A0 mode: What is more important air mass or frequency?

[Peter K-G]

45 minutes ago, Bodacious Cowboy said:

The difference between knowledge and wisdom:

Knowledge is knowing that a tomato is a fruit.

Wisdom is knowing that you shouldn't put a tomato in a fruit salad.

My MBA tells me that there are only 4 in that pyramid?

Can't remember any tomatoes...

[Andreas Preuss]

16 hours ago, Peter K-G said:

You might be jumping into conclutions about the "changes" after a modification?

My experience is that modifications made, that you observe as an immediate impact, many times goes back to the original state, after  some days or even weeks.

I mentioned I think several times that I wait for conclusions after a 'stretch-in' time for the instrument. At least one day.

[Andreas Preuss]

7 hours ago, Anders Buen said:

There was an experiment done at Oberlin one year where a fine maker chose to cut the ribs, I think about 5-7mm, on a viola. There was a slight difference but I think we had problems finding clear differences in the spectra. 

Hmm, I don't think you can compare experiments on violas with violins. Violas are really different animals.

But let's take the experiment as a such. I am recently questioning if the findings in some experiments can be generalized. It would interest me for the viola experiment what exactly were its proportions such as top thickness arching height and weight, because I believe that in particular the proportions of the top can alter experimental results.

Its really not easy.

-------------------

Concerning the assembly - disassembly effect, yes this sometimes happens. However I have taken this violin already over 20 times apart and I noticed this effect only at a stage when the back was definitely too weak. As usual no proof other than what I can hear.

-------------------

Concerning the rib height reduction to 20mm, I wouldn't mind doing this provided I get exactly the sound result I want.  At least I feel free on a 'new concept' not to adhere religiously to Strad measurements.

Anyway, I am still puzzled why the air resonance was from the beginning so low.  The body is as short as possible (350mm) but maybe the unusual width (115mm measured flat) makes the air resonance so low. F holes are a kind of normal, treble side 78mm bass side 85 mm measured in longest direction.

 

 

 

Edited May 15, 2021 by Andreas Preuss
comment on the second and third post

[Andreas Preuss]

4 hours ago, Marty Kasprzyk said:

I agree --bigger f  holes are better.

Claudia Fritz (attached paper) found that it takes about a 20% change in A0 frequency to be even detectable. But If you change the amplitude of A0 it takes only about 10% change to be detectable.   George Bissinger (attached paper figure 4) found the a big difference between "bad" and "good" violins was that good violins had a higher amplitude A0. 

One way of increasing the A0 amplitude is to increase the f hole open area.  Thus increasing the size of the f hole opening might be a better way of increasing the A0 frequency (not very important) than decreasing the rib height.

 

Fritz--perception of changes.pdf 727.49 kB · 1 download Bissinger, directivity.pdf 1.16 MB · 1 download

I think this calls for another experiment on my new concept violin. 

I was still thinking of making another top with improved arching shape.

Concerning the increase of the f-hole surface it seems that unfortunately this can't be done on the width of the f- hole stems. The first top on the new concept violin had the bass side  f hole too wide open and filling it could improve the too fuzzy sound. So this would mean the alteration needs to be done on the total length.

Are there any calculations how much a 5% surface increase of the F holes alters the amplitude of A0?

(since you are talking about amplitude to be more important than pitch. Doesn't this mean as well that air mass itself plays a role? The less air mass the body vibration has to shake around the higher the amplitude.)

----------

Additional comment

Since already many years I am making violins on the assumption that a really good violin needs simultaneously 2 things: A good developed overtone range in the singer formant and a good mechanism just to 'pump air'. For the construction of a violin this is somehow a contradiction, because (generally speaking) for overtones a stiff structure is needed while for the air pumping mechanism a loose structure is better. To learn how to optimize the balance between both is the 'secret' of experience.

Edited May 15, 2021 by Andreas Preuss
add comment

[Don Noon]

34 minutes ago, Andreas Preuss said:

Since already many years I am making violins on the assumption that a really good violin needs simultaneously 2 things: A good developed overtone range in the singer formant and a good mechanism just to 'pump air'. For the construction of a violin this is somehow a contradiction, because (generally speaking) for overtones a stiff structure is needed while for the air pumping mechanism a loose structure is better. To learn how to optimize the balance between both is the 'secret' of experience.

It is possible to have a flexible structure at low frequencies and effectively a stiff structure at high frequencies.  Mass doesn't like to move at high frequencies... thus the reaction mass of the bass bar and the center of the back (supporting the soundpost) are effectively stiff at the high frequencies, but you can still have enough flex in the plates to pump air at the lows.

Getting the balance right is still an experience thing.

[Anders Buen]

9 hours ago, Marty Kasprzyk said:

I agree --bigger f  holes are better.

Claudia Fritz (attached paper) found that it takes about a 20% change in A0 frequency to be even detectable. But If you change the amplitude of A0 it takes only about 10% change to be detectable.   George Bissinger (attached paper figure 4) found the a big difference between "bad" and "good" violins was that good violins had a higher amplitude A0. 

One way of increasing the A0 amplitude is to increase the f hole open area.  Thus increasing the size of the f hole opening might be a better way of increasing the A0 frequency (not very important) than decreasing the rib height.

Yes, increasting the A0 frequency would take a larger f-hole area and not a smaller one as I wrote in error. 

An other way of getting stonger A0´s is by using lighter and more flexible plates of the violin, in particular the top plate. So Bissingers finding simply may be the result of lighter plates in the fine instruments than the modern ones he measured. 

There is one or two graphs in this conference proceedings article indicating this based on some data mining I have done.  https://www.researchgate.net/publication/228502618_WHAT_IS_OLD_ITALIAN_TIMBRE 

[Anders Buen]

I do not think a larger area of the f-hole chenges the amplitude of the A0 much bacuse the relation between the wavelenght at 275 Hz and the hole size is so large. Rounding the sides so the air runs more smoothly across the corners on both the outside and inside will make it just a little stronger due to a reduced Q value (inverse damping factor).

An other factor influencing the A0 level is the humidity content of the wood. The more moisture the more flexible the plates, and thus the stronger the A0. The moisture will also lower the A0 frequency somewhat, at a high MC content.

Edited May 15, 2021 by Anders Buen
Extra line on effect from humidity

[Andreas Preuss]

4 hours ago, Anders Buen said:

I do not think a larger area of the f-hole chenges the amplitude of the A0 much bacuse the relation between the wavelenght at 275 Hz and the hole size is so large.

For some reason this intrigues me a little. Very often I believed that a minimal change had no influence and the experiment told me in the end the opposite. So sorry to ask for confirmation: were there any tests done on this with a thin top?

However, I chose by purpose the bass side f hole to be longer because on this side the real 'pumping motion' takes place. In other terms only on the bass side f hole top and back can move in opposite direction but not on the sound post side.

Would this mean too that making the bass side f-hole longer has  theoretically a bigger effect on A0 amplitude than the treble side f-hole?

4 hours ago, Anders Buen said:

Rounding the sides so the air runs more smoothly across the corners on both the outside and inside will make it just a little stronger due to a reduced Q value (inverse damping factor).

So basically accumulated rosin at the edge of antique instruments contribute to smoothing the airflow?

From the standpoint of style, rounding f- holes is aesthetically pretty weird. I often think that in those terms one of the two solutions must be better than the other:

1. f hole borders cut perpendicular to the arching surface (slightly tilted)
2. f- hole borders cut perpendicular to the rib surface.

 

 

 

[Anders Buen]

4 minutes ago, Andreas Preuss said:

For some reason this intrigues me a little. Very often I believed that a minimal change had no influence and the experiment told me in the end the opposite. So sorry to ask for confirmation: were there any tests done on this with a thin top?

However, I chose by purpose the bass side f hole to be longer because on this side the real 'pumping motion' takes place. In other terms only on the bass side f hole top and back can move in opposite direction but not on the sound post side.

Would this mean too that making the bass side f-hole longer has  theoretically a bigger effect on A0 amplitude than the treble side f-hole?

So basically accumulated rosin at the edge of antique instruments contribute to smoothing the airflow?

From the standpoint of style, rounding f- holes is aesthetically pretty weird. I often think that in those terms one of the two solutions must be better than the other:

1. f hole borders cut perpendicular to the arching surface (slightly tilted)
2. f- hole borders cut perpendicular to the rib surface.

 

 

 

I am an acoustics consultant with good insight into how slatted panel Helmholz absorbers work and perform. I have shared information into what happens if the f-hole sides are rounded. Many older instrments do have runded edges due to wear and tear over he years. I do not think you get much difference from altering the opening area from say x % to X+5% on the level, but moving the A0 closer to the B1- may have an effect.
If you want to have any confirmation on the effect from the opening area of f-holes, you will have to get help somewhere else, or do and experiment on this yourself. Maybe Marty has a reference for his statement.

I do not care if readers believe what I write or not, or try it or not. I do not have any need to sell my arguments or theories to anybody. I just happen to know lot about how violins and fiddles work acoustically.

[Andreas Preuss]

Anders, if I sounded like questioning your authority on acoustical matters, then I have to apologize. This was not my intent. 

I read your comments always with big interest and are very thankful for the information you are sharing. 

-----------------

Back to the experiments. As I said above, augmenting the width of the f-hole stems, seems to be not a good idea from what I experienced. I would be very hesitant to do this from an aesthetical standpoint too.

If on the other hand making the f-holes longer than usual doesn't promise too much changes, then there is only the stiffness of the top left for getting a higher amplitude on A0, I suppose?

[Marty Kasprzyk]

4 hours ago, Anders Buen said:

I do not think a larger area of the f-hole chenges the amplitude of the A0 much bacuse the relation between the wavelenght at 275 Hz and the hole size is so large. Rounding the sides so the air runs more smoothly across the corners on both the outside and inside will make it just a little stronger due to a reduced Q value (inverse damping factor).

An other factor influencing the A0 level is the humidity content of the wood. The more moisture the more flexible the plates, and thus the stronger the A0. The moisture will also lower the A0 frequency somewhat, at a high MC content.

I agree. It takes a huge increase in the f hole area A to raise the A0 frequency.  I think it follows the A^0.27 relationship that Bissinger found.

John Coffey's 2013 paper (attached) beats this A0 subject to death.  After 65 pages describing his carefully done experiments and analytical studies he concluded:

"I suspect from these studies that the main function of the f -holes on the sound from a violin is simply to let the sound out – to allow the back plate to contribute to sound radiation and so give adequate loudness."

But the wall compliance seems to have a big effect.  Bissinger's translation (J. Violin Soc. Am.:VSA Papers 2019 Vol. XXXVIII, No.1)) of the paper by Hermann Meinel "On Frequency Curves of Violins" has a graph (attached) which shows how the A0 amplitude increases greatly as the plates are thinned.

609760676_JMC-HelmholtzResonance--Up-ct.pdf

[Roger Hill]

16 hours ago, Don Noon said:

Roger, first order is that the A0 won't be any different at altitude, assuming a normal room temperature.  Speed of sound is the releveant variable in calculating a cavity resonance...

Air pressure has no effect at all in an ideal gas approximation. This is because pressure and density both contribute to sound velocity equally, and in an ideal gas the two effects cancel out, leaving only the effect of temperature. (Ref:  https://www.sciencedaily.com/terms/speed_of_sound.htm)

However, there might be a small second-order effect, as the wall stiffness (assumed to remain the same) may be relatively more rigid in the net mass/spring calculation.  I can't imagine it would be any more than a few Hz, not a big deal.

