Lowest possible arching for the top - does it work with any material?

[Andreas Preuss]

19 hours ago, David Burgess said:

Sorry, Andreas, I have not yet experimented with every possible combination.

Lowest arching height posted so far? Probably zero (or a little less), on flat-topped fiddles. Those I have played so far didn't "give me a stiffy" , so I continue to make arched tops.

An zero arch is the absolute extreme and this wasn't really what I was thinking about. 

I know one maker here in Japan who sticks strictly to one figure (I think it was 15.5mm) and more than often I asked myself how this can make sense.

Teaditional measurements certainly have a low risk in messing up but maybe for the same reason 'something' in the sound is missing.

[Andreas Preuss]

17 hours ago, Don Noon said:

In my experiments, it appears that lowering the top arch reduces the B1+ frequency, but not the B1-.  On my one beater fiddle, I made a top with 8.5mm arch (from gluing surface to top, so the actual curvature was more like 5mm).  It was bad.  The B1+ was so low that it merged with B1- to make one supermode.  Wolfy  and uneven.  At 13.5mm, I made a couple of tops that worked reasonably.  Not great, but certainly functional.  For all these experiments, I used very good, stiff, torrefied wood.  Normal wood might want a higher arch.

Don, from what you are describing there I understand that wood treatment (in your case torrrified wood) can make the necessary difference from normal height to below normal height. And because torrefying increases the sound speed in wood this could be summed up in the following 

The higher the sound speed in the wood (eventually artificially enhanced with torrefying or similar) the lower the arching can be made. 

How low is in the end a question of trial and error. 

[Don Noon]

8 hours ago, Michael Szyper said:

I would expect a slab to have a higher crossgrain / longgrain stiffness ratio than a quarter from the same log. (With decreased overall stiffness). Am I wrong?

Yes... you are wrong... if I'm reading you correctly.  Quartered is stiffest crossgrain, slab less stiff, and ~45 degrees off-quarter is a wet noodle.

4 hours ago, Andreas Preuss said:

Maybe cross grain stiffness for the top in violas needs to be low but not on violins. 

I have had a variety of crossgrain stiffness on violins too, and haven't noticed a problem with the low-stiffness ones.  We take a huge bite out of crossgrain stiffness with the F-holes, intentionally.  I would not want to use top wood that was extremely low in longitudinal stiffness, though.

1 hour ago, Andreas Preuss said:

I know one maker here in Japan who sticks strictly to one figure (I think it was 15.5mm) and more than often I asked myself how this can make sense.

Because it works?

Actually, it turns out 15.5 mm is what I have settled on as my "standard" arch... a bit lower for my small-body model, and a bit more for my large pattern.  I might also go higher if I want a different tone (more refined, but less power?)

[Don Noon]

8 minutes ago, Andreas Preuss said:

The higher the sound speed in the wood (eventually artificially enhanced with torrefying or similar) the lower the arching can be made. 

How low is in the end a question of trial and error. 

While that seems to make sense, I don't have any actual trials to back that up.  It is also quite possible that the playability and tone issues described by Michael Appleman may dominate, and the material properties less so, if at all.  I would guess the latter.

Michael's description of his 12 mm arch seems similar to my 8.5 mm arch, although I suspect mine was more severe and unusable.  I have made 13.5 mm arch experiments that were OK, but not great, and 14.5 mm arch was in the zone of being very good.  And 17 mm that was good too.  But around 15-16 just seems to work best for me, and I'm not sure that the wood properties make that much difference (yet) on what arch to use.  There have been opposing opinions by some good makers, which is an indication to me that there is no definite right answer.

[Andreas Preuss]

28 minutes ago, Don Noon said:

Because it works?

Actually, it turns out 15.5 mm is what I have settled on as my "standard" arch... a bit lower for my small-body model, and a bit more for my large pattern.  I might also go higher if I want a different tone (more refined, but less power?)

So this means that you restrict the selection of your top wood to what works with this arch? 

Or would you dare to make 15.5mm with a heavier piece of spruce of lower stiffness (and lower sound speed)?

