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How does a violin reproduce overtones? - Theorizing a model


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13 hours ago, Andreas Preuss said:

I ignore facts which claim things I can’t verify in experiments in an audible way. I always need to hear something. So on the other hand, even if I get a completely different graph and don’t hear anything it’s just telling me don’t go further. In the end I only need recipes which work. I leave the explanation to those who have the knowledge. 

Remember, the Northern Italians already ran a continous series of these trail and evaluation experiments, for over 5 centuries.  They carried this on from late medieval times until the early phases of the industrial revolution disrupted the continuity of their making tradition.  

Across countless iterations of bowed and plucked lute type stringed instruments, they explored differing choice in the making, and evaluated results the way you describe.  Not by knowing why something they tried worked, but by deciding if it work. By judging results by eye and ear rather than good or bad theory.

And, they essentially encoded their learning in traditions of preferred geometry and proportion choices.

All of their centuries of collective learning informed the violin, leading to its peak of success in the preferred traditional geometry choices of late Cremona makers like Strad and Del Gesu.

 

Like others, I also enjoy enjoy trying to understand why violins behave as they do.  But this is a very separate curiousity from seeking to know how to build good violins.

Consider some of the more definite experimental results from this thread.  We have for example the concrete results that both a too thick top and a too light treatment of linings/edges are bad.   But the examples of the old masters already told us not to do those things.

Scratching the itch to understand is one thing.  But to improve our making, it's probably much more efficient to focus on learning the ways of the old masters.  Their traditions of structured geometry choices embed over 5 centuries of collective learning from trial and aesthetic evaluation tinkering and exploring.

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21 hours ago, Andreas Preuss said:

No matter how I look on the whole problem, the key to a projecting sound is the ‘singer Formant’ region of the sound spectrum. (The other day I read a paper which examined the ‘sound power’ of Swedish tenor Jussi Bjorling. And well, his peak sound output was at 2800Hz and his voice trained to add to each sung note high frequencies in that region) 

In this context I was wondering if it would help to filter in a recording setup all frequencies which are not thought to be important .

On the other hand, if I look on the spectrum of one played note I should be able to see somewhere which overtones are strongest?

In terms of instrument making it seems that this is all in the strength and width of the bridge hill resonance. While some adjustments apparently can be made on the bridge itself, the cross stiffness of the top is of major interest. Did anyone ever try to increase the top cross stiffness with additional bars to see how the spectrum changes? My unscientific guess is that this would work best at the narrowest part of the plate between the c bouts. 

I agree that the "singers formant" is important. But it does not work well without proper stength of the fundamentals. A small violin may have plenty of the high frequency projecting sound, but will lack power. A singer with weak fundamentals and strong singers formant will sound somewhat like a "throut singer". A powerful and projecting violin need both. The same for a singer for large stages. Go back to the literature and get the whole picture. 

I think you can play with this both using filters in plugins for Audacity or in real life. Pick a children size violin for the test of lacking fundamentals or fill its f-holes with cotton.

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5 hours ago, Don Noon said:

Basically, everything blanked out by the fingerboard, which is more than your diagram.  This is a mode at ~3000 Hz, and shows there's something significant going on under the fingerboard.  I'd like to see the details.

98990704_3khztitian.jpg.f9aba49aceb813d2585beb197185b3b7.jpg

Marty,  I don't see how you can attribute a preference to A0 alone, as it is a function of construction features which may (and I would say probably are) creating other tonal effects which are preferred.  Most notably, I see that lighter tops appear to be even more strongly correlated to preference, and presumably lower A0 is inversely correlated with plate weights... thus lighter plates might be the driver for preference, and lower A0 just a meaningless side effect.

I think it is notable that the highest preference went to the viola with the 2nd lightest plate, but was also among the highest A0 frequencies.

 

There is no reason for more sound output under the fingerboard. However, there is a room between the top and the fingerboard, as well as between the bridge and the neck heel. There may build up resonances that appear as stronger sound radiation. Difficult to predict in detail, but the first axial resonance comes at 343/(2L) where the L is the distance between parallell surfaces.