Thanks, Don.  Good explanation.  The fact that I can't hear something that (for practical purposes) is not there, is probably not good evidence that my hearing is still ok.  My wife may be right.............

[Anders Buen]

2 hours ago, Marty Kasprzyk said:

I agree. It takes a huge increase in the f hole area A to raise the A0 frequency.  I think it follows the A^0.27 relationship that Bissinger found.

John Coffey's 2013 paper (attached) beats this A0 subject to death.  After 65 pages describing his carefully done experiments and analytical studies he concluded:

"I suspect from these studies that the main function of the f -holes on the sound from a violin is simply to let the sound out – to allow the back plate to contribute to sound radiation and so give adequate loudness."

But the wall compliance seems to have a big effect.  Bissinger's translation (J. Violin Soc. Am.:VSA Papers 2019 Vol. XXXVIII, No.1)) of the paper by Hermann Meinel "On Frequency Curves of Violins" has a graph (attached) which shows how the A0 amplitude increases greatly as the plates are thinned.

609760676_JMC-HelmholtzResonance--Up-ct.pdf 6.02 MB · 0 downloads

Much good stuff here. I think the f hole area A and the resonance frequency goes as A^0,5. Increasing the area 10 % should give 5% change to the A0 frequency. Starting at 275 Hz one would end at 288 Hz which is substantial for a violin, even though the 13 Hz isn't all that much. I believe the V^-0,3 thing as given by Bissinger and Kazprzyk, is related to the "spring part" of the expression. The f-kole size contributes to the moving "mass part". However, I could be wrong, and Marty could be right that the Area effect is weaker.

The Coffey paper never entertained me much, as I could not find useful information in it fast. My intuition on it is that the conclusion on the history of the f-hole shape is not likely to be correct. However, I could be incorrect.  

Edited May 15, 2021 by Anders Buen
spelling error in one word

[Anders Buen]

2 hours ago, Andreas Preuss said:

Anders, if I sounded like questioning your authority on acoustical matters, then I have to apologize. This was not my intent. 

I read your comments always with big interest and are very thankful for the information you are sharing. 

-----------------

Back to the experiments. As I said above, augmenting the width of the f-hole stems, seems to be not a good idea from what I experienced. I would be very hesitant to do this from an aesthetical standpoint too.

If on the other hand making the f-holes longer than usual doesn't promise too much changes, then there is only the stiffness of the top left for getting a higher amplitude on A0, I suppose?

No problem, I do not know why I get grumpy at times. Maybe not enough exercise in the Corona time (gyms are closed here). - Sorry for that!

I would believe you already have a pretty strong A0 as the B1- is so low in frequency. It also sound deep and strong you say, so why do you want even more? Make it sound more like a Viola? Marty had a violin with an exceptionally strong A0 at the VSA Oberlin workshop one year. It almost sounded like a viola. 

[Peter K-G]

This thread is getting more interesting, and I'm sorry for provoking Anders, when he actually shares interesting real information!

I can't help much in the quantitave studies, because I allways find myself doing qualitative research.

If anyone is interesting in how to control A0 or B1-,B1+ in Hz and dB level I'm willing to help

[Don Noon]

Two things...

1) There was a paper a while back about the length of the F hole having far more effect on A0 frequency than the area.  I quizzed the author about it and came away convinced.  I don't have data on Gibson mandolins, but comparing the sound hole area of the F hole vs. round hole versions of the same model and comparing it to the A0 mode would likely be a clue.  Sure, there are two F's and one round, but comparing the effectiveness of the area is the idea.

2) Getting a stronger A0 by means of lower damping doesn't seem too attractive, in that the resonance gets peakier... the tuned frequency gets stronger, but the adjacent notes don't get helped as much.  So that one note might stick out more.  Probably not a big deal, but chasing lower A0 damping isn't something I'd go after.  Lower damping at higher frequencies, where there are many adjacent modes, is a different story

[Peter K-G]

To answer the OP:

A0 mode: What is more important air mass or frequency?

