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How does a violin reproduce overtones? - Theorizing a model


Andreas Preuss

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4 hours ago, Anders Buen said:

I do not think so. But if you put your mic under it there may be some difference. Remember the diemsnions of the ears the length of the ear canal and the enhanced sensitivity in the high frequencies.m They come from resonances in the ear canal.

The size and shape of the ear helps to indentify the direction of the incoming sound together with the brain processing. 

If a midrophone had a curved fingerboard behind it near in a free field, I am sure it will influence the resulting recorded sound and spectra. A physical object start to diffract sound from wavelength/4 in dimension and reflect fully from about a wavelentgh dimension. 15cm of fingerboard is quite clearly visible to 15cm wavelength and shorter. 

With the mic between a fingerboard and a flat surface, we have a mic in a half open pipe due to the reflections. On a violin it becomes a bit more complex due to the curved top and taper. I think it bcomes more like a half open cone focussing in two directions. We would not record anything in such an environment, and it is impossible to draw any conclusions regarding the origin of sound.

Even if the mic is outside of the fingerboard dimensions, there will still be influence from the under fb area. The sound generated there has to come out somewhere. And we can stil, «see» the underside of the fb in the top on each side near the fb.

Somehow I got your point. But…

… do you really think this effect can be perceived at 2m distance (or more)?
 

I would rather think this is something the player perceives while playing in a sort of different ‘feel’ 

if I have time tomorrow I’ll make a quick test on this. 

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6 hours ago, Anders Buen said:

I do not think so. But if you put your mic under it there may be some difference. Remember the diemsnions of the ears the length of the ear canal and the enhanced sensitivity in the high frequencies.m They come from resonances in the ear canal.

The size and shape of the ear helps to indentify the direction of the incoming sound together with the brain processing. 

If a midrophone had a curved fingerboard behind it near in a free field, I am sure it will influence the resulting recorded sound and spectra. A physical object start to diffract sound from wavelength/4 in dimension and reflect fully from about a wavelentgh dimension. 15cm of fingerboard is quite clearly visible to 15cm wavelength and shorter. 

With the mic between a fingerboard and a flat surface, we have a mic in a half open pipe due to the reflections. On a violin it becomes a bit more complex due to the curved top and taper. I think it bcomes more like a half open cone focussing in two directions. We would not record anything in such an environment, and it is impossible to draw any conclusions regarding the origin of sound.

Even if the mic is outside of the fingerboard dimensions, there will still be influence from the under fb area. The sound generated there has to come out somewhere. And we can stil, «see» the underside of the fb in the top on each side near the fb.

The book "Why You Hear What You Hear" by Eric J. Heller describes this 1/4 wave length reflection amplitude amplifying effect in his chapter 7.2 'Walls as Passive Amplifiers".  

Since the frequency f times the wave length L equals the speed of the wave length c he shows 

f< c/8d where d is the distance to the wall.

If you put into this equation a speed of sound of 343m/sec and  a distance between the bottom of the fingerboard and the top plate of 10mm or 0.01m the result is two fold an amplitude boost at 4287 Hz or less as shown below:

f = 343/(8*0.01)= 4287Hz

This 4287Hz or less frequency is right in the region of the desirable "bridge hill" of a violin's response curve.

Heller also explains that sound power is proportional to amplitude squared so the sound power is four times greater to the listener than if the wall didn't exist.

So maybe soundboard's sound reflection might help a little to the violin's sound output.

 

This reminds me of the story of a women who tried to give her just pronounced dead husband some chicken noodle soup to revive him. The doctor said it wouldn't help and she replied --"well there's no harm in trying".

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7 hours ago, Anders Buen said:

15cm of fingerboard is quite clearly visible to 15cm wavelength and shorter. 

Yes... that 15cm wavelength would see the fingerboard as a line, and go right around the sides of it.  The fingerboard width is only 4.2cm, and you'd need to be getting to around 8 kHz for the fingerboard to show up as a reflecting area.

