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How does a violin reproduce overtones? - Theorizing a model


Andreas Preuss

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Uncle Juke wrote "do you believe mathematics was used in the development of the violin?"  No, I do not think mathematic as it come to calculating, algebra. But well mathematic based on geometry. That kind of mathematic at the time of Amati was science. Many structure are based on geometry and I believe I have found a very simple 2D to 3D solution with no calculation necessary, just constructing. I also belive the person how once made this geometric construction new what he was doing and what he could expect producing.

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1 hour ago, reguz said:

Uncle Juke wrote "do you believe mathematics was used in the development of the violin?"  No, I do not think mathematic as it come to calculating, algebra. But well mathematic based on geometry. That kind of mathematic at the time of Amati was science. Many structure are based on geometry and I believe I have found a very simple 2D to 3D solution with no calculation necessary, just constructing. I also belive the person how once made this geometric construction new what he was doing and what he could expect producing.

  Do you consider yourself more of an artist or more of a carpenter/craftsman? 

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9 hours ago, Marty Kasprzyk said:

Yes lightness is really good for increasing sound output but the limitation is the emergence of bad wolf notes. 

So far I didn't have any major problems with wolf notes. I had only some notes which were a little woolfy. Makes me wonder if the frame can control wolf notes to a certain degree.

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8 hours ago, David Beard said:

Vibration itself isn't loss.  It's dampening in to heat that is loss, and radiation of as sound also.

Most vibrations, like the neck, will  cycling through the instrument until dissipated as either sound/noise radition or heat. I can't think of any other dissipations for a violin.

But it is using energy where it DOES NOT produce sound even if it is not lost. If energy loss equals only friction, I don't know what it is all about anyway. Too complicated with no benefits.

Anyway, those abstract calculations tell me only that if I can alter the assumed 4 percent to 5 I have an increase of 25% which is a lot.

I remember quite well, when my father, a physicist, bought the book read it page by page. When I looked into it I saw only those Einsteinian formulas and thought 'Forget it!' A little later my dad was scribbling with pencil things in the book and when I asked him what he is doing he got into a small rant what Cremer is all wrong about. 

I rather spend my free time to sharpen chisels for my next experiment and maybe I have a good idea...

 

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I think it is a common trait for sound sources that they are not very efficient at producing sound when you look at the mechanical energy involved and the energy dissipated through sound. This applies to engines, impact hammers, or any source really. I think it applies to loudspeakers as well. They probaly radiate more power as heat than sound.

I think the reference sound power level is 10^-12 W. The sound power level goes as 20log(Wsource/Wref). To get say 100 dB sound power the Wsource is only 10^(-12)*10^5 W = 10^-7 W. So when somebody bragg about their 1000 W sound system you can smile and tell them that only a very small fraction of that becomes sound.

Edited by Anders Buen
Corrected and updated the calculations
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16 minutes ago, Andreas Preuss said:

What does this explain in simple words?

The amplitude of the bowed string fundamental, and sucessive harmonics above that with no influence from the body nor the bridge, just the signal in to the bridge. Essentially a sawtooth signal. 

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As a comparison on energies and sound. A very strong sound source in construction work are different kinds of impact hammers, either hand held for the smaller ones, typically less than 60 kg, or held by a machine for the bigger ones 0,1t to 10 t or even more. Essentially they do the same thing as hammering stone to break it, it is done by an engine and a bigger more efficient tool. 

I have made a collection of data for these and they produce more noise the heavier they are, and some other characteristics more interesting for the nerds. The data for them does also include hydraulic pressure and flow. It is thus possible to estimate the mechanical power they require. And they do sometimes come with a sound power level marking, LwA = 115 dB or something like that. (A violin is about 95 dBA for comarison, but it varies :-))

If I compare the required power to drive these tools with the noise they produce, the relation is about 0,1% noise energy in relation to the work and power they use. The highest number I have is 2,1% noise in relation to the mechanical power they use, (possibly a miscalculation or something wrong with the input data). 

So a violin is a pretty much more efficient sound producer than a pigghammer, or jackhammer, or whatever you call them, at its 4% maximum.

Edited by Anders Buen
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40 minutes ago, Andreas Preuss said:

What does this explain in simple words?

The bowed string produces a sawtooth wave.  You can hear one through your computer's speaker at  https://onlinetonegenerator.com

If your speaker is lousy with lots of big resonance peaks and deep valleys in its frequency response curve you might get a sound like a violin's.  If your speaker is really bad it might sound like a Strad.

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31 minutes ago, reguz said:

Uncle Duke You wrote "Do you consider yourself more of an artist or more of a carpenter/craftsman?". 

It seem to me obvious that you did not read any of my papers on the internet. What is your profession?

I don't know how to read let alone be able to figure out if you even know how to sharpen plane and chisel blades.  What about cleaning paint brushes?

I am a semi-retired house painter thinking about what else is there to do in life.  

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11 hours ago, Marty Kasprzyk said:

Yes lightness is really good for increasing sound output but the limitation is the emergence of bad wolf notes. 

There is also the problem of low impedance.  Energy gets sucked out of the string too quickly, making it harder to start up string motion.  Then you need to add speed and pressure to the bow, and when it DOES start up, it's too loud.  And to keep the string going, you need more bow speed, and you run out of bow length.

Very light violins play differently, but not in a good way.

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46 minutes ago, Marty Kasprzyk said:

The bowed string produces a sawtooth wave.  You can hear one through your computer's speaker at  https://onlinetonegenerator.com

If your speaker is lousy with lots of big resonance peaks and deep valleys in its frequency response curve you might get a sound like a violin's.  If your speaker is really bad it might sound like a Strad.