Both!

Because if you give slightly too much "mass", and hit near a note, you are in trouble, and as I sayd previously giving it more power by adding an octave above B1+, you are going to want to open the violin and give it a new BB.

[Anders Buen]

L

52 minutes ago, Don Noon said:

Two things...

1) There was a paper a while back about the length of the F hole having far more effect on A0 frequency than the area.  I quizzed the author about it and came away convinced.  I don't have data on Gibson mandolins, but comparing the sound hole area of the F hole vs. round hole versions of the same model and comparing it to the A0 mode would likely be a clue.  Sure, there are two F's and one round, but comparing the effectiveness of the area is the idea.

2) Getting a stronger A0 by means of lower damping doesn't seem too attractive, in that the resonance gets peakier... the tuned frequency gets stronger, but the adjacent notes don't get helped as much.  So that one note might stick out more.  Probably not a big deal, but chasing lower A0 damping isn't something I'd go after.  Lower damping at higher frequencies, where there are many adjacent modes, is a different story

The length and the area of the f-holes are linearly dependent. A loner f-hole cut more wood and decreases the "bridge island" stiffness somewhat, if the same graduations are used. I do not know if the article and work took that into account. Most likely not. For the hole itself, I think that a narrow hole will be more lossy than a round one, as more of the air pumping in and out are free to move inside the circle. The particles close to the borders will behave more lossy because of their velocity against the edges. A circle will have the least border to area ratio as compared to a f-hole.

I think I have two tests with f-hole rounding. The effect is located close to the f0, and was 2-3 dB ish. I think I have shared plots here some years ago. Probably not so interesting for the played notes. But for the impacts the body get for each shifts in bow direction or just starting bowing or stopping, the body sound, these effects should be very clearly audible. If we assume 2 dB increased level, that amounts to about 1,8 times lower Q factor, which affects the reverberation time of the A0 by the same amount, 1,8, which is far more than the just noticeable difference of about 5%. The A0 becomes more "ringy" and you will hear it.

 

[Anders Buen]

A0 mode: What is more important air mass or frequency?

What matters is the amplitude, the frequency, how strong it is in relation to the midrange of the violin and how close it is to the B1- (for a violin).

The effect of the interior air mass or volume has on the A0 has been addressed by Marty. For the amplitude of the A0 the interior mass has a limited effect. The plates does move a little and contribute to the strength of the resonance, but most of the sound power probably comes from the f-holes. 

However If the volume of the violin box is changed, something else is going to be changed too, which may influence the sound of the violin and how it is to play. 

[Marty Kasprzyk]

5 hours ago, Anders Buen said:

A0 mode: What is more important air mass or frequency?

What matters is the amplitude, the frequency, how strong it is in relation to the midrange of the violin and how close it is to the B1- (for a violin).

>

That's a good question.  The traditional violin's lower notes on the G string aren’t very loud as shown in the old 1937 Saunders's tests of Strad violins (attached graph).  If you like this (flaw, deficiency, idiosyncrasy?) then you should try to place the A0 frequency in the usual spot around 280Hz.

Schelleng had shown in 1962 in his attached graph  that the G string’s low frequency out-put was due to the low end tail (light line) of the A0 resonance was out of phase with the low end tail of the B1- resonance (dashed line) so the two vibrations cancelled each other as shown in the (heavy line).

So if the A0 resonance frequency is rather high and close to the B1-frequency the lower notes will have a very low fundamental frequency amplitude and they will be weak and also not very deep sounding like a typical Strad violin.

About a  half century later in 2013 John Coffey (previously attached report)also noticed this phase cancellation effect between the tails of A0 and B1- resonances and he recommended:

"Theory predicts a 180 ○phase change of sound radiated from the f-holes relative to that radiated from the top plate, as the frequency increases from below to above A0. Below A0 these sources interfere destructively, reducing the sound volume. This suggests that A0 should optimally be only a little above 196 Hz (open G) on a violin – say at A (220 Hz)."