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12 minutes ago, Don Noon said:

Yes... that 15cm wavelength would see the fingerboard as a line, and go right around the sides of it.  The fingerboard width is only 4.2cm, and you'd need to be getting to around 8 kHz for the fingerboard to show up as a reflecting area.

It will reflect from much lower frequencies than 8kHz. From around 3,4kHz at least. 

The room under the fingerboard is about 19cm long. The first resonance there between the bridge and neck heel comes at 900 Hz. The next comes at at 1800 Hz then 2,7 kHz and 3,6 kHz The neck heel end will be larger than its own surface because of the reflections from surfaces around. 
The reflection conditions are not ideal, but they cant be neglected, at least not in measurements. 

Edited by Anders Buen
More on the room and resonances under there.
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2 hours ago, Andreas Preuss said:

Somehow I got your point. But…

… do you really think this effect can be perceived at 2m distance (or more)?
 

I would rather think this is something the player perceives while playing in a sort of different ‘feel’ 

if I have time tomorrow I’ll make a quick test on this. 

I do not know. I am interested in the measurement part of this. And to advice against conculsions about  a better high frequency output from there, by using a mic under there. 

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On 7/29/2021 at 7:21 AM, Don Noon said:

Once the thickness gets into something reasonable, then the high frequencies become more mysterious and unfathomable.

12 hours ago, Andreas Preuss said:

It is really the question why. 

The answer is that it's really complicated.  We're dealing with a complex curved shell with a complex curved outline with complex curved cutouts in the middle, made out of highly anisiotropic organic material that also changes properties depending on slope and perhaps also have random natural variations.  And that's just a start.  There's more.

12 hours ago, Andreas Preuss said:

Do we really know that all stiffness properties remain the same when the violin vibrates?

That, thankfully, is one complexity I think we can rule out.  But we have plenty more to keep things mysterious and unfathomable.

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Wood properties like the elastic moduli and yield/fracture points are affected by dynamic loadings, like strain rate. However, these are significant only at high strain rates typically seen during impact and blast events.

Except for the occasional showpieces from composers like Wieniawski and Paganini, I doubt a violin will see such high strain rates. :lol:

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10 hours ago, Don Noon said:

The answer is that it's really complicated.  We're dealing with a complex curved shell with a complex curved outline with complex curved cutouts in the middle, made out of highly anisiotropic organic material that also changes properties depending on slope and perhaps also have random natural variations.  And that's just a start.  There's more.

That, thankfully, is one complexity I think we can rule out.  But we have plenty more to keep things mysterious and unfathomable.

I didn't think there was much to this.  If you make the plates too thick the violin sounds harsh.  If you make thin them too much the violin sounds tubby.  Something in-between sounds good, The only question is when call it quits while thinning the plates.

This reminds me of Kenny Rogers's song "The Gambler" 

 

 

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9 minutes ago, Marty Kasprzyk said:

If you make the plates too thick the violin sounds harsh.  If you make thin them too much the violin sounds tubby.  Something in-between sounds good, The only question is when call it quits while thinning the plates.

Things get a LOT simpler if you ignore the wood, arching, and form, and only look at thickness.

Playing top-level poker (not that I'd know) is a lot more than knowing when to hold or fold; I like: "know what to throw away, and what to keep", which applies to a lot of stuff in my shop, as well as ideas.

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10 hours ago, Don Noon said:

Things get a LOT simpler if you ignore the wood, arching, and form, and only look at thickness.

So we need four equations to figure out the four unknowns.:rolleyes:

——————————

I’d say in those parameters arching is most interesting.

We know that relatively light material is the starting point, thickness should be rather thin, form (if you meant outline)  doesn’t have so much room for changes, so only the arching is left for more thorough experimentation. 

For a really good acoustic comparison of different archings it might be interesting to change the arching of one top by pressing it into different heights and shapes. 