There are formulas for oblique resonances which may be related. The traveled path for the wave should meet the reflected one in phase to get a resonance. If they meet in antiphase, a weak spot will appear. Resonances appear for every whole number times the fundamental. 

E.g. the first mode between the neck heel and bridge comes at 900 Hz. The next one at 1800Hz and the third at about 2707 Hz in the region of interest. 

I have never seen anything on this before, it is an idea to explore. We do have an acoustic camera at work where such things might be able to be be investigated. I need a helper though, not easy in this summer holiday times.

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2 hours ago, David Beard said:

Remember, the Northern Italians already ran a continous series of these trail and evaluation experiments, for over 5 centuries.

Yes, but I would say it is a bit audacious to think that ALL trial and error was for the purpose of sound (let alone our obsession of ‘projection’)

In my view Stradivari was the one who redefined something fundamentally in this tradition which made his instruments outstanding. Any reports from musicians make the comparison between Stainer and Strad and describe Strads instruments as low arched creating a ‘powerful’ sound (whatever this meant in the 18th century)

Ihave some doubts that this can be explained on a purely geometry design driven level. What I rather see is that Strad changed materials and size of linings and apparently figured out that top weight DOES matter in combination with the right material. Last not least trial and error based arch design is certainly much easier when always working with wood from the same tree.

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On 7/27/2021 at 6:48 PM, Peter K-G said:

At this time of the year I always take some measurments of my close copy violins (high RH) comparing to previous years.

Modes and overtones change as predicted, but one of them with lesser performance wood is always dull with much less overtones in summertime, than the other ones (they loose some strength in overtones too, but not as much)

I think the wood has more influence than the other factors.

 

 

17 hours ago, Andreas Preuss said:

Which area do you mean precisely? The tightest curve of the arching is in area where you can see it, just above the ff. (red) 

if you are thinking more of the area marked in green the arching can be pretty flat already depending of how much arch height reduction you allow from the highest point. 652ECFFB-F370-4C7B-88F2-B74EE2FCFC36.thumb.jpeg.9fef1c5788dd384261e86d54fbc54a8b.jpeg

if it is the latter you can almost think of arch deformation as a cause(so in the end it is related to forces and stress) which deform a perfect circle segment line length arch into a an arched flattened under the bridge and bulging up under the fingerboard and tailpiece. 
 

But no matter what you do with wood, I think that all receipes based on some sort of calculations are short of the optimum. I am rather looking for something where (exaggeratedly saying) the string force can deform the entire structure to its best sounding properties. Repeated wetting is nothing I am trying to avoid.

 

8 hours ago, Don Noon said:

Basically, everything blanked out by the fingerboard, which is more than your diagram.  This is a mode at ~3000 Hz, and shows there's something significant going on under the fingerboard.  I'd like to see the details.

98990704_3khztitian.jpg.f9aba49aceb813d2585beb197185b3b7.jpg

Marty,  I don't see how you can attribute a preference to A0 alone, as it is a function of construction features which may (and I would say probably are) creating other tonal effects which are preferred.  Most notably, I see that lighter tops appear to be even more strongly correlated to preference, and presumably lower A0 is inversely correlated with plate weights... thus lighter plates might be the driver for preference, and lower A0 just a meaningless side effect.

I think it is notable that the highest preference went to the viola with the 2nd lightest plate, but was also among the highest A0 frequencies.

 

 

2 hours ago, Anders Buen said:

There is no reason for more sound output under the fingerboard. However, there is a room between the top and the fingerboard, as well as between the bridge and the neck heel. There may build up resonances that appear as stronger sound radiation. Difficult to predict in detail, but the first axial resonance comes at 343/(2L) where the L is the distance between parallell surfaces.

There are formulas for oblique resonances which may be related. The traveled path for the wave should meet the reflected one in phase to get a resonance. If they meet in antiphase, a weak spot will appear. Resonances appear for every whole number times the fundamental. 