So I recently strung up one of my experimental violas with an E string to give EADG tuning like a violin.  It has a low A0 frequency around 220 Hz like Coffey had suggested.  Sure enough its frequency response curve did have a much higher responses from 196 to about 250Hz compared to one of my violins (see attached graph) and the Saunders loudness curves did show the viola have much better G string loudness (another attached graph) as predicted.

So finally getting back to the original question of how close the A0 frequency should be to B1-?

Forget all this stuff and just make them the same old traditional way so you can sell them.

 

 

 

[uncle duke]

24 minutes ago, Marty Kasprzyk said:

 This suggests that A0 should optimally be only a little above 196 Hz (open G) on a violin – say at A (220 Hz)."

Maybe a little higher than the 220hz A.  The sometimes blaring stopped A note story gets old sometimes.

I wonder what changes would occur after a thin new york style shim is put in after a low AO is decided upon.  

[jezzupe]

On 5/15/2021 at 6:51 AM, Andreas Preuss said:

Anders, if I sounded like questioning your authority on acoustical matters, then I have to apologize. This was not my intent. 

I read your comments always with big interest and are very thankful for the information you are sharing. 

-----------------

Back to the experiments. As I said above, augmenting the width of the f-hole stems, seems to be not a good idea from what I experienced. I would be very hesitant to do this from an aesthetical standpoint too.

If on the other hand making the f-holes longer than usual doesn't promise too much changes, then there is only the stiffness of the top left for getting a higher amplitude on A0, I suppose?

ff hole shape and size has a dramatic effect on the top plates stiffness.particularly if one starts experimenting around with different shapes that are not "standard" It is very challenging to come up with a shape that encompasses about the same amount of area as a standard ff hole, that is 1. structurally sound and will not induce cracks  and 2. is ascetically pleasing.3. rivals or helps compromise the tops stiffness "properly"

That being said I feel there are limitations when one is "locked" into using certain designs based on the aspect of "copying" something.

I found working with standardized thin flat plywood plates{due to uniformity and consistency of strength vectors} the best way to experiment with "shapes that compromise stiffness" and the easiest way to "see" the results of ones ideas empirically and immediately.

I think the basic original ff shape is hard to beat related to "not inducing cracks" and it obviously works. But if one takes about 100 plates and starts cutting away, there are shapes that compromise the stiffness more than others, my intent in my experiments was top produce a hole that compromised stiffness and or induced flexibility under dynamic states that would not be prone to cracking or caving in.

Again when dealing with a flat plate that has had some type of hole cut in it, and then having the edges uniformly fixed, one can use their hands to apply pressure to the plate to "feel" the difference in stiffness,if "you" mess around with several shapes you can surprise yourself as some shapes are deceptive and or do things you would not expect

Then of course there is the concept of asymmetric sized holes in different locations than "standard" , or left and right in different locations as well as different sizes from each other.

It is hard to predict how these shapes will work with a soundpost and bassbar , yet we certainly can examine them in unsupported states as free plates fixed on the edges 

This also crosses over into different wood species and their inherent elastic properties as compared to other dissimilar species   

[jezzupe]

3 hours ago, Marty Kasprzyk said:

 

 

 

That's a good question.  The traditional violin's lower notes on the G string aren’t very loud as shown in the old 1937 Saunders's tests of Strad violins (attached graph).  If you like this (flaw, deficiency, idiosyncrasy?) then you should try to place the A0 frequency in the usual spot around 280Hz.

Schelleng had shown in 1962 in his attached graph  that the G string’s low frequency out-put was due to the low end tail (light line) of the A0 resonance was out of phase with the low end tail of the B1- resonance (dashed line) so the two vibrations cancelled each other as shown in the (heavy line).

