High frequency response as a result of longitudinal arching properties - Experiments with a zero cross arch violin top - what happens when the long arch height is increased

[Andreas Preuss]

After the discussion on Don Noons thread 'The importance of the top crossarch radius above the F holes' I am making now my own experiments on this. So to make things technically simple I just go for the opposite what is assumed to be good. Accordingly the high frequency response should be either very uneven or altogether very low.

It took not too much time effort to make a flat board violin top plate 3.5mm thick with slotted f-holes. The bass bar bends the whole plate to its lengthwise arched shape, but the entire plate is flexible enough to be bent further. 

Here are some pictures

 

 

Data of the plate

c. 3.8g/cm3
yearrings are perpendicular to the surface to ensure maximum cross grain stability.

plate weight without bass bar is 65g

weight of the bass bar 7g

lengthwise the plate is not precisely in splitting direction, the grain is slanted roughly at a 5 degree angle

f-hole length: bass side: 65mm, treble side: 50mm

distance between the f-hole slots at the narrowest distance 62mm

Experimental procedures

I am using the body of my new concept violin which has an arched rib garland.

1. Glue the flat top on it and set the violin up to take a frequency response plot which serves as reference for all following alterations.

2. Take the top plate off and build a much higher arching profile on the ribs to increase the longitudinal arching height. currently it is around 4mm and if it is manageable I want to triple the height to 12mm.

3. Prolong f-hole length on the thick plate in two increments of 1 cm first on the bass side followed by the treble side. (Evantually I am going to fill up the f holes to rebuild a shorter length.

4. thin down the top plate in 2 increments of 10%. so something like 65 to 58.5 and from 58.5 to 52.5. Because this is proportional to the overall thickness the thickness should mark 3.5, 3.15., 2,85 respectively. Eventually, depending on the result, I might consider go further down. For the thickness reduction I am planning not to go below 3.0 around the soundpost area.

I am not intending to alter anything on the bass bar. 

Lets see what is coming out. I am open to any suggestions in which order to make the alterations to the plate and/or further experiments with this plate.

 

[Marty Kasprzyk]

The sharp pointed ends of the "f" holes are stress risers which can cause cracks to start there.  You might consider putting in patches at the ends ahead of time. 

The well rounded eyes of conventional f holes greatly reduce the stress concentrations.

[Andreas Preuss]

5 hours ago, Marty Kasprzyk said:

The sharp pointed ends of the "f" holes are stress risers which can cause cracks to start there.  You might consider putting in patches at the ends ahead of time. 

The well rounded eyes of conventional f holes greatly reduce the stress concentrations.

Yes indeed. Good suggestion. 

[Don Noon]

I'm all for folks other than me taking on these kinds of experiments.  However, this one is very far from testing what I think of as normal geometry, so it is not clear if the results would be directly useful.  Maybe it would point to other experiments that need exporing.

With a nominally flat top that is being bent to create a longitudinal arch, presumably the arch will be a very gentle, fairly uniform long radius curve rather than being relatively flat along the middle and stronger arch in the upper and lower bouts.  In theory, such a gentle arch would have strong influence on the low frequencies and perhaps the transition hill, but behave about the same as a flat plate at the higher frequencies.  And no help from the crossarch.  It will be interesting to see what results you actually get.

In some ways, your experiment is similar to an experimental violin by Al Fischer that I have... bent top, low arch, C-shaped sound holes.  The response spectrum (below) is a bit odd in the signature modes, very strong and broad transition hill, and weak in the highs until the hill ~4 kHz.  The 4k peak is about where the "critical frequency" bump should be for a flat plate, and not likely to be influenced by arching this gentle.  The wings of F-shaped holes also have an influence on the transition hill, so there's that difference too.  On the whole, I don't think it sounds very good.

[Marty Kasprzyk]

16 hours ago, Andreas Preuss said:

After the discussion on Don Noons thread 'The importance of the top crossarch radius above the F holes' I am making now my own experiments on this. So to make things technically simple I just go for the opposite what is assumed to be good. Accordingly the high frequency response should be either very uneven or altogether very low.

It took not too much time effort to make a flat board violin top plate 3.5mm thick with slotted f-holes. The bass bar bends the whole plate to its lengthwise arched shape, but the entire plate is flexible enough to be bent further. 

Here are some pictures

 

 

Data of the plate

c. 3.8g/cm3
yearrings are perpendicular to the surface to ensure maximum cross grain stability.

plate weight without bass bar is 65g

weight of the bass bar 7g

lengthwise the plate is not precisely in splitting direction, the grain is slanted roughly at a 5 degree angle

f-hole length: bass side: 65mm, treble side: 50mm

distance between the f-hole slots at the narrowest distance 62mm

Experimental procedures

I am using the body of my new concept violin which has an arched rib garland.