E.g. the first mode between the neck heel and bridge comes at 900 Hz. The next one at 1800Hz and the third at about 2707 Hz in the region of interest. 

I have never seen anything on this before, it is an idea to explore. We do have an acoustic camera at work where such things might be able to be be investigated. I need a helper though, not easy in this summer holiday times.

WOOD

(And violins made to what wood you have)

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4 minutes ago, Andreas Preuss said:

Yes, but I would say it is a bit audacious to think that ALL trial and error was for the purpose of sound (let alone our obsession of ‘projection’)

In my view Stradivari was the one who redefined something fundamentally in this tradition which made his instruments outstanding. Any reports from musicians make the comparison between Stainer and Strad and describe Strads instruments as low arched creating a ‘powerful’ sound (whatever this meant in the 18th century)

Ihave some doubts that this can be explained on a purely geometry design driven level. What I rather see is that Strad changed materials and size of linings and apparently figured out that top weight DOES matter in combination with the right material. Last not least trial and error based arch design is certainly much easier when always working with wood from the same tree.

The essence of their cultural evolution and success is that none of them started over.  They all stuck to tinker with different combinations of traditional choices, reuses of traditional choices, and occasionally small extensions.

It was a VERY conservative process.  

With the geometry choices, we have the advantage of being able to see them fairly directly and completely.  And you can look at their choices and compare from instrument to instrument.  Stradivari wasn't some renegade reworking the system. He mostly made just slightly different combinations of the same choices you can observe being used in other earlier making.  He did quite a bit of returning to Andrea Amati.  Much more than being innovative, he was just probing and effective.

As with the evaluations and directions of exploration, I agree isn't wasn't all just sound/playing evaluation.  Strad particular seem to explore refinements of choice aiming for the visual.

But also, it seems they pursued 'notions' to some extent.  This is very clearly evident in Del Gesu foe instance.  He for example pursued elongating the extension of the soundhole shape above and below the eyes.  And, as you pointed out, Strad pursued flatter top arches rather more than had been done.

 

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2 hours ago, Anders Buen said:
On 7/28/2021 at 7:12 AM, Andreas Preuss said:

I agree that the "singers formant" is important. But it does not work well without proper stength of the fundamentals.

No objection.

Just from the standpoint of making it is much more difficult to trigger high frequency range and amplitudes than doing things for the fundamentals. And, IMO, a miraculous constellation of signature modes and their amplitudes does not influence in any measurable way the high frequencies. 
 

(this was more or less my motivation to create this thread  and exchange ideas and viewpoints)

 

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3 hours ago, Anders Buen said:

There is no reason for more sound output under the fingerboard.

I think there may be... we just don't understand it yet.  I think it is pretty clear from close listening to a voice-coil driven body that there is a lot of high frequency sound coming from the upper bout.

3 hours ago, Anders Buen said:

There may build up resonances that appear as stronger sound radiation. Difficult to predict in detail, but the first axial resonance comes at 343/(2L) where the L is the distance between parallell surfaces.

This is an internal air resonance idea, which might not be obvious to others.  I drilled a number of small holes in the back plate of a violin, just big enough for a small microphone, to check for this.  I could not find any evidence of such a resonance, even though it seemed like a good idea.  Ribs too, to check for lateral resonances.  Nada.

A0, for sure matters.  A1 can be measured, but doesn't seem to do a lot.  Above that, I don't see much evidence.

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12 hours ago, Don Noon said:

This is a mode at ~3000 Hz, and shows there's something significant going on under the fingerboard.  I'd like to see the details.

What ‘scenarios’ could be interesting? Invisible nodal lines?
In any case I would assume that the bass bar in that area makes the whole area vibrate in phase.

Otherwise, if the violin was excited at 3000Hz does this apply for lower notes as well? My understanding is that each body resonance stands for itself. 

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4 minutes ago, Andreas Preuss said:

1) In any case I would assume that the bass bar in that area makes the whole area vibrate in phase.

