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Peter K-G

Modern violin mensur and setup

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After some creative discussions with Jacob and David Burgess in topic:

Fingerboard wedge instead of correcting neck angle - http://www.maestronet.com/forum/index.php?/topic/328814-fingerboard-wedge-instead-of-correcting-neck-angle/

 

I have learn some valuable simple basics about why modern setup is how it is. There is a lot of discussions about 158º string angle over the bridge top. From modern mensur and maths we can see where the 158º comes from, but it is difficult to achieve because the tailpiece side is likely to be ~76º
this would make an angle of 155º.

 

To clearify this we need to fix some parameters so to not go into endless mind crunching:

 

1. Fixed string lenght of 330 mm between nut and center of bridge top
2. Fixed base line of 180º for neck/nut and body length to center of bridge 130/195 mm
3. Backside of the bridge is perpendicular to the 180º base line.
4. The Angle calculated on the neck side is between strings and bisector through the bridge

 

Maths don't lye, we will get half of the 158º (79º) with modern setup (325/330). Again following the above fixed parameters.

 

This would then be the correct illustration and calculation, using Lady Blunt Stradivari as an example:

 

post-37356-0-09742700-1375346691_thumb.jpg

 

 

 

 

 

 

 

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Hi Peter....I don't know how relevant it is to your calculations but the Lady Blunt setup is not really modern. The neck overstand is about 3mm lower than modern standard.

 

Good point! That's the reason why the "baseline" is located way below the top/rib joint on this particular violin.

 

Thanks

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I don't wish to poo-poo the question, or the search for a formula, but I've dealt with so many old fiddles that simply don't conform to the norms.

I take a look at the arching height, make the saddle, the overstand, and the elevaion a bit higher or lower, depending on how I feel it should be, and hope for the best. I make the bridge look right, and importantly, feel right- when you straighten the bridge it should feel comfortable when it's standing correctly.

I don't know that making detailed measurements help so much on violins, perhaps a little more on cellos.

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Peter,

I loved the diagram. Unfortunately, theoretically, at least, a key aspect is simply wrong.  The angles on either side of the bridge MUST be equal, or else the resultant force will tend to tip over the bridge.  In practice, they might be found as you present them, but still, there will be a tendancy to tip over the bridge. Well, I guess that is good for violin repairpersons, who will get more work, making new bridges.

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After some creative discussions with Jacob and David Burgess in topic:

Fingerboard wedge instead of correcting neck angle - http://www.maestronet.com/forum/index.php?/topic/328814-fingerboard-wedge-instead-of-correcting-neck-angle/

 

I have learn some valuable simple basics about why modern setup is how it is. There is a lot of discussions about 158º string angle over the bridge top. From modern mensur and maths we can see where the 158º comes from, but it is difficult to achieve because the tailpiece side is likely to be ~76º

this would make an angle of 155º.

 

To clearify this we need to fix some parameters so to not go into endless mind crunching:

 

1. Fixed string lenght of 330 mm between nut and center of bridge top

2. Fixed base line of 180º for neck/nut and body length to center of bridge 130/195 mm

3. Backside of the bridge is perpendicular to the 180º base line.

4. The Angle calculated on the neck side is between strings and bisector through the bridge

 

Maths don't lye, we will get half of the 158º (79º) with modern setup (325/330). Again following the above fixed parameters.

 

This would then be the correct illustration and calculation, using Lady Blunt Stradivari as an example:

 

attachicon.gifNeckAngle_Mensure_Calc.jpg

 

 

 

 

 

 

 

This reminds me of a math test question:

imagem07.pdf

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That is simply Pythagorean theorem.

 

a² + b² = c²

3² + 4² = c²

9 +16 = 25

 

c = 5

 

Peter, I still don't get the reason for the position of the base in your drawing. Can you explain ?

 

r.

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Peter,

I loved the diagram. Unfortunately, theoretically, at least, a key aspect is simply wrong.  The angles on either side of the bridge MUST be equal, or else the resultant force will tend to tip over the bridge.  In practice, they might be found as you present them, but still, there will be a tendancy to tip over the bridge. Well, I guess that is good for violin repairpersons, who will get more work, making new bridges.

I'm not sure what reference line you mean for the angles to be equal to, but if we are using the plane of the top of the ribs as "horizontal", I don't think I've ever seen a violin with both angles equal, or even very close to it. The tailpiece side is always steeper than the neck side, IME, and that would seem to be the primary reason  the bridge centerline is tilted back, although it often seems that the resultant of the string tension vectors often still lands much closer to the front of the bridge, or sometimes even in front of it. This does tend to produce a bending / overturning moment, FWIW, but friction usually overcomes this as already mentioned. Have I been seeing things wrong all these years?

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Peter I just thought I would also point out that a right angle will not bisect a triangle unless that triangle is isoceles. (Both sides are the same length.)

That being said you have got me looking into this subject with more care so I owe you a big thanks.

 

Cheers.

 

r.

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Hi Peter,

 

I do not understand why you eliminated both the saddle height and the thickness of the tailgut in your calculation as both contribute to diminishing the string angle at the bridge. I also agree with Melvin that the Lady Blunt is not a completely modern setup and probably should not be used as an example.

 

Bruce

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My goodness Peter, is there anything of this bone left at all on which to chew?

 

Now, here are some FACTS:

 

1. Since it is NOT POSSIBