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How does a violin reproduce overtones? - Theorizing a model


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I think basically so.

I believe electrical theory includes the notion that energy will take the easiest path.  And I think a similar thing happens with vibrations.

But with vibrations, it seems to be frequency dependent.   

High frequencies and high noose seem very ready to roll around in anything that kinda of presents as a stiff shell.

Lower frequencies want to setup as standing waves, either at a natural resonance frequencies, or driven at a frequency not too far from a resonance.

But it seems to take a bit more energy for these lower waves to set up.  When that doesn't happen, energy seems to readily go instead to higher harmonics and high noise.

 

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2 hours ago, Andreas Preuss said:

Question: Is it really coincidence that the area where Colin Goughs Stress diagram shows the highest stress is the zone where Don Noon measured most of the overtone output? 

I am familiar with Colin's work on mode shapes, but I don't recall any analysis of plate stresses. You would need to provide a reference for me to look at.

The term "most of the overtone output" needs further clarification. The shapes of many modes may show significant deflection in the same general area. If this area is relatively thin and far from strong support areas, like the garland, sound post and bass bar, it would not be surprising to see high stresses.

 

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My opinion, as related to Don's response is that the correlation "seems" to be related and they are but they are not, it's more of a default than anything else, meaning

The thinner, less mass areas are obviously prone to more excitation than thicker areas , but it's not because of "stress" as Don says, but in my option it's simply because the thin areas reside next to thick areas. Thick areas can be used to "direct" or "send" vibrations to thin areas by simply acting like water canals that "drain" "steer" "direct" "send" "move" vibration energy to thin areas. IMO this is the meat and potatoes of understanding "graduation" and "just what is it we are trying to do here?" 

Thin areas act like "pools with a drain"" for vibrations , if you had a round plate 1/2" thick and in the very center you took a "wood ice cream scooper" and removed an area and made a area 2 mm thin, and then attached a driver , we would definitely be able to measure more motion/excitation in the thin area 

If a plate were at 2.5 mil equally over the entire surface, once force is applied via the strings, to the bridge , the downforce would compress the top and at this point the individual characteristic of that particular piece of wood would start to kick in and the plate would "settle" ie. distort to it's load carrying shape, now assuming we had a bassbar and post in, and the violin stays structurally sound at this point once compressed and "settled" there may be areas where distortion has occurred that will have "extra" stress induced via bulging stresses locally where distortions have happened, and even though everything is 2.5, those "bulges" which can cause "arches within the arch" that is small compressive forces creating concave areas which create convex distortion locally next to the "diveted area" Those micro undulations will "act" as if they were "thicker" even if they are not, they are simply areas "bolstered by micro curved distortions" And thus if we did a 3d map you would still see that areas would be more or less elastic and more or less excited than others just like a "regular" carved top that of course will not be a dead nuts 2.5 everywhere.

And so it is the "map"of graduations, the thick and the thin, along with the inherent characteristics of the piece of wood that will allow you to "choose" where you would like things to "do things"  like move more here than there....then you simply have to refine this by being able to as Ervin Somogyi says "build to stress"

Long ago we had a discussion about how I was doing what I was doing, and that is all about looking for ranges of motion in my flexed/stress plates, and how one can train there hands to have repeatable results as well as be able to work around any type of wood characteristic

that why I can make make instruments from several different types of species materials and get basically similar results  and have them all sound like "me"

Really it's all about developing refined mechanical sympathy , but with wood.

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The only way I'm going to verify the following is to start playing violin again - the overtones come from the upper bout section.  Weather or not it is a belly, varnish, or a back plate issue I really can't pinpoint. 

I'm enamored with classical guitar again - forgive me.

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I have weight the Ouvry violin I have before and the weight fully loaded for playing was 480 - 490 grams.  His is the best I have for overtone production while being played.  For myself, losing unneeded gram weights with wood works for me but apparently didn't matter much to he.  Must be something else but who am I as a fiddle maker?  Nobody yet.

My first thoughts are what Mr. Z mentioned to Don - use really good wood.  Then there is arching and then varnish, imo.  Could be a certain rib height along with corpus length.  Just my guesses.    

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1 hour ago, Don Noon said:

It is also a deflection diagram, which is very different from a stress diagram.

You say ‘also’ and my understanding is that deflected areas must be under stress.

In any case, the sound box reacts differently if you try to take the stress away. I think Marty’s violins demonstrate this pretty conclusively.

String angle variations DO alter the stress conditions and a clearly audible. The lighter the body becomes the more crucial the string angle will be.

 

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1 hour ago, Andreas Preuss said:

1) You say ‘also’ and my understanding is that deflected areas must be under stress.

2) In any case, the sound box reacts differently if you try to take the stress away. I think Marty’s violins demonstrate this pretty conclusively.

3) String angle variations DO alter the stress conditions and a clearly audible. The lighter the body becomes the more crucial the string angle will be.

1) My "also" was referring to Jezzue's comment.  Your understanding about deflected areas being under stress is not generally correct, although in any specific case there might be some relation.  But again, as it relates to vibration properties, neither stress nor deflection amount to anything significant in a violin body.

2) No, and No.  Marty's violins demonstrate that if you make something radically different, you can get radically different results... but not why.  A violin tuned to half tension will still have basically the same response profile*, and that's a much more direct test.

3) String angle involves lots of other variables... arching height, bridge height, overstand, neck angle, saddle height.  It is impossible to separate out cause and effect when changing string angle, since you have to change some else to accomplish the string angle change.  Try keeping the string angle the same, but raise the bridge 2 mm, and see if there's an audible change.  IMO any audible effect of changing string angle is more likely a side effect of what you had to do to change the angle.

*response to a given input.  Of course, playing a violin at half tension will have a very different response... but it it the strings that are responding differently.

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I'm not so sure for a driven system that string tension is quite so irrelevant?

I suspect the post and bar, in relation to the bridge feet and string tension serve as a sort of crossover system that is quite sensitive to the string tension.

For some frequencies, the post will look immovable, and for other frequencies it will look movable.  Same with the bar.  The frequencies that can move the post and bar I suspect will change with a large change in string tension.   And, these things will change the balance of frequencies and energy that travel certain physical paths and drive certain parts of the violin and it's response.

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5 hours ago, Don Noon said:

String angle involves lots of other variables... arching height, bridge height, overstand, neck angle, saddle height.  It is impossible to separate out cause and effect when changing string angle, since you have to change some else to accomplish the string angle change.  Try keeping the string angle the same, but raise the bridge 2 mm, and see if there's an audible change.  IMO any audible effect of changing string angle is more likely a side effect of what you had to do to change the angle.

Yes, but this was not my point.

if you have a given soundbox and change only the string angle (with raise or lower pitch from the neck) without changing the bridge height, it does change the overall sound.

(Changeing the angle with bridge modifications does of course change other important parameters from the side of the bridge)
 

I see this in relation to the overall stiffness of the sound box and thinly built instruments are more sensitive to string angle changes (adjustments) than brick type of instruments.I have done this now often enough on my new concept violin and there are repeating patterns. One interesting thing is that if I string the NCV down put it away for only a day and string it up again the tension has not set in which can be seen at the too low string distance to the fingerboard. Once the tension has equalized it settles down where it was before, Sound changes are audible between just strung up and one day later. 

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9 hours ago, David Beard said:

The frequencies that can move the post and bar I suspect will change with a large change in string tension.

Why?  Mass will be unchanged, so the stiffness of the body would have to change.  How does string tension change the stiffness of the body?  

One thing that will change: tailpiece mode frequencies as determined by string/tailgut suspension, and those can certainly impact what the instrument does.

 

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To give an example to reinforce Don's comment about the difference between deflection and stress:

Consider a cantilever beam fixed at one end, i.e., a beam sticking horizontally out of a wall, and subject to a point load some distance from the wall.

The deflection will be highest at the free end, but the stresses will be highest at the fixed (non-deflected) end. 

Strain (relative change in deflection per unit length) is strongly related to stress. If everything in some small area is deflecting by mostly the same amount, the area will experience small strain and thus small stress, but can show a dramatic deflection.

Deflection diagrams can also misleading unless the boundary constraints are based in some real-life scenario. In the case of a real cantilever beam projecting out of a wall, we know the deflections are relative to an actual, physically fixed end of the beam. So we can intuit something about the deflection and possible strains and stress throughout the beam.

But what about a violin sitting on a table top. Is there any point actually physically constrained relative to the deflection of the rest of the violin? Turn it on it side. The deflected shape of the violin does not change. We say the violin is an "unconstrained body" and we must arbitrarily selected a point where all degrees of freedom are specified as zero to stop the numerical solution from blowing up. One would normally illustrate that point on a deflection drawing so one could judge relative deflection among the various parts of the object.

As a final point in what has surely turned into an excessively long-winded rant on the science of solid mechanics, notice that the areas of high deflection on the violin diagram are all about the same color. That means the material in those areas have all deflected about the same amount, which means they are most likely under low strain which implies low stress. This is assuming the deflections are taken along the same direction.

 

 

 

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1 hour ago, Don Noon said:

Why?  Mass will be unchanged, so the stiffness of the body would have to change.  How does string tension change the stiffness of the body?  