2) Otherwise, if the violin was excited at 3000Hz does this apply for lower notes as well? My understanding is that each body resonance stands for itself. 

1) I am confident that you assume incorrectly, and that is what is interesting... exactly where and how the plate actually vibrates.

2)  ?  Yes, each resonance is its own thing... but I have no clue what you mean by that first part.

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2 hours ago, Don Noon said:

1) I am confident that you assume incorrectly, and that is what is interesting... exactly where and how the plate actually vibrates.

Then this means thickness of the bass bar in that area does something to high frequencies. 
(and as a side note, the Zaret bass bar does something by adding a lot of mass in that area. 
 

2 hours ago, Don Noon said:

2)  ?  Yes, each resonance is its own thing... but I have no clue what you mean by that first part.

I meant, the picture you are showing from Strad 3D is only one high frequency. At a lower frequency maybe nothing is going on under the fingerboard ? 

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17 hours ago, David Beard said:

 

Scratching the itch to understand is one thing.  But to improve our making, it's probably much more efficient to focus on learning the ways of the old masters. 

David, I would answer on this ‘Yes and no.’

i completely agree that makers in Cremona intuitively developed their art with trial and error and intelligent guesswork without modern scientific analysis bringing to the music world many of the finest instruments. 

The biggest question mark for me is that I don’t know what sound they had in mind using baroque construction method with a different string angle, smaller bass bar, different bridge and different strings. (We talked about this before)

This raises always the question what role the modernization of those famed violins would change (improve or spoil?) ?

Thats why I started to think about concepts to get a better understanding. And now I really believe that those Cremonese masters didn’t think about complicated things. So it boils down to: ‘make a thin and light top and adjust the rest to it.’ The test is ‘practice, practice, practice!’

i only know that if I work within the framework of Cremonese masters I can get their results but nothing else. There were a few makers after the golden age which were able to build violins on their own and non Cremonese concept. Guadagnini, Pressenda, Poggi , Kantuscher. 
 

I don’t see any reason why not to elaborate another concept and honestly, seeing how many years you spent on all the wonderful things you have brought to light, I don’t think this is more work than what you have done. 
 

But when thinking of concepts,  there are many unexplored techniques and materials which were not available in the golden age of violin making. Stradivari was IMO one of the most progressive and inventive violin maker. Following his example means not to duplicate or revive what has been made before, but go into new territories based on what has been achieved before.

14 hours ago, David Beard said:

Strad particular seem to explore refinements of choice aiming for the visual.

Hmmm, someone who made over 30 violin models? I see this more as sound experiments in the 18th century. For the rest, all is made on the principle ‘fast and efficient’ with intelligent cheating to make things look more perfect than they were. (Filler at bee stings, blackening rib chamfers, ‘mass produced’ purfling, straight line design volutes (seen from the front) etc. etc.)

Niccolò Amati had a drive for aesthetic refinement only paralleled by Pietro Guarneri Mantova (who made violins as a hobby but not for a living) and Jacob Stainer.

—————

But regardless all the Cremonese stuff, what do you personally think is the most important thing we need to understand when we want to build an instrument rich in overtones?

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14 hours ago, Don Noon said:

This is an internal air resonance idea, which might not be obvious to others.  I drilled a number of small holes in the back plate of a violin, just big enough for a small microphone, to check for this.  I could not find any evidence of such a resonance, even though it seemed like a good idea.  Ribs too, to check for lateral resonances.  Nada.

A0, for sure matters.  A1 can be measured, but doesn't seem to do a lot.  Above that, I don't see much evidence.

It is known to be resonances in the cave inside, but not outside as I indicate. I mean under the fingerbord, above the top plate or including reflections from the top plate and the fingerboard. Any possible repetitive route there can become a resonance.

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14 hours ago, Andreas Preuss said:

No objection.

Just from the standpoint of making it is much more difficult to trigger high frequency range and amplitudes than doing things for the fundamentals. And, IMO, a miraculous constellation of signature modes and their amplitudes does not influence in any measurable way the high frequencies. 
 