1. Glue the flat top on it and set the violin up to take a frequency response plot which serves as reference for all following alterations.

2. Take the top plate off and build a much higher arching profile on the ribs to increase the longitudinal arching height. currently it is around 4mm and if it is manageable I want to triple the height to 12mm.

3. Prolong f-hole length on the thick plate in two increments of 1 cm first on the bass side followed by the treble side. (Evantually I am going to fill up the f holes to rebuild a shorter length.

4. thin down the top plate in 2 increments of 10%. so something like 65 to 58.5 and from 58.5 to 52.5. Because this is proportional to the overall thickness the thickness should mark 3.5, 3.15., 2,85 respectively. Eventually, depending on the result, I might consider go further down. For the thickness reduction I am planning not to go below 3.0 around the soundpost area.

I am not intending to alter anything on the bass bar. 

Lets see what is coming out. I am open to any suggestions in which order to make the alterations to the plate and/or further experiments with this plate.

 

The cross grain stiffness with a flat plate and bass bar is very low.  Before you do your step 2  I suggest adding some cross braces to see how the frequency response curve changes.

Guitar makers use flat plates with various bracings to adjust its sound character.

[Andreas Preuss]

1 hour ago, Don Noon said:

I'm all for folks other than me taking on these kinds of experiments.  However, this one is very far from testing what I think of as normal geometry, so it is not clear if the results would be directly useful.  Maybe it would point to other experiments that need exporing.

With a nominally flat top that is being bent to create a longitudinal arch, presumably the arch will be a very gentle, fairly uniform long radius curve rather than being relatively flat along the middle and stronger arch in the upper and lower bouts.  In theory, such a gentle arch would have strong influence on the low frequencies and perhaps the transition hill, but behave about the same as a flat plate at the higher frequencies.  And no help from the crossarch.  It will be interesting to see what results you actually get.

In some ways, your experiment is similar to an experimental violin by Al Fischer that I have... bent top, low arch, C-shaped sound holes.  The response spectrum (below) is a bit odd in the signature modes, very strong and broad transition hill, and weak in the highs until the hill ~4 kHz.  The 4k peak is about where the "critical frequency" bump should be for a flat plate, and not likely to be influenced by arching this gentle.  The wings of F-shaped holes also have an influence on the transition hill, so there's that difference too.  On the whole, I don't think it sounds very good.

Interesting. 
 

in theory I can make a flat center zone when the plate is thin enough to bend its ends at a tighter radius. I think that’s a good idea to expand this experiment. However, i think that Torbjörn Zethelius made a good point a couple of years ago looking at the best preserved and supposingly the least played instruments from the workshop of Antonio Steadivari. The long arch of those instruments doesnt have a flat center. So there is a good chance that the flatted zone comes rather from deformation
 

I have already an idea to transform the f-hole slots to a sort of stylised f-hole design if necessary. 
 

concerning the cross arch in the zone above the F-holes I think it’s only a question of the overall rigidity in that area. 
 

With a sufficient thin plate I could make the experiment in the opposite direction bending the cross arch. But therefore I have to make a new rib garland reason for which I am starting with the long arch.

 

On this occasion experiment I  am not expecting any tonal miracles either but doing exact the opposite of what is assumed to be good is the best way to know if an assumption is correct. 

[Andreas Preuss]

8 minutes ago, Marty Kasprzyk said:

The cross grain stiffness with a flat plate and bass bar is very low.  Before you do your step 2  I suggest adding some cross braces to see how the frequency response curve changes.

Guitar makers use flat plates with various bracings to adjust its sound character.

I am thinking of strategically placed cross bars in order to keep them to a strict minimum. 
 

Recently I had the funky idea to use crossbars as a support to fix a regular bass bar with screws to the plate. This could make tonal adjustments with the bass bar very simple. You could then try different types of wood to adjust the weight and also change the direction of the bass bar quite effortlessly. If it’s worth doing  this way is open. 

[Don Noon]

46 minutes ago, Marty Kasprzyk said:

With closely spaced bracing like this, it should behave similar to a thicker, lower-density plate.  This would almost certainly lower the critical frequency response bump to something lower than 4 kHz (theoretically), although crossgrain it's likely still beyond hope to get the critical frequency in a useful zone.  The other question is what happens to the damping, with all that mismatched grain direction.