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9 minutes ago, Marty Kasprzyk said:

The complicated violin shape and arching are merely Baroque period fashions aren't necessarily any better sounding than simple flat sided boxes of appropriate size.

The sound quality is mostly dependent upon the skill and appearance of the player.

 

Sounds good but I doubt that it has the complexity of really good violins. I can’t imagine a top player using the cigar box violin for difficult pieces, especially if a delicate sound balance is needed. First piece which comes to mind is Schubert’s fantasy with the extreeeeemly long opening note. Or on the other hand a piece where a player needs really to attack the instrument hard needs some different type of sound and response from the instrument. 

——————

Too thick or too thin is always related to the rest of the body and now after numerous experiments I can say that a boxy sound of a ‘too thin’ top plate can be adjusted in most of the cases with the rib structure and neck angle (string angle). Latest addition in the recipe tool box is the x-shaped bass bar. (Will make a separate post on the latest development of the new concept violin soon)

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21 hours ago, Anders Buen said:

It will reflect from much lower frequencies than 8kHz. From around 3,4kHz at least. 

The room under the fingerboard is about 19cm long. The first resonance there between the bridge and neck heel comes at 900 Hz. The next comes at at 1800 Hz then 2,7 kHz and 3,6 kHz The neck heel end will be larger than its own surface because of the reflections from surfaces around. 
The reflection conditions are not ideal, but they cant be neglected, at least not in measurements. 

The room under the fingerboard is 134mm long. (Stop length is 195 mm) At the neck heel the fingerboard is 32.5mm wide and at the end 42.0mm.

Anyway, I made the experiment today I can only say that I wouldn’t have thought that i would hear any difference.

The difference was most evident when playing the violin.  It had a different sound quality and (strangely!) felt easier to play with the cardboard under the fingerboard. I would describe the difference in the sound quality as ‘denser’ or ‘richer’ compared to the violin without the cardboard under the fingerboard. 
 

i made a listening test as well and there was no difference really. We made similar listening tests with bridges and could hear differences. 

My thoughts on such things is that even if listeners can’t hear it, if players feel more comfortable with whatever change has been made on the setup of a violin, it is worth doing it. 

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18 minutes ago, Andreas Preuss said:

The room under the fingerboard is 134mm long. (Stop length is 195 mm) At the neck heel the fingerboard is 32.5mm wide and at the end 42.0mm.

I think of the distance from the neck end to the bdrige as the «room» under the fingerboard. The bridge will reflect (and produce) some sound and thus sort of bahave like a «wall» or radiating wall. Not much radiation, but some. 

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1 hour ago, Andreas Preuss said:

So we need four equations to figure out the four unknowns.:rolleyes:

Except for the fact that each of those unknowns is made up of infinite variables.

1 hour ago, Marty Kasprzyk said:

The sound quality is mostly dependent upon the skill and appearance of the player.

Still sounds like a flat box.  Watching with the sound off is better.

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1 hour ago, Marty Kasprzyk said:

The complicated violin shape and arching are merely Baroque period fashions aren't necessarily any better sounding than simple flat sided boxes of appropriate size.

The sound quality is mostly dependent upon the skill and appearance of the player.

 

SOUNDS GREAT!!!

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4 hours ago, Marty Kasprzyk said:

The complicated violin shape and arching are merely Baroque period fashions aren't necessarily any better sounding than simple flat sided boxes of appropriate size.

1) a curvy outline enhance the contrast between 'plain of plate' pliability versus 'plain of rib' stiffness.   (Physical difference)

2) coming in at the waist aids playability.

3) trapezoid and simplified violins had well publicized and examined runs in early 1800s, but not success.

4) the complicated arching and shapes as evolved support the sound well.  And have been greatly successful.

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On 7/28/2021 at 11:02 PM, Don Noon said:

 

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Looking again at this diagram. To me the black shadow at the border of the fingerboard indicates that all is vibrating in phase.