(this was more or less my motivation to create this thread  and exchange ideas and viewpoints)

There are of course connections between the properties of the body, the bass bar, setup and the high frequency response. I agree that it ios difficult to make both the low end and high end work well. If you can choose either both are pretty easy. The highs being more dependant on the bridge and setup.

The thicker the top the pointier and clearer the «singers formant» in my experience and understanding, given a well fitted light and stiff bridge. Many modern makers, up until quite recently, made the plates and bodies too stiff, lacking punch in the low frequencies. 

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15 hours ago, Peter K-G said:

 

 

 

WOOD

(And violins made to what wood you have)

Totally meaningless as everything matters. However ive read or heard one really great maker say that a good maker can make a good violin out of almost any wood. To make a great violin, takes great wood. 

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6 hours ago, Andreas Preuss said:

Then this means thickness of the bass bar in that area does something to high frequencies. 
(and as a side note, the Zaret bass bar does something by adding a lot of mass in that area. 
 

I meant, the picture you are showing from Strad 3D is only one high frequency. At a lower frequency maybe nothing is going on under the fingerboard ? 

Probably.  It's difficult to say what the "something" is, and whether it's desirable or not.

Lower modes have larger antinode patches, so it's easier to see what's happening even with the hidden zone under the fingerboard.  Each mode has its own shape... but from looking thru the Strad3D modes, it appears to me that the upper bout has more HF activity, which matches my experiments and hearing.

23 minutes ago, Anders Buen said:

It is known to be resonances in the cave inside, but not outside as I indicate. I mean under the fingerbord, above the top plate or including reflections from the top plate and the fingerboard. Any possible repetitive route there can become a resonance.

Looking at the air wavelength, even at the high frequencies, I think the fingerboard is too narrow to do much in the way of reflection or setting up any kind of resonance.  The sound will just squish around the fingerboard.

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15 hours ago, Andreas Preuss said:

And, IMO, a miraculous constellation of signature modes and their amplitudes does not influence in any measurable way the high frequencies. 

38 minutes ago, Anders Buen said:

The thicker the top the pointier and clearer the «singers formant» in my experience and understanding, given a well fitted light and stiff bridge. Many modern makers, up until quite recently, made the plates and bodies too stiff, lacking punch in the low frequencies. 

While the high frequencies do seem to be more mysterious and unfathomable, my experience with regraduating very thick tops (I mean REALLY thick student type violins) is that the high frequencies (2-4 kHz) can be attenuated by overly thick tops.  The bigger change is in the lower frequencies, though.

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

 

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1 hour ago, Andreas Preuss said:

David, 

>

But regardless all the Cremonese stuff, what do you personally think is the most important thing we need to understand when we want to build an instrument rich in overtones?

A better question would be ...."when we want to build an instrument with rich overtones?

Most orchestra instruments, including the violin, are designed to cut off all the really high note overtones which give harsh sound effect.  For a violin you want to have a frequency response curve with steep fall-off starting at about 3 or 4 kHz. To get a rich affect you want to have the first few harmonics quite strong.

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1 hour ago, Don Noon said:

Looking at the air wavelength, even at the high frequencies, I think the fingerboard is too narrow to do much in the way of reflection or setting up any kind of resonance.  The sound will just squish around the fingerboard.

I think it can, and the main contribution is the bridge I think. There will be reflections and mirror sources there making the room bigger than we may think. The fingerboard also is curved making it focussing. 

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6 hours ago, Andreas Preuss said:

David, I would answer on this ‘Yes and no.’

i completely agree that makers in Cremona intuitively developed their art with trial and error and intelligent guesswork without modern scientific analysis bringing to the music world many of the finest instruments. 

The biggest question mark for me is that I don’t know what sound they had in mind using baroque construction method with a different string angle, smaller bass bar, different bridge and different strings. (We talked about this before)

This raises always the question what role the modernization of those famed violins would change (improve or spoil?) ?