 

[Don Noon]

25 minutes ago, Andreas Preuss said:

So this means that you restrict the selection of your top wood to what works with this arch? 

Or would you dare to make 15.5mm with a heavier piece of spruce of lower stiffness (and lower sound speed)

It might mean that I wouldn't use any heavy, low-stiffness wood except for experiments, and that the wood I would use is in a relatively narrow range.

Or it might mean that I haven't been able to determine what the interrelation is between wood properties and arching.

Or a bit of both.

[Andreas Preuss]

2 hours ago, Don Noon said:

It might mean that I wouldn't use any heavy, low-stiffness wood except for experiments, and that the wood I would use is in a relatively narrow range.

Or it might mean that I haven't been able to determine what the interrelation is between wood properties and arching.

Or a bit of both.

Sounds almost like 'Maybe I know, maybe I don't' 

Or maybe we are searching the wrong equation? 

[Andreas Preuss]

23 hours ago, Marty Kasprzyk said:

One consequence of low arches is that the bridge has to be correspondingly higher to maintain bowing clearances.  Increasing the bridge height H while maintaining standard foot width W increases the  bridge H/W ratio (like cello bridges have).  This increased lever-arm in turn increases the bridge's vibration forces on the top plate during bowing which simultaneously increases both loudness and worsens any wolf notes.

If you want to try lower arch heights I suggest either decreasing the C bout width to achieve good bow clearance and/or using wider bridge feet.

 

If you plotted top plate arch heights vs. construction year for Amati, Stainer, Strad, DG violins you might conclude that the plates should be pretty flat by now.  But fossils show evolution stopped about 200 years ago.

So there is a chance that it has in reality more to do with the relation between bridge height and arch cross stiffness?

Lowering the arch means flattening the curves and more the cross arch than the length arch. At the same time the bridge feet can act more aggressively on the surface.

So there must be a point where the arch has just the resistance the bridge feet need?

And in practical terms a lower arch then needs a stiffer bass bar. (Or maybe a bar running diagonally over the top?

[Peter K-G]

Or change in wood supply or change in sound/music preferences or...

[Don Noon]

7 hours ago, Andreas Preuss said:

So there is a chance that it has in reality more to do with the relation between bridge height and arch cross stiffness?

...

And in practical terms a lower arch then needs a stiffer bass bar. (Or maybe a bar running diagonally over the top?

Some odd things happen with a lower arch.  I have observed that the M2 plate mode remains about normal, but the M5 is far, far lower than normal.  I think what's going on is that the arch doesn't stiffen crossgrain bending much, and the off-quarter angle of the steep areas actually wimpifies it.  With lower arch, it's closer to quarter-cut, and stiffer crossgrain.  Longitudinally, the arch puts more grain stretching into effect, rather than just pure bending as in a flatter plate, thus stiffer.

With these thoughts in mind, and if you HAD to use a low arch, perhaps you would want wood with extremely high longitudinal stiffness and not so much in crossgrain stiffness, and an extra-stiff bass bar.  This might get the signature modes in a better place, with more space between them. But I think the bass bar is limited in what it can do; my 8.5 mm arch experiment had B1+ around 50 Hz lower than normal, and you'd need a huge beam of a bass bar to compensate for that.

However, that wouldn't compensate for other low-arch side effects, i.e. bridge height and wolfing, and also tonal effects.  I think that low arching puts more power into the transition hill area, and weakens the highs, giving a more "boxy" and unrefined sound if it's too low.  And for me, going under 14.5 mm arch would be worrisome regardless of wood properties, unless I was building a fractional size.

[Andreas Preuss]

1 hour ago, Don Noon said:

Some odd things happen with a lower arch.  I have observed that the M2 plate mode remains about normal, but the M5 is far, far lower than normal.  I think what's going on is that the arch doesn't stiffen crossgrain bending much, and the off-quarter angle of the steep areas actually wimpifies it.  With lower arch, it's closer to quarter-cut, and stiffer crossgrain.  Longitudinally, the arch puts more grain stretching into effect, rather than just pure bending as in a flatter plate, thus stiffer.