One thing that will change: tailpiece mode frequencies as determined by string/tailgut suspension, and those can certainly impact what the instrument does.

 

Does this not go back to "by product" stress? , meaning the string tension is creating the downforce on the bridge , the bridge translates that force to the top, the top then compresses , creating the "arches within arches" at which point we could "assume" "by product" stress would be created in the peaks of the double arches ? as well as the area around the bridge ? So thus if we reduced the tension and thus downforce , would this not create less by product stress? 

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1 hour ago, Don Noon said:

Why?  Mass will be unchanged, so the stiffness of the body would have to change.  How does string tension change the stiffness of the body?  

One thing that will change: tailpiece mode frequencies as determined by string/tailgut suspension, and those can certainly impact what the instrument does.

 

Maybe I'm wrong. 

Won't the cantilevered twisting relationship between the post, treble bridge foot, and the treble area of the bridge foot change?

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59 minutes ago, David Beard said:

Won't the cantilevered twisting relationship between the post, treble bridge foot, and the treble area of the bridge foot change?

According to my measurements and rough calculations, string tension might add ~2% to the structural stiffness of the body at the bridge... IF the string deflection is 1:1 with the bridge motion.

However, the relevant factor is the mode center of rotation relatve to the nut/saddle line... i.e. if the mode rotation is about that line, then the string isn't being deflected in a way that causes a string restoring force.  And most modes that I am aware of have centers of rotation rather close to that line.

It ain't gonna be much.  

 

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12 minutes ago, Don Noon said:

According to my measurements and rough calculations, string tension might add ~2% to the structural stiffness of the body at the bridge... IF the string deflection is 1:1 with the bridge motion.

However, the relevant factor is the mode center of rotation relatve to the nut/saddle line... i.e. if the mode rotation is about that line, then the string isn't being deflected in a way that causes a string restoring force.  And most modes that I am aware of have centers of rotation rather close to that line.

It ain't gonna be much.  

 

What I'm mostly think of is the twist of the bridge island by the post pushing up and the treble bridge foot pushing down.

The downward push of the bridge foot is almost entirely from the strings.

Changes in this little twist seem likely to be the quickest and therefore the highest frequency movements of the top.

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45 minutes ago, David Beard said:

What I'm mostly think of is the twist of the bridge island by the post pushing up and the treble bridge foot pushing down.

The downward push of the bridge foot is almost entirely from the strings.

Changes in this little twist seem likely to be the quickest and therefore the highest frequency movements of the top.

Would that not be somewhat dependent on the backs stiffness? as the post is supported by the "floor" or back. This to me is one of the head scratcher's in that in my own instruments on occasion, as well as many examples out there, we can have some pretty dramatic graduation differences with some pretty thick spine'd backs, where the back would seem to be much stiffer,much more resistant to body curl from the pulling forces as compared to thinner more flexible backs that would seem to deflect much more than a thick spine'd one , yet I heard both thin and thick back violins sound good, which leads to I think the agreed on "well the top is doing most of the work"

I would think a thinner backed instrument would undulate under dynamic states much more than a thick one and certainly would resist twist more? We may be getting into Reguz territory on this one

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Seems like there's the continuing concept of static stress somehow influencing body vibrations, which to first order it doesn't.  If you want to think about static stress squishing out some micro-clearances between the top and the post or bridge foot, which would change mode stiffness primarily in the higher frequencies... go ahead.  I have no measurements to argue with for or against.

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50 minutes ago, Don Noon said:

Seems like there's the continuing concept of static stress somehow influencing body vibrations, which to first order it doesn't.  If you want to think about static stress squishing out some micro-clearances between the top and the post or bridge foot, which would change mode stiffness primarily in the higher frequencies... go ahead.  I have no measurements to argue with for or against.

Ok. I think I get the point.  As long as the static load is enough to preengage all the material flexes involved, and not so much as to crush or overwhelm any of the flexures, then the amount of load doesn't change material stiffnesses or the system in that way.

However, intuitively something stills seems wrong in this.

 

It seems like the tension of the post setting matters greatly in terms of practical results.  But how can this tension be important but the string tension not be important.  That's confusing.

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20 minutes ago, Don Noon said:

Seems like there's the continuing concept of static stress somehow influencing body vibrations, which to first order it doesn't. 

Using the preliminary "Burgess Soundpost Setting" technique I'm thinking static stress could influence vibration.

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23 minutes ago, David Beard said:

It seems like the tension of the post setting matters greatly in terms of practical results. 

It's on my list of things to investigate, as it is counter to basic theory.  I have just been putting in posts with the same modest force every time, so I don't have experience with how big of a deal it is.

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