Regardless, I am thinking again about an experiment. I would glue several cross grain sticks to stiffen that area. 
 

There are some makers who extend a tongue of increased thickness from the top block. However on Strad top thickness maps nothing like this can be seen. 

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17 hours ago, Andreas Preuss said:

Looking again at this diagram. To me the black shadow at the border of the fingerboard indicates that all is vibrating in phase.

Regardless, I am thinking again about an experiment. I would glue several cross grain sticks to stiffen that area. 
 

There are some makers who extend a tongue of increased thickness from the top block. However on Strad top thickness maps nothing like this can be seen. 

So you want to stiffen an already very stiff area ?...because

"However on Strad top thickness maps nothing like this can be seen"

Because not only is the block area not extended, I don't think there are any popsicle sticks glued in those areas to cross stiffen, barring any latter repair work.

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21 minutes ago, jezzupe said:

So you want to stiffen an already very stiff area ?...because

I tried already the reverse (thinning down) and I couldn’t hear any significant changes. So my logic is to stiffen that area.

‘Already strong’ is very relative. Looking at the three points where string forces act on the body (neck heel, bridge, lower nut) the neck with its leverage force applies the strongest forces on the body. Restorers know that thickness of the top around the top block is important for the neck.

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6 hours ago, Don Noon said:

No.  In the animations, those nearby hotspots are in opposite phase... for that paricular mode.

So you are thinking of a sort of high frequency emitter which is  getting activated for any note played? And for those very high frequencies very small areas are sufficient to be heard even in a big hall. (Similar to Quarz watch beepers long ago)

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1 hour ago, Andreas Preuss said:

So you are thinking of a sort of high frequency emitter which is  getting activated for any note played? And for those very high frequencies very small areas are sufficient to be heard even in a big hall. (Similar to Quarz watch beepers long ago)

I'm thinking that the arching in the upper bout... particularly the tight crossarch... creates larger antinode patches and therefore more efficient emitters (plural).  The plate is too big to behave in one way across a wide frequency band, and will inevitably break up into a whole slew of different mode shapes at different frequencies.  I'm trying to figure out how to get the most efficient radiation across all (or many) of those mode shapes.  It's complicated, and will take many trial-and-error tests to make any headway, if it is even possible.

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4 hours ago, Andreas Preuss said:

I tried already the reverse (thinning down) and I couldn’t hear any significant changes. So my logic is to stiffen that area.

‘Already strong’ is very relative. Looking at the three points where string forces act on the body (neck heel, bridge, lower nut) the neck with its leverage force applies the strongest forces on the body. Restorers know that thickness of the top around the top block is important for the neck.

I think it's better to trust what we see in the classical examples.  Namely in the upper bout that is:

a) Comparatively wide channels.

b) Medium strong edge and lining work. (weaker than cBout area, but stronger than lower bout work)

c) Light or no bass bar extending very far into the upper bout

d) for top only, elevation of long arc sustaining partly or significantly into bout area. Meaning peaks of cross arches stay relatively high.

e) relatively thinned top plate in upper bout (perhaps patches of thinness instead of even theough bout)

 

Combined, these things leave the arched portion of the plate comparatively thinned and mobile and separated from moderately solid edges.

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fwiw my feelings are that there are 3 states of quadrant motion , the upper, the lower and the two together, while I am quite sure that both the upper and lower are actioning during dynamic states of motion that it is the lower bout that is doing most of the motion and that when we see the 3d animations that lots of the combo lower and upper motion is being primarily driven by the lower bouts motion or the upper has it's own vibration/undulation patterns but when we see the macro combination of both the upper and lower it's lower that is the main influencer of the combined motions, that being said, my intuition and the "god wants to make it "kiss" for you{keep it simple stupid} is that I started leaving my upper bouts in the top thicker, somewhat allowing the "pain in the ass"factor of how much harder it is based on its tightness to scoop out that area as compared to the bottom larger bout/lungs area, it's all most like "the god of your choosing" knows that this area is a pain, and makes it so you can be a little more slack with your graduations in that region, not as much finger plane action needed...