With these thoughts in mind, and if you HAD to use a low arch, perhaps you would want wood with extremely high longitudinal stiffness and not so much in crossgrain stiffness, and an extra-stiff bass bar.  This might get the signature modes in a better place, with more space between them. But I think the bass bar is limited in what it can do; my 8.5 mm arch experiment had B1+ around 50 Hz lower than normal, and you'd need a huge beam of a bass bar to compensate for that.

However, that wouldn't compensate for other low-arch side effects, i.e. bridge height and wolfing, and also tonal effects.  I think that low arching puts more power into the transition hill area, and weakens the highs, giving a more "boxy" and unrefined sound if it's too low.  And for me, going under 14.5 mm arch would be worrisome regardless of wood properties, unless I was building a fractional size.

Interesting, Don.

The Poggi had 13mm. Maybe I should make an Audacity graph for reference. 

[Emilg]

5 hours ago, Andreas Preuss said:

Interesting, Don.

The Poggi had 13mm. Maybe I should make an Audacity graph for reference. 

There have been some threads about low arching in the past. This is an interesting one about old Italians, Melvin mentions a few in the 12-13mm range:

 

[curious1]

As Don said, arch height does not seem to affect cross grain stiffness much but as the arch is lowered  the plate will need to be left thicker to maintain longitudinal stiffness. A thicker plate will increase cross grain stiffness in relation to longitudinal stiffness. The relational difference between M2 and M5 leads to all sorts of secondary effects in the transition range and bridge hill and the ensuing tonal differences.

Lower arches sound different generally because the cross grain bending is relatively stiffer.

[Don Noon]

22 minutes ago, curious1 said:

Lower arches sound different generally because the cross grain bending is stiffer.

I was hoping you'd chime in on this, since I know you pay a lot of attention to this kind of thing.

In addition to crossgrain bending considerations, there is also the "ring mode" effect, which is a function of the radius of curvature and the speed of sound in the material (note: it is independent of thickness).  Since lower arching must have a larger radius of curvature, there will be a significant effect on the ring mode frequency.  I suspect that this is the reason that some aspects of violin tone seem to remain nearly constant even after significant regraduation.

I should note that in higher arching, the radius of curvature is smaller and the ring mode should be higher... but then with the steeper angled cuts, the speed of sound will be much lower locally... it's complicated, as usual.

[curious1]

21 minutes ago, Don Noon said:

I was hoping you'd chime in on this, since I know you pay a lot of attention to this kind of thing.

In addition to crossgrain bending considerations, there is also the "ring mode" effect, which is a function of the radius of curvature and the speed of sound in the material (note: it is independent of thickness).  Since lower arching must have a larger radius of curvature, there will be a significant effect on the ring mode frequency.  I suspect that this is the reason that some aspects of violin tone seem to remain nearly constant even after significant regraduation.

I agree

 

21 minutes ago, Don Noon said:

I should note that in higher arching, the radius of curvature is smaller and the ring mode should be higher... but then with the steeper angled cuts, the speed of sound will be much lower locally... it's complicated, as usual.

ya, gets complicated fast

 

[Andreas Preuss]

Getting back to this.

If a flatter arching is better for a higher cross grain stiffness it should be possible to get a similar effect by setting the direction of the yearrings on a slight angle to the underside of the plate.

[Don Noon]

20 minutes ago, Andreas Preuss said:

If a flatter arching is better for a higher cross grain stiffness it should be possible to get a similar effect by setting the direction of the yearrings on a slight angle to the underside of the plate.

If you mean the usual idea of joining the plates so that the slanted rings make a V at the center, then yeah... the overall plate crossgrain stiffness should be higher.  But now the plate is slightly less stiff in the middle, and more stiff away from the centerline.  It will be different... but unclear what the net acoustic effect would be.

[Marty Kasprzyk]

About fifteen years ago I wondered why violins used arched plates whereas most guitars used flat plates.  I have now made 22 differently designed violins and violas using flat plates to see what problems might result and occasionally I've shown photos of these on MN.