So if the A0 resonance frequency is rather high and close to the B1-frequency the lower notes will have a very low fundamental frequency amplitude and they will be weak and also not very deep sounding like a typical Strad violin.

About a  half century later in 2013 John Coffey (previously attached report)also noticed this phase cancellation effect between the tails of A0 and B1- resonances and he recommended:

"Theory predicts a 180 ○phase change of sound radiated from the f-holes relative to that radiated from the top plate, as the frequency increases from below to above A0. Below A0 these sources interfere destructively, reducing the sound volume. This suggests that A0 should optimally be only a little above 196 Hz (open G) on a violin – say at A (220 Hz)."

So I recently strung up one of my experimental violas with an E string to give EADG tuning like a violin.  It has a low A0 frequency around 220 Hz like Coffey had suggested.  Sure enough its frequency response curve did have a much higher responses from 196 to about 250Hz compared to one of my violins (see attached graph) and the Saunders loudness curves did show the viola have much better G string loudness (another attached graph) as predicted.

So finally getting back to the original question of how close the A0 frequency should be to B1-?

Forget all this stuff and just make them the same old traditional way so you can sell them.

 

 

 

but that way we don't get to suffer for our art 

[Anders Buen]

The shape of the f-holes are not all that important when the inner wings are present. Hardanger fiddles have longer f-holes and the outer side are lower and more in line with the borderline of the plate. The inside is high, and higher than on violins, because the central cross arch of HF are flatter while the archeight in general is more or less similar to violins. So you see into a HF from the side.

Many great HF’s have violin tops. And the sound isn’t different in any clear way from the traditional design. Other factors are more important like the lighter and shorter strings, and the bridge. 

[Andreas Preuss]

13 hours ago, Marty Kasprzyk said:

Forget all this stuff and just make them the same old traditional way so you can sell them.

Very important point. 

The main reason for me not even eliminate the corners from the outline. It took 200 years to develop the design from Andrea Amati to Antonio Stradivari. Any new pattern can only survive in the evolutionary process when it can proof to be fitter than the previous models. 

On 5/16/2021 at 5:38 AM, Anders Buen said:

What matters is the amplitude

I was recently listening (with good headphones!) on youtube many recordings of Tsigane by players who supposedly played it on a GDG. I concentrated on the few opening bars all played on the G and D string. I always and for any recording and any room acoustic get this feeling of 'a lot of air is being pumped in and out'. Almost to the degree that those instruments sound boxy. And maybe they really do. I assumed this can be interpreted as a strong A0 resonance on those instruments.

(OTOH I think that the boxiness of those high class fiddles is balanced against just a broad and full overtone range, which smudges the effect of a boxy sound.)

 

9 hours ago, jezzupe said:

I found working with standardized thin flat plywood plates{due to uniformity and consistency of strength vectors} the best way to experiment with "shapes that compromise stiffness" and the easiest way to "see" the results of ones ideas empirically and immediately.

Would be interested to see the model which looked to you good at the beginning but completely contradicted your expectations.

On 5/16/2021 at 5:38 AM, Anders Buen said:

For the amplitude of the A0 the interior mass has a limited effect.

Not that I doubt what you are saying, but this makes me scratch my head, because if not the air mass, what caused the tonal change after the first rib height reduction...... (?) (And somehow quite clear change for the better in the sense that a permanently exisiting sound problem of this particular instrument could be solved)

I am thinking on a very simplified model that the air is a kind of bumper. So this would mean to me that 'mass' in absolute weight does maybe not have such a big influence. This means reducing air mass by filling whatever material around the rib inside does not have a big effect. (It doesn't as I had seen in one of my first experiments) But what about the thickness of this 'air cushion'? Something like 'the thinner the harder it gets'?

9 hours ago, jezzupe said:

I think the basic original ff shape is hard to beat related to "not inducing cracks"

To me any opening on the top (at the approximate location of the ff) no matter what shape are a risk factor for cracks including f-shaped holes.