like a good idea. It needs to incorporate a demodulator to decode to amplitude and phase of the vibrating body at each point of measurement. Oh and while you are at it. Set the tomograph at 0.001" accuracy and sweep the entire Strad. That way we can make ABS plastic duplicates to sell as models for violinmakers to measure. 100% gross margin and Split the profit 50/50

Good Luck Please report results. I am fascinated by such endeavors. Good or bad. Often, more is learned from a mistake.

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I think the "juke-box" playing violin you made reference to might be the "Adrianola". It was invented & manufactured by a Mr. Adrian- I don't recall his first name. He had two or three different models in his tavern, "Adrian's Indian Echos", near Montello, Wisconsin, which also housed his extensive native American artifact collection. I remember playing the machines in the '60's. they were definitely "juke-boxey". Ron.

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"I think we strayed a little from the original thread.

I encourage EternalStudent to pursue all endeavors in analysis of the violin. More will be learned in the pursuit than can be imagined, no matter what the outcome."

Thank you. The first step, as I see it, is, to collect data, thereby being very careful to get, as far as possible, only data about the area of interest and not to jump to conclusions.

"Q1) difficult to do to the level of acuracy needed to be able to draw conclusions with microphones. Signal to noise of current sensors not up to the task."

Fully agreed.

"laser sensors are accurate but lasers are usually limited to a single point. The string alone does not project much sound at all. Kind of like a tuning fork. Quiet until you touch the handle to a table top that amplifies its signal."

I thought about sensing the string where it touches the bridge. Piezoelectric sensors might do the job. A rather "primitive" method could also be to mount tiny cylindric reflecting pieces to the bridge, point a very thin laser beam at them, and guide the beam over a rotating mirror to a screen. This could even make it possible to isolate the horizontal, vertical and longitudinal components of the oscillation. Just an idea out of the back of my head. A continuously excited string could as well be sensed optical using a light source above and a v - shaped mask and fototransistor below the string. moving the mask up the string will give the amplitude and phase at each point of the string. Just ideas. Do you see any pitfalls?

"Q2) there are several papers published on this subject and much can be learned from listening,seeing,feeling the great instruments and comparing to what one has hand crafted."

I have seen some of them, and studying at least the most important will of course be "conditio sine qua non" before starting any investigation. I am thinking, among others, of the formant theory and analysis. If I remember correctly I have read somewhere, that one of the properties of good violin sound is, that the colour has a lot of the vowel "i"(like in "bee") opposite to "e" (the german pronounciation). But that is just one facette of a very complex subject. A lot of reading to do before any further work.

"How about a phased array of microphones that completely surround the violin and measure the phase and amplitude output of the violins."

That was basically what I did many years ago, at least over the top of the violin. The problem here is the acoustical "decoupling" of the mikes, they should receive only the sound emitted from the point exactly below them. Also the distance between the mike and the point it should measure is important, because, given the short wavelengths at high frequencies, differences of 1 cm will cause considerable phase shifts. But this is just a minor problem.

"Q3)From what I have read, Chladni patterns provide some pertinent information but do not give the whole picture. there is still room for work. As was suggested, how about a chladni patterning of the entire instrument using laser tomography/interferometry."

Here I did not that much think of Chladni patterns, the intention was to get a model of the motions of the different areas of the body relative to each other. Chladni patterns tell us, where the knots are, but nothing about the phase of the areas between the knots (whether they are up or down at a certain time), and therefore nothing about how the oscillation proceeds through the instrument. Of course Chladni patterns will also be one of the results of that experiment.

"Sounds like a good idea. It needs to incorporate a demodulator to decode to amplitude and phase of the vibrating body at each point of measurement."

That is a pure technical point (but a pretty difficult one). As soon as the problem of moving the laser precise enough, sensing the reflected laser beam properly and transferring the data to a computer in real time is solved, the rest is software - difficult to write, but there are partial solutions (libraries) available.

"Oh and while you are at it. Set the tomograph at 0.001" accuracy and sweep the entire Strad. That way we can make ABS plastic duplicates to sell as models for violinmakers to measure. 100% gross margin and Split the profit 50/50 "

Definitely cool, I could use the money very well, for Michaels Cannone copy and a mini cooper (in that order)

Seriously, I would not want this. We could even go farther, feed the data into an NC - machine and produce at least the main parts of our Strad and Del Gesu copies, but that wold be facsimiles compared to the artwork which comes out when a good violin maker builds an instrument "after the pattern" of a Strad or Del Gesu.

"Good Luck Please report results. I am fascinated by such endeavors. Good or bad. Often, more is learned from a mistake."

Thank you. I will. Report. And make lots of mistakes.

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"The level of complexity of the violin as a system for scientific analysis/simulation is comparable to that of an RF transmitter operating in a nonlinear region of the power curve."

I think so.