:P The funniest description of 'Strads secret' I ever read.

I was sometimes thinking that certain characteristics high class players notice on famed instruments are nothing else than systematic imperfections when they were built.

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1 hour ago, Don Noon said:

There is also the problem of low impedance.  Energy gets sucked out of the string too quickly, making it harder to start up string motion.  Then you need to add speed and pressure to the bow, and when it DOES start up, it's too loud.  And to keep the string going, you need more bow speed, and you run out of bow length.

Very light violins play differently, but not in a good way.

From my experiments with the new concept super light vioIin can only say that when it was in its initial stage with all parts too thin and too wobbly, the description fits pretty well except that adding speed and bow pressure couldn't change anything. (at least with my bowing technique)

Major changes came basically all from altering the stiffness and dimension of the ribs. I believe that at its best stage there was a tendency of what you are describing, but I see this when available to the player in a small dose as a sort of non plus ultra, because it enables the player to have unlimited ways of modifying the sound. They learn as well to find instinctively the right contact point on the string for a given bow speed and pressure to get the maximum out. 

Accordingly, at its best stage, the new concept violin had still a little too much of this effect. Weight was with a heavy back around 330g which is still much lighter than a normal violin. 

Again, my unscientific guess goes into looking more at the cross stiffness which I see as the main factor for this phenomen. If the total of  cross stiffness on the body and the top in particular is too weak, energy gets sucked out faster than the player can feed.

In this context I see the problem with thin top plates that the cross grain stiffness seems to drop at much higher rate than the stiffness along the grain when going from thin to thinner. I think at the tinning down process of the top there is one exact point where the player feels that he can control everything. All starts with building a functioning membrane.

Addition:

I see weight only as the necessary evil for getting stiffness. So good material with high stiffness and low weight helps a lot. 

 

Edited by Andreas Preuss
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1 hour ago, Marty Kasprzyk said:

If your speaker is really bad it might sound like a Strad.

240 - 6000 Hz +/- 18dB sure wouldn't knock the socks off of any audiophiles, but that's about where most violins fall.  It's the details of the peaks and dips (and some other things)  that make the difference between great and crap.

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4 hours ago, Andreas Preuss said:

But it is using energy where it DOES NOT produce sound even if it is not lost. If energy loss equals only friction, I don't know what it is all about anyway. Too complicated with no benefits.

Anyway, those abstract calculations tell me only that if I can alter the assumed 4 percent to 5 I have an increase of 25% which is a lot.

I remember quite well, when my father, a physicist, bought the book read it page by page. When I looked into it I saw only those Einsteinian formulas and thought 'Forget it!' A little later my dad was scribbling with pencil things in the book and when I asked him what he is doing he got into a small rant what Cremer is all wrong about. 

I rather spend my free time to sharpen chisels for my next experiment and maybe I have a good idea...

 

An active vibration or standing wave isn't 'using up' that energy.  Think of it as storing the energy.

From the storage in a resonance, the energy can: 1) linger, 2) go back to the instrument or another resonance, 3) radiate as sound, 4) plastically deform something, or 5) dissipate as heat.

Only the last three of those actually lose energy from the system.

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One more aspect we don't commonly discuss: capacitance and time lag.

The violin is an energy transducer.  The resonances of the masses hold energy for a while, and have 'capacitance'.

Capacitance takes time both to fill and to empty.

These are real aspects of violin behavior.

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14 minutes ago, David Beard said:

One more aspect we don't commonly discuss: capacitance and time lag.

The violin is an energy transducer.  The resonances of the masses hold energy for a while, and have 'capacitance'.

Capacitance takes time both to fill and to empty.

These are real aspects of violin behavior.

Agreed! An example is the strings. Sometimes you can hear other strings than the played one rings. The strings are reverberant, more than the body. The tailpiece can also ring, although it usually is difficult to hear. But it can influence the dynamics around the bridge. 

I have very light tailpieces fastened with new silver thread. A harder metal alloy than pure silver. With a high tuned hardangerfiddle, the open G can lie close to a torsional mode in the tailpiece which sucks energy off the string making it die out unnaturally fast while plucking. The energy also move back and forth between the string and tailpiece, a typical effect of weakly coupled modes. Wit a magnet on one wing of the tailpice the situation improves. 

It is possible to calculate the structural decay time of a mode if you know the width of the resonance at half power and the resonance frequency. 

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16 hours ago, Andreas Preuss said:

That's what I am more and more thinking about. Try to imagine the top of a violin as a drumskin. So the lighter and thinner the better. But this requires alterations to the rest of the body. I think building a rigid frame around the top plate to make it work acoustically confirms this idea pretty well. 

Isn't this what Christian is doing here?

117318309_christianbayon.thumb.JPG.5245d0b82952e6868df8c99a755fe872.JPG

 

 

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5 hours ago, David Beard said:

An active vibration or standing wave isn't 'using up' that energy.  Think of it as storing the energy. or 5) dissipate as heat.

Only the last three of those actually lose energy from the system.

Is ot possible the energy simply permeates through the wood and varnish to the outside surface.  Things seem to be better after the violin has warmed up to at least the human body temperature.

Side note - long ago, I was told that air can actually go through concrete - that gave me the thought for the above comment.

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18 minutes ago, uncle duke said:

Is ot possible the energy simply permeates through the wood and varnish to the outside surface.  Things seem to be better after the violin has warmed up to at least the human body temperature.

Side note - long ago, I was told that air can actually go through concrete - that gave me the thought for the above comment.

1) as heat, or 2) as vibration leaving the instrument as sound.

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