the end result is an upper bout that is stiffer and not so "balanced" .graduation wise, and the end result of that is that because the the upper area is more resistant to larger motion that it sends more energy/motion to the lower bout region.

frequency and vibration being somewhat like electricity that it will seek the easy way out, or water that will find the fastest way to flow , will always disperse the energy fastest and release, in the form of motion, the most in the thinner larger areas, or simply thin areas will show more motion than thick ones 

and so my suggestion is instead of adding "bracing" you may just want to work on various graduation schemes as well as the arching and the long arch in that area as it slopes to the upper block.

My opinion is that the upper 3 3/4" inches of the top bouts on both the back but primarily the top, and what you do with it there, will influence the lower bout all most as much as what you do in the lower bouts...or the top 3-4" of the violin dramatically influences the motion of the 10" below it.

Some in the past have theorized it as if the back was the tweeter and the top the woofer I think it's much more of a region thing with the upper bout being much more the tweeter {high frequency, particularly under the fingerboard and that the the lower regions are out putting the lows primarily and that "quality" of sound is the combination of the two together and that your "carving" is like adjusting the eq sliders, and that there is a gradient, and because of wood property randomness I do not think there is a "map" or repeatable process that can be done to ensure success, barring what I do which is choose arbitrary ranges of motion under flex stressing  that does create somewhat of a repeatable process that can be adjusted based on what the wood "is" 

In trying to explain to Don "hyper flapping" which I now think would be better described as "flutter" and how that influences the air motion/creates micro turbulence  right off the face of the plate surfaces.

the best way I can describe this is using another instrument {the tongue drum} and how if you hit a "tongue" hard with a rubber mallet you can literally feel the "stinging" vibration of the air motion about up to two inches off the surface of the metal "tongue" 

A violin will do similar things while being played, you can literally feel the energy disperse into the air in varying "quadrants" as low to high notes are being played.

This gets into really working with a patient violinist who is "into it" like "you" are and will allow you to hover over them while they play things at your direction as you "feel" the areas of "hyper flapping" as the dynamic states are happening in real time. 

I think Don is thinking in the right direction, and I feel that getting there will be done in a much more "feel the vibes" kinda way vs thicknessing or arching, all though very important.

the human hand is very sensitive , I feel this "mapping" for optimization across the modes can be done and that it is done by using you hand to detect air disturbance via vibration and that each note has a specific region{s} that is excited and that the "output" level, or simply how much vibration you feel in your hand, and how far away your hand is when you can detect the "vibes" has much to do with figuring out optimized carving for each group of notes and or modes of motion.

The violin does not project these vibrations into the air nearly as much as a tongue drum, but they certainly can be felt.

You can do this your self with the open notes by making sure your shoulder rest is on good so you can chin pinch it, then simply start with with the open G, play it vigorously over and over and with your left hand , about an 1/8" off the surface start feeling for these "hyperflapping" regions. I takes about 10 minutes to really go over the instrument with your left hand feeling for these areas of hyper excitation of the air directly over "that" region.

Quite simply every note will have areas that you will feel this air "sting" where as 1 inch to the left you will not feel it for example, and so instead of an exaggerated visual 3d animation you will "map" regions where you can feel the "air move" off the surface face as well as the rim edge and ribs   

It's kinda like braille in that instead of the letter G being represented by bumps here, here and here, the pitch G "air stings"{you can feel the vibration in the air directly over "that" area} here, here and here . you can also just touch the plate very very lightly and tell the differences in areas of where is really moving and where is not.

This also is directly connected to perhaps even more so with amplitude that tone, but the optimization of tone "lives" in the balance of regional amplitude blending of the various regions in concert with each other.

 

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