[uncle duke]

That particular guitar plate is laminate- spruce?, graphite and spruce again meaning in short, be careful with violin table experiments.

[Andreas Preuss]

7 hours ago, uncle duke said:

That particular guitar plate is laminate- spruce?, graphite and spruce again meaning in short, be careful with violin table experiments.

Since a while I enjoy not being careful.

But no, its not a Matthias Dammann guitar top of laminated spruce. (Which presumably has a higher density than 0.38g/cm3)
 

I want to understand certain principles. And overall I am interested in a construction allowing more possibilities of sound calibration than the classical method.

[LCF]

8 hours ago, Don Noon said:

With closely spaced bracing like this, it should behave similar to a thicker, lower-density plate.  This would almost certainly lower the critical frequency response bump to something lower than 4 kHz (theoretically), although crossgrain it's likely still beyond hope to get the critical frequency in a useful zone.  The other question is what happens to the damping, with all that mismatched grain direction.

Maybe there is a uniform effect for bulk properties in the low frequency zone but the multiple boundary conditions imposed by those structural cells could give interesting and complex resonance patterns at higher frequencies, ripples via multiple degrees of freedom. Whether that  might be useful is a different question! 

 

Glossing over a few very important  details it's interesting to note that the wavelength of sound in air at 4kHz is approx 80mm and assuming also that wavelength in the plate would be similar for radiation to occur, 80mm is in the size range of the convex cross arch area under discussion. 

 

 

[Marty Kasprzyk]

49 minutes ago, Andreas Preuss said:

Since a while I enjoy not being careful.

But no, its not a Matthias Dammann guitar top of laminated spruce. (Which presumably has a higher density than 0.38g/cm3)
 

I want to understand certain principles. And overall I am interested in a construction allowing more possibilities of sound calibration than the classical method.

I use a 0.6mm thick top plate with balsa wood braces for my violas. I change the brace's thickness, height and pattern to easily change the shapes of the violas' frequency response curves.

[Dr. Mark]

12 hours ago, LCF said:

4kHz is approx 80mm and assuming also that wavelength in the plate would be similar for radiation to occur, 80mm is in the size range of the convex cross arch area under discussion. 

Whoa there dude!  Take a deep breath...

[Andreas Preuss]

16 hours ago, Don Noon said:

With a nominally flat top that is being bent to create a longitudinal arch, presumably the arch will be a very gentle, fairly uniform long radius curve rather than being relatively flat along the middle and stronger arch in the upper and lower bouts.  In theory, such a gentle arch would have strong influence on the low frequencies and perhaps the transition hill, but behave about the same as a flat plate at the higher frequencies.  And no help from the crossarch.  It will be interesting to see what results you actually get.

In a carved plate there is no other way to go along the grain than making a relatively flat surface which follows as close as possible the grain direction. But as on a bent plate the grain goes always in the direction of the arching (provided that the flat plate itself was rather carved than sawn along the grain because any tree twists in ),  there is most likely no need to make a flatter area in the middle. 

I am with you in terms that the cross stiffness is an important factor for the outcome of high frequencies. However the means to achieve this are not limited to a tight crossarch. For high frequencies we need to watch the cross stiffness of all components. So I was always more concerned about

1. red flags in the X mode than the Ring mode on free plates, and in particular the X mode of the top plate, and

2. a rib garland which doesn't provide enough resistance (stiffness) to lateral movements.

3. Or you build a super heavy back which can maintain this sort of resistance over the corner blocks. (Thats how I see the constructions of Guiseppe Guarneri del Gesu.

It is IMO the total of the cross stiffness of the body which is an important factor for the outcome of high frequencies.  (as if a loose cross stiffness would lead to the evaporation of energy necessary for high frequencies) This is also supported by experiments doubling and tripling the linings on the top plate side which improved to some degree the behavior of the higher frequencies and overall loudness. (I admit that this is by far not enough to make it a magic recipe)

For my New Concept Violin my general idea is finding means to go flatter and eventually thinner on the top plate while maintaining the same structural stiffness.  At the moment I am trying to regulate this with bending the pre-bent top lengthwise, but if bending crosswise turns out better results, then I will most likely overthrow the old idea completely. I guess you agree that it it is wise to abandon ideas which prove to bring no positive results.

BUT!

here we go for the first result:

Some notes:

Sounded better than I expected especially in terms of sound volume. For the quality I still would like to have more coarseness.