These have been reinforced on their inside surfaces with various lattice bracing schemes often used in guitars.  The brace number, width, and height in both the longitudinal directions and cross directions can be varied independently thus the longitudinal to cross direction stiffness can adjusted over a very wide ranges to see what happens.  This can't be done with standard arched plates.

Reducing the cross direction stiffness (lower and fewer cross braces) increases loudness but excessive reduction increases wolf note severity.  This is similar to what happens with over thinning arched plates.  But this can be then corrected by adding more cross braces afterward and many back and forth brace change iterations can be easily done.

It is expected in new product development engineering (like evolution in nature) that design changes will lead to a convergence to a desired goal optimum.  However my instrument's sound characters seems to be diverging and my results keep on getting wider and wider.  In vibration systems this is an "under damped" oscillation and in human behavior studies it would be credited to a scatter brained kid not having sufficient adult supervision (damping).

 

[Davide Sora]

3 hours ago, Andreas Preuss said:

Getting back to this.

If a flatter arching is better for a higher cross grain stiffness it should be possible to get a similar effect by setting the direction of the yearrings on a slight angle to the underside of the plate.

 

2 hours ago, Don Noon said:

If you mean the usual idea of joining the plates so that the slanted rings make a V at the center, then yeah... the overall plate crossgrain stiffness should be higher.  But now the plate is slightly less stiff in the middle, and more stiff away from the centerline.  It will be different... but unclear what the net acoustic effect would be.

The answer to get stiffness features more similar to a flat board could be a bent plate, if you like it.

[Andreas Preuss]

 

9 hours ago, Don Noon said:

If you mean the usual idea of joining the plates so that the slanted rings make a V at the center, then yeah... the overall plate crossgrain stiffness should be higher.  But now the plate is slightly less stiff in the middle, and more stiff away from the centerline.  It will be different... but unclear what the net acoustic effect would be.

Ok, let's put it like this. We can't predict with any precision what happens but we know at least that the reversed v shape at the center joint must be avoided. 

 

[Andreas Preuss]

7 hours ago, Davide Sora said:

 

The answer to get stiffness features more similar to a flat board could be a bent plate, if you like it.

I tried to bend plates for my super light violin project. If you do this you need to fit the ribs to the crooked plate underside especially at the corners. 

Another possibility is actually if you don't start with a flat underside of the top plate. This would be only as much as you can bend it down to the ribs once the plate is thin and flexible enough. 

[Andreas Preuss]

8 hours ago, Marty Kasprzyk said:

Reducing the cross direction stiffness (lower and fewer cross braces) increases loudness but excessive reduction increases wolf note severity.  This is similar to what happens with over thinning arched plates.  But this can be then corrected by adding more cross braces afterward and many back and forth brace change iterations can be easily done.

That's quite interesting. However, the all-over acoustical behavior of arched plates must be different somewhere.

In general I think we don't spend enough time to look on the wood we are using. 

For the arching then medullary rays become in a certain way interesting because they run perpendicular to the year rings. 

[Three13]

9 minutes ago, Andreas Preuss said:

I tried to bend plates for my super light violin project. If you do this you need to fit the ribs to the crooked plate underside especially at the corners. 

Another possibility is actually if you don't start with a flat underside of the top plate. This would be only as much as you can bend it down to the ribs once the plate is thin and flexible enough. 

Aren’t the top ribs of Del Gesu’s violins tapered just past the upper bout so that the top is bent slightly?

[Don Noon]

23 minutes ago, Andreas Preuss said:

 We can't predict with any precision what happens but we know at least that the reversed v shape at the center joint must be avoided. 

How do we know that?  It seems reasonable, but I certainly don't know it for a fact, as I have never tried it.  I have tried plenty of terrible things that shouldn't work, and usually the results weren't as bad as you'd think.

[Andreas Preuss]

5 hours ago, Three13 said:

Aren’t the top ribs of Del Gesu’s violins tapered just past the upper bout so that the top is bent slightly?

Not only DG but basically all violins made originally in Baroque style. 

I doubt that the purpose was bending the plate.