Rib Taper hypothesis #43,759

[sospiri]

Because the belly has bookmatched boards, when they are bent down 2mm onto the block, they are effectively being bent 2mm in opposite directions.

The right board bent 2mm to the right of how it was growing and the left board 2mm to the left.

I have no idea what to make of this, since the stresses will change after glueing (olde English spelling) but at least it's something to console my enquiring, inquiring mind with until the days lengthen again.

Feel free to lambast, debunk, ridicule etc.

[Delabo]

Perhaps that's why them  made them a little thicker on the corners to help alleviate some of that stress ?

Sort of dividing the length into three ?

[Andreas Preuss]

I wonder if 'to the left' and 'to the right' really matters.

 

[sospiri]

51 minutes ago, Delabo said:

Perhaps that's why them  made them a little thicker on the corners to help alleviate some of that stress ?

Sort of dividing the length into three ?

The intention of the slope from the side to the middle seems to have  been to increase the stress, or at least introduce an extra tension.

15 minutes ago, Andreas Preuss said:

I wonder if 'to the left' and 'to the right' really matters.

 

If the boards are bookmatched then the tapers are effectively in opposite directions relative to the vertical growth of the wood. So a 2mm taper is effectively a 4mm taper.

Does this work with non bookmatched tops I wonder? I have to think about that one. 

I'm just looking for reasons to include traditional methods or reject them. The Cremonese rib taper is something I have to rationalize before I can proceed. I want a reason to include it or ignore it. And wouldn't it be better to have a good reason to include it?

Imagine how good we could feel if we could convince ourselves we had unravelled another of Stradivari's secrets, maybe? Perhaps?

 

[Delabo]

5 minutes ago, sospiri said:

The intention of the slope from the side to the middle seems to have  been to increase the stress, or at least introduce an extra tension.

Well that's the theory, but has it ever been proven ?

Is it  a sort   of  ((((((((boing))))))))))  ((((((((((boing)))))))) effect that the theory is aiming at ?

The wood resonates better under stress ?

I guess a drum skin is a bit like that - and a wooden ruler on the edge of a school desk like we all use to play around doing when the teacher was boring.

 

[sospiri]

1 hour ago, Delabo said:

Well that's the theory, but has it ever been proven ?

Is it  a sort   of  ((((((((boing))))))))))  ((((((((((boing)))))))) effect that the theory is aiming at ?

The wood resonates better under stress ?

I guess a drum skin is a bit like that - and a wooden ruler on the edge of a school desk like we all use to play around doing when the teacher was boring.

 

It's not a theory. It's really only hypothetical. And we don't even know if the 2mm rib taper was on the belly and back or just the belly. I'm going with the latter because it fits the hypothesis.

What we do know is that the neck block was 2mm lower than the upper corner blocks. It was measured as such even before Vuillaume got his hands on any Strads.

 

[Andreas Preuss]

2 hours ago, sospiri said:

The intention of the slope from the side to the middle seems to have  been to increase the stress, or at least introduce an extra tension.

If the boards are bookmatched then the tapers are effectively in opposite directions relative to the vertical growth of the wood. So a 2mm taper is effectively a 4mm taper.

 

The only comment I can make on this is that I once made a violin and forgot to do the taper. 

So I made the effort to open it carve the taper with all sorts of tools around the neck root (some quite annoying work) and close the fiddle again. The tonal change was on a pure subjective level just nothing. 

Otherwise I think it was Carlo Bergonzi who didn't taper the ribs from upper corner blocks to top block. (I don't know from the top of my head if this applies to all of his instruments) So we can ponder how important this feature is in respect to sound.

[sospiri]

14 minutes ago, Andreas Preuss said:

The only comment I can make on this is that I once made a violin and forgot to do the taper. 

So I made the effort to open it carve the taper with all sorts of tools around the neck root (some quite annoying work) and close the fiddle again. The tonal change was on a pure subjective level just nothing. 

Otherwise I think it was Carlo Bergonzi who didn't taper the ribs from upper corner blocks to top block. (I don't know from the top of my head if this applies to all of his instruments) So we can ponder how important this feature is in respect to sound.

Do you taper the back and belly? I was thinking of tapering just the belly. 

[Andreas Preuss]

23 minutes ago, sospiri said:

Do you taper the back and belly? I was thinking of tapering just the belly. 

Only the belly. But honestly since the correction experiment, not any more with any thoughts towards sound. 

I think there is a reason to taper the back of double basses and gambas. I would rather be interested to know if this concept was transferred to violins in a transformed manner.

I am thinking often how the order of assembly can be used to find tune the sound. (Regardless if this was old Italian method or not)

If the back is glued last one could to a certain degree fine tune the inner air volume. With a taper from upper blocks to top block this would facilitate it I practice because you wouldn't need to plane over the large top block- neck root area. Never tried it but might be worth a shot.

or just increasing the taper should in theory change the leverage force at the neck root.

Playing around with such thoughts is interesting, if such thoughts bring the postulated sound-trigger-effect is a different matter. 

[sospiri]

4 minutes ago, Andreas Preuss said:

Only the belly. But honestly since the correction experiment, not any more with any thoughts towards sound. 

I think there is a reason to taper the back of double basses and gambas. I would rather be interested to know if this concept was transferred to violins in a transformed manner.

I am thinking often how the order of assembly can be used to find tune the sound. (Regardless if this was old Italian method or not)

If the back is glued last one could to a certain degree fine tune the inner air volume. With a taper from upper blocks to top block this would facilitate it I practice because you wouldn't need to plane over the large top block- neck root area. Never tried it but might be worth a shot.

or just increasing the taper should in theory change the leverage force at the neck root.

Playing around with such thoughts is interesting, if such thoughts bring the postulated sound-trigger-effect is a different matter. 

I agree with the leverage hypothesis because it is logical and demonstrable physics.

I agree it might be connected to ease of assembly, but it is just as easy to dismiss this idea.

The volume hypothesis doesn't hold water because the taper on Strads is only in the upper block area.

I don't  agree with Bruce Carlson's aesthetics hypothesis. If it was done to improve the look, then why not taper all the way from the lower corners. 

I think Strad's ribs were 1 1/4 inches and they haven't shrunk in height only in length.

1 1/4 inches is 31.75 mm and most of them still are.

The block height doesn't fit so well into inches. But the compass marks on the moulds have been linked to these measurements.

In searching for a reason, the realisation of the left and right opposition effectively doubling the bending suddenly came to me recently. 

[David Beard]

A geometry stiffness is introduced. Side to side resistance to neck movement is increased.  Simple geometry.

[Michael_Molnar]

A bend increases stiffness.

[David Beard]

The 'box' formed by plates and side is changed.

Consider a bookcase made rectangular with four equal sidea. No shelves or cross bars. Corners hinged.

This shape can eaily shift side to side.  The top and bottom will stay parallel is this structure shifts side to side.

Now change the top of this case to shorter than the bottom.  Now the case is in a trapezoid form instead of a rectangle.

You can still easily shift side to side, but when you do the too and bottom boards won't stay parallel, the top board will now strongly tilt as you collapse the case side to side.

 

And, I'm sorry, I misspoke in the first post.  It is in and out of plane motion at the neck that is inhibited, not side to side.    And, its not out of plane bending at the neck that is stiffened, by out out of plane motion of the upper bout sides and neck in the same direction.  The taper will to some digree act to oppose that freedom.

[ctanzio]

9 hours ago, Michael_Molnar said:

A bend increases stiffness.

To be clear, it depends on the direction of the loading.

Consider table with a thin, flat top. A weight placed at is center will cause the top to noticeably deform downward.

Bend the flat top into an upward arch. That same weight will now cause less downward deformation of the top in the direction of the load.

Now place one side of the flat table against a wall and give a push on the other side. It would greatly resist any deformation. But an arch top table would deform more in the direction of the push.

I do not see a 2mm slope in the ribs doing anything to increase load resistance of the plates. It is just not enough of a geometrical change to the basic shape of the plates to offer much help. It would, however, introduce measurable stresses in the box, and I see two possible advantages of this:

1. Stressing the plate due to the taper would change the frequencies of the natural modes of vibration. Like tightening a drum head.

2. The bend along the taper would place the belly into tension along its length. After stringing up the violin, the tension would be relieved as the belly is bent back due to the string loads at the scroll box and tailpiece peg. Prestressing beams and plates in the opposite direction of an expected applied load is an old and well-practiced engineering trick to allow a thin geometry to handle a larger load without buckling.

Or maybe an ancient maker screwed up a rib when trimming the linings and said, "Oh well, I will taper the rib on the other side the same amount and add a little extra glue because Don Giovanni wants his new violin and I do not have enough wood to cut new ribs." The Don was so happy with his exotic looking violin that soon all the other makers in the village were tapering their ribs.

 

 

 

[sospiri]

1 hour ago, ctanzio said:

 The bend along the taper would place the belly into tension along its length. After stringing up the violin, the tension would be relieved as the belly is bent back due to the string loads at the scroll box and tailpiece peg. Prestressing beams and plates in the opposite direction of an expected applied load is an old and well-practiced engineering trick to allow a thin geometry to handle a larger load without buckling.

 

The bend doesn't change after stringing up. The neck bends upwards, but not at the neck root.

[sospiri]

10 hours ago, Michael_Molnar said:

A bend increases stiffness.

 

10 hours ago, David Beard said:

The 'box' formed by plates and side is changed.

Consider a bookcase made rectangular with four equal sidea. No shelves or cross bars. Corners hinged.

This shape can eaily shift side to side.  The top and bottom will stay parallel is this structure shifts side to side.

Now change the top of this case to shorter than the bottom.  Now the case is in a trapezoid form instead of a rectangle.

You can still easily shift side to side, but when you do the too and bottom boards won't stay parallel, the top board will now strongly tilt as you collapse the case side to side.

 

And, I'm sorry, I misspoke in the first post.  It is in and out of plane motion at the neck that is inhibited, not side to side.    And, its not out of plane bending at the neck that is stiffened, by out out of plane motion of the upper bout sides and neck in the same direction.  The taper will to some digree act to oppose that freedom.