"The string is the oscillator generating a rounded sawtooth wave form. The signal passes into higher impedance of the bridge. This impedance mismatch reflects a portion of the incident wave that excite odd modes within the string to dampen the string and blur the fundamental. The bridge/tail filters the fundamental input and is the nonlinear impedance match between the string and the higher impedance of the top. The bridge/tail vibration transmits the fundamental at different phases for the different path lengths into the top which now acts as a nonlinear amplifier. Odd modes harmonics and intermodulation distortions are all produced. The higher impedance of the top reflects a portion of the power into the bridge thus effecting that system to produce further harmonics etc. the top nonlinearly amplifies the sound and transmits it into the lower impedance of the surrounding air. The sound post and ribs acting as separate paths that go thru the same effects as the bridge excite the back at different phases and impedances."

That is about how I see it. Out of the top of my head I am not sure about the "lower" and "higher" of the impedances, but I think that does not matter for the moment.

"To isolate the string from the body from a practical sense would change the effective impedance that the string and bridge sees and alter the dynamic between the body and the string giving a false result. To sense acoustical vibrations produced by such a system and to accurately make a comparison that deembeds the body from the string is next to impossible with todays technology."

I see that now. jmasters suggested to leave the string completely out and excite the bridge directly (Instrument strung up but strings dampened). Generally my intention is to get information about how the violin works at kind of a macro level by systematiyally changng one parameter keeping the others constant. This may be a silly idea, but I can't think of a better way right now. A mathematical model would com much much later (if ever).

"A passive sense of the string would not have enough signal to noise to accurately compare the string to a body excitation as the body is providing significantly more gain in the system equation."

I beg to slightly disagree here. There are possibilities to sense the string optically. Please see my response to violinmark (the light source and v-shaped mask approach). But again I may be completely wrong or the result won't tell us anything.

I will not go on as this could take years to write.

"Now throw wood thickness, density, sound velocity in different wood, the curtate cycloid of the curvature of the wood, the cosine squared curvature of the the wood, the vibration of the neck imparting a feedback oscillation into the string, the effects of different size shaped cavities and the dynamic of F hole size and position on sound transmission. Reference work by Dr Hutchins and Chladni et al. If somebody had $9-10 milion I could probably get a team of 20 started on it and get back with some results in about 10 years."

Give me an unlimited budget and ten years, and I will give you a receipt?

Seriously, I think you are right if you go down into detail as deep as yor excellent analysis above suggests. Staying at kind of a mid-level and do empirical research might give some results earlier, not that detailed, possibly inaccurate and impossible to model mathematically, but maybe sufficient to ask better questions.

"Some interesting graphs that I have seen in the past was a broad band comparison of acknowledged great violins played along side that of med and poor violins and there was a noticeable difference. Also don't forget that the ear is a filter. What a microphone picks up and shows on a graph is not filtered and thus different is not always better or worse."

Agreed again. Just one point: what a mike picks up is what _reaches_ the ear, of course not, what the ear makes out of it and even less, what the brain makes out of the input from the ear. We can of course not include this filtering and interpretation in our research, there are no two human ears and brains in the world, which filter in exactly the same way I think.

"Some things are best understood on the macro level and left to learning from example and experience of an artist."

I'd just like to throw in the "mid level" I mentioned above.

"I will still try to tap tune my plates though. Also don't forget the ear is a filter and the microphone is not. what shows up on graph paper may not be significant in sounding better."

See above. We can only measure what reaches the ear, not what the ear makes out of it. But I think we can safely assume, that the same ear and brain reacts in the same way when the same acoustical signal reaches the ear. (All other parameters kept as constant as possible)

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"" A rather "primitive" method could also be to mount tiny cylindric reflecting pieces to the bridge, point a very thin laser beam at them, and guide the beam over a rotating mirror to a screen. This could even make it possible to isolate the horizontal, vertical and longitudinal components of the oscillation. Just an idea out of the back of my head. A continuously excited string could as well be sensed optical using a light source above and a v - shaped mask and fototransistor below the string. moving the mask up the string will give the amplitude and phase at each point of the string. Just ideas. Do you see any pitfalls? ""

Pardon my barging in. I am not following carefully what it is you are measuring. However, there is nothing primitive in bouncing a light beam from a mirror and measuring the output. When a graduate student, we did not use laser light sources, but there were "choppers". These were simply wheels with a few notches to pass the beam. They were on a motor shaft so that the light source would come in pulses at a given frequency. The desired signal was then detected with a "phase-locked amplifier" I think it was called. You can see the advantage. One looked only for the signal that was periodic in the same sense as the original light beam. Signal to noise was helped a great deal.

I suppose that today with cheap computers, one could sort out the phase-locked signals that way. Phase-locked amplifiers were interesting things though. Rather expensive boxes of expensive hardware.

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