For the bridge I took a normal bridge I had used before, with straight regular cut and to compensate for the missing height on the low arch I superglued tiny blocks of beechwood under the feet

String angle 159 (the neck dropped more than I had wished)

strings Jargar Superior

bridge weight 2.4g with the supporting blocks under the feet

arching height c.3-4mm

cross arching height above the f-holes c.1.5mm. (The cross arch height comes presumably from having created a higher arch on the flat top plate - with springing the bass bar on it - than the rib arch. So I had to press down the plate on the c bouts when closing the instrument.)

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

Now I am just wondering if I should follow the initial path of planned alterations, or if I should start with thinning from the outside and prolonging f-holes stepwise. Suggestions are welcome.

[Don Noon]

Do you know the speed of sound of the spruce?  

Assuming you started with 3.5mm thick, the critical frequency "bump" in the response should be around 3200 Hz (if theory is anywhere near correct).  With thinning, the response should improve in amplitude (lighter) and shift to higher frequencies.  Theoretically.

[Andreas Preuss]

2 hours ago, Don Noon said:

Do you know the speed of sound of the spruce?  

Assuming you started with 3.5mm thick, the critical frequency "bump" in the response should be around 3200 Hz (if theory is anywhere near correct).  With thinning, the response should improve in amplitude (lighter) and shift to higher frequencies.  Theoretically.

How could I measure the speed of sound? I have still the leftovers from cutting out the plate but no piece of the entire length of the board. 

The critical frequency bump is independent from arching properties? Anyway, what does it mean if the critical frequency is too high or too low, or the amplitude is too low?

 

[Don Noon]

2 hours ago, Andreas Preuss said:

How could I measure the speed of sound? I have still the leftovers from cutting out the plate but no piece of the entire length of the board. 

https://maestronet.com/forum/index.php?/topic/321492-ridiculously-easy-way-to-measure-speed-of-sound/

Davide Sora also put together a nice video of the method: https://www.youtube.com/watch?v=jU4h2Ievtq4

If you can cut a uniform cross-section stick 200 mm long or more, it should be pretty easy.  Less than 200 mm, the longitudinal resonance frequency gets pretty high, and might be hard to find.

2 hours ago, Andreas Preuss said:

The critical frequency bump is independent from arching properties? Anyway, what does it mean if the critical frequency is too high or too low, or the amplitude is too low?

For spruce and the thicknesses we're talking about, the critical frequency (longitudinal) is up in the 3 - 4 kHz range, where the bending waves in the wood are too short to be affected by the gradual arching.  The lower frequencies, yes, they will see the arching effect.

The "critical frequency" is where there's a maximum in sound radiating efficiency, and (again, theoretically) a hill in the response plot.  Whether it's at 3 kHz or 4 kHz is up to the listener to decide what it means to tone.  Amplitude is also affected by mass... again, it's all up to the tonal preference of the listener or player.

 

[LCF]

15 hours ago, Dr. Mark said:

Whoa there dude!  Take a deep breath...

No gain without breathlessness.

[Andreas Preuss]

23 hours ago, Don Noon said:

If you can cut a uniform cross-section stick 200 mm long or more, it should be pretty easy.  Less than 200 mm, the longitudinal resonance frequency gets pretty high, and might be hard to find.

Unfortunately I can't get a reliable measurement  for the speed of sound. I had a piece of 220mm length and after several attempts I found that most likely the speed of sound might be 5800m/s though this didn't come from the strongest peak. What would this tell me about the outcome of the graph?

[Don Noon]

When in doubt, 5800 m/s is a good guess for reasonably decent spruce... and that's what I use for my estimates.  Unless you have highly abnormal spruce, there's not much to say that would be different.

[Andreas Preuss]

I spent the whole day making alterations to the flat arch violin top. And now I am sitting at my computer trying to figure out why I liked some results. 

I didn't begin with augmenting the arching height, but decided first to mess around with the top plate as is. For a brief overview:

1. prolonging the f - holes
2. thinning the top above the f-holes
3. deepening the scoop at the C bouts 
4. reducing the thickness between the f-holes

I tried to condense the results to the essentials and eliminated in between steps which didn't really show any significant changes in the sound plot.

Here is the sound plot before I started. I corrected the neck angle otherwise everything is just as in the raw setup above. I played the instrument four times turning after each scale 90 degrees. Distance to the mic was approximately 1 m.

 BEFORE

Actually when I compared this graph to others taken from arched violins, one wouldn't assume that the top has almost no arching. (?)

I prolonged the f-holes in four steps starting with the treble side to see what happens when both f-holes have the same length. Then I continued by prolonging the f-hole on the bass side, again on the treble side and finally on the bass side again. To keep the disbalanced proportions the treble side f-hole got 16mm longer, the bass side f-hole 20mm longer. I used a very small thin saw to keep the surface area of the f-hole.

AFTER PROLONGING THE F HOLES

As can be seen there is hardly any difference. Maybe the region between 1.3 kHz and 3.5 kHz is more on one average level. Playing the instrument there was no obvious change in the sound. 

Then I decided to attack the zone which @Don Noon believes is critical for very high frequencies. So I started to thin down the area above the f-holes and under the fingerboard. I didn't measure how much material I scooped away but something between estimated .5 and 1.0mm. I didn't touch the area up to 2.5cm from the border and basically tried to lower the surface overall to the same degree. 

AFTER THINNING DOWN THE ZONE ABOVE THE F-HOLES

This alteration could be heard. And it got worse in the sense that the sound lost definition and clarity. 

So I stopped there and thought next it might be interesting to hear what happens when the scoop at the C bouts is digged out. First I scooped out the bass side from the widest point of the upper bout going down all the way to the widest point of the lower bout. If the area at the border is seen as a sort of hinge, the idea was to loosen the top plate from the rigid rib garland and give it more freedom to move. 

 

AFTER MAKING THE SCOOP ON THE BASS SIDE

I liked the sound at this stage best. I think the areas of the sound graph I marked with the green lines explain what I heard. The sound had the best definition so far and also a slight roughness. I think the well defined sound originates from the sound band between 12.3kHz and 3.0kHz. the averaged response which I marked with the green line goes slightly up. This is a rather rare feature. Additionally the decline between 4kHz and 7kHz is not too steep which seems to explain the light roughness of the sound. I only the two peaks above 3KhZ (yellow arrows) were more prominent it would have been even better. Thereafter I made the scoop on the treble side which didn't alter much, if anything the roughness got a bit smoothened out.

Since it is all experimental I went further on and reduced the thickness between the f holes. I was thinking of doing the reverse graduation, or at least going down from 3.5mm to 3.0mm didn't look too risky to me. But this alteration turned out to be quite disastrous as can be seen on the last graph. The sound became much weaker, lost definition and is a sort of colorless

AFTER REDUCING THE THICKNESS BETWEEN F-HOLES

 

[Marty Kasprzyk]

The 512 recording size is too low to show the reasonance peaks and their valleys in the low frequency range ( A0,B1-,B1+ etc.) whch are important to see.

[Andreas Preuss]

5 hours ago, Marty Kasprzyk said:

The 512 recording size is too low to show the reasonance peaks and their valleys in the low frequency range ( A0,B1-,B1+ etc.) whch are important to see.

I am focusing on the high frequencies here and just IMO you see better what is going on in low(er) resolution. I think also this reflects better the perception of the human ear which can't really spot single peaks but rather overall loudness. Anyway for completeness I inserted the graphs in 4096 resolution. The only thing which might be interesting there is the amplitude of the A0 resonance. 

Otherwise, to have a clearer picture of the high frequencies it might be interesting to look on peak density above 1.4kHz? In the end it looks to me like this: if a musician makes a description between a good and a bad instrument it is mostly about overtone behavior and this in particular when it comes to sound projection. 

[Tim M]

Quote

I liked the sound at this stage best. I think the areas of the sound graph I marked with the green lines explain what I heard. The sound had the best definition so far and also a slight roughness. I think the well defined sound originates from the sound band between 12.3kHz and 3.0kHz. the averaged response which I marked with the green line goes slightly up. This is a rather rare feature.

That makes sense to me. Dunnwald called the frequency band from about 1200 to 1800 (roughly) the nasal band. I think of it as the annoying part of the midrange, above "bass" and "boxy" and below "edgy". Anders Buen showed that Strads had relatively low output in those frequencies (something like 80% of the amplitude of the lower bands, and a similar proportion of that for the high-mids and low-highs). Interesting that you got that dip from thinning the top at the edges at the C-bouts. Is that what you mean by digging out the scoop?

[Marty Kasprzyk]

On 10/5/2026 at 9:46 AM, Andreas Preuss said:

>

For my New Concept Violin my general idea is finding means to go flatter and eventually thinner on the top plate while maintaining the same structural stiffness. 

>

 

 

George Bissinger concluded that a baffled flat wood plate had a higher sound production efficiency at frequencies below about 1000Hz than a typical arched plate violin or a thin walled cylinder as seen in the attached plot taken from his paper which is also attached

Acustica 05 UnifMatNModeVnAcoust.pdf