They must have had a reason that involved both form and function. It was never just form, always form and function. These design concepts go back thousand of years.  So the more people give and opinion about possible functional reasons, the better.

[ctanzio]

1 hour ago, sospiri said:

The bend doesn't change after stringing up. The neck bends upwards, but not at the neck root.

The laws of physics say otherwise. When the neck bends up, it applies a shear and bending load to the violin box at the neck root. The violin box must deform to develop counter shear and bending loads or else the neck will continue to bend upwards until it snaps off.

 

[uncle duke]

1 hour ago, sospiri said:

The bend doesn't change after stringing up. The neck bends upwards, but not at the neck root.

how do you know that?  we all know you're just shooting in the dark per say.

since this is fiddle #1 for you flatten the bottom ribs first, scribe your 31.75 mm all around, bring upper ribs down to where they are all even height and then taper from upper belly corner blocks to neck to at least a one mm taper - a little more if you think you can.  Then taper the bottom ribs around a 1/2 mm or leave flat. 

Tapering of ribs is the least of your worries.

[Andres Sender]

Sometimes the truth is a little backwards from the common conception, i.e. the fingerboard scoop isn't to add string height in the middle, it's to reduce string height at the end.  Similarly, perhaps the taper wasn't to reduce the air volume, but rather to preserve the feel for the player when the air volume was increased.  That way we are looking at a greater air volume change, the serving of the needs of a community known to be sensitive to change, and integrating with the difference in rib height that (arguably?) occurs around that time.

[sospiri]

4 hours ago, ctanzio said:

The laws of physics say otherwise. When the neck bends up, it applies a shear and bending load to the violin box at the neck root. The violin box must deform to develop counter shear and bending loads or else the neck will continue to bend upwards until it snaps off.

 

The neck root will move by a tiny amount, the neck, a little more. How this is related to the rib taper, I have no idea.

[David Burgess]

1 hour ago, sospiri said:

The neck root will move by a tiny amount, the neck, a little more. How this is related to the rib taper, I have no idea.

The neck root is connected to the top and back, which are connected to the ribs, which are connected to the scapula, and thence connected to the leg bone.

Someone should write a song about that so these things can be as easily learned as the ABC's, or the names of "the twelve disciples".

I too do not understand how the rib taper makes anything stronger, beyond a year or two, since wood is such a plastic material. So far, I am more inclined to go along with Bruce's theories of it being an aesthetic consideration. But I am not prepared to rule out that it might have been some sort of superstition.

[Michael Darnton]

Just noting that supposedly early Amatis were tapered from one end to the other. No idea for sure if it was on the front or the back :-) Don't know when it stopped or if they always did that to the end. At the moment I have an exceptionally clean one from the mid 1600s that tapers evenly and it *appears* to happen on the top side, but that's just an impression. Also, in spite of the really stellar condition of this violin, I can't guarantee that the rib heights are original.

Roger H's suggestion that Strad's taper on the front, from the upper blocks upward enabled Strad to tilt the neck back a couple of degrees more while still continuing the projection of the top/rib joint sounds like the best idea for this to me.

Andres' idea is interesting in that it starts to solve the problem the chin rest eventually solved, and keeps the player's left arm happy at the same time. On the bass they do the back so the player can get his body over more towards the front---doing it on the front would have no advantage--but the violin situation is different.

[Michael_Molnar]

I too agree with Hargrave’s theory. My point about the bend was that it changes ever so slightly the top plate dynamics. Nevertheless, that was not the compelling reason to implement it.

[David Beard]

We don't know why.

[Jim Bress]

The tapering of the upper bout ribs always reminds me of the "grandma's ham" story. I see examples of violins where the c-bout ribs appear to have less height than the bouts. Just pictures, so no measurements support what's actually happening, but it's not a good look. For me, this lends some credibility to Buce's hypothesis. I taper the top from the upper blocks, but see no reason to get fussy about a precise amount of taper.  It's just turned into a working practice at this point.

Grandma's ham:

A young girl was watching her mother bake a ham for a family gathering and noticed her mom cutting off the ends before placing it in the oven.

“Mom, why do you cut the ends off before baking the ham?” she asked.

“Hmmm… I think it helps soak up the juices while it’s baking. I’m not sure, though. That’s just the way your grandma always did it, so I’ve just always cut them off. Why don’t you call grandma and ask her?”

So, the little girl phoned her grandma and asked “Grandma, mom is making a ham and cut off the ends before placing it in the oven. She said that it’s probably to help soak up the juices but wasn’t sure. She said you’d know because she learned how to cook from you.”

“That’s true. I do cut off the ends of the ham before baking. But I’m not sure why either. I learned how to cook from my mom. You should ask her.”

So, the inquisitive little girl called her great grandmother and asked “Great grandma, mom and grandma said they learned how to cook a ham from watching you. Do you cut off the ends of the ham to help it soak up the juices?”

The great grandmother chuckled. “Oh, no sweetie. I just never had a pan big enough to hold a whole ham, so I always had to cut off the ends to make it fit.”