Thats why I started to think about concepts to get a better understanding. And now I really believe that those Cremonese masters didn’t think about complicated things. So it boils down to: ‘make a thin and light top and adjust the rest to it.’ The test is ‘practice, practice, practice!’

i only know that if I work within the framework of Cremonese masters I can get their results but nothing else. There were a few makers after the golden age which were able to build violins on their own and non Cremonese concept. Guadagnini, Pressenda, Poggi , Kantuscher. 
 

I don’t see any reason why not to elaborate another concept and honestly, seeing how many years you spent on all the wonderful things you have brought to light, I don’t think this is more work than what you have done. 
 

But when thinking of concepts,  there are many unexplored techniques and materials which were not available in the golden age of violin making. Stradivari was IMO one of the most progressive and inventive violin maker. Following his example means not to duplicate or revive what has been made before, but go into new territories based on what has been achieved before.

Hmmm, someone who made over 30 violin models? I see this more as sound experiments in the 18th century. For the rest, all is made on the principle ‘fast and efficient’ with intelligent cheating to make things look more perfect than they were. (Filler at bee stings, blackening rib chamfers, ‘mass produced’ purfling, straight line design volutes (seen from the front) etc. etc.)

Niccolò Amati had a drive for aesthetic refinement only paralleled by Pietro Guarneri Mantova (who made violins as a hobby but not for a living) and Jacob Stainer.

—————

But regardless all the Cremonese stuff, what do you personally think is the most important thing we need to understand when we want to build an instrument rich in overtones?

I would say to this often recited line that "they did 500 years of experiments" that.....500 years is nothing really and that they sure didn't experiment with all possible design or outcomes, there is plenty of room to experiment, just don't expect to sell those experiments 

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11 hours ago, Don Noon said:

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

It is really the question why. 
 

Reminds me a bit of what a physicist friend of mine made as his PHD thesis about earthquakes. In a demonstration model he put sand in a box and put a stone in the middle. Then he applied vibrations to the box slowly increasing the frequency. At a certain frequency the sand became liquid and the stone on top just sank in and disappeared in an instant. (He could model an equation to calculate the frequency necessary to liquidify the sand)

Do we really know that all stiffness properties remain the same when the violin vibrates? The thing is probably that there is no way to measure it.

(Don, I see you shaking your head)

I still think it is worth to look at the neck stability. The neck applies with its leverage action enormous forces to the top block area. High frequencies come from rigid structures and I see in that area a weak point. (Maybe the driving forces of plate vibrations under the fingerboard come from there?)

The stiffness distribution of the whole body is what matters. And here it matters where and how the stiffness is created. But there are always different solution to increase stiffness and it is in the end not the same if stiffness of the top is created by its own thickness or just the rib garland. I am always getting back to the same principle (recipe) of making the top very thin and very light and adjust the rest to it. 
 

Maybe this is again my wrong assumption, but any vibrations of the neck in particular could be regarded as lost energy because it can’t create sound. Though it seems impossible to block entirely neck vibrations, minimizing them might be an efficient trigger for the overtone distribution in a spectrum. (Makes me wonder what would happen if we could block completely the neck vibrations) 

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8 hours ago, Anders Buen said:

I think it can, and the main contribution is the bridge I think. There will be reflections and mirror sources there making the room bigger than we may think. The fingerboard also is curved making it focussing. 

This would mean that a fingerboard set at a bigger distance to the top surface makes a different sound? (The new concept violin has at this point a neck overstand of 10mm)It would be a pretty easy experiment to tape a thick cardboard under the fingerboard to hear what happens. My guess is that nothing happens which can be heard.

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18 minutes ago, Andreas Preuss said:

This would mean that a fingerboard set at a bigger distance to the top surface makes a different sound? (The new concept violin has at this point a neck overstand of 10mm)It would be a pretty easy experiment to tape a thick cardboard under the fingerboard to hear what happens. My guess is that nothing happens which can be heard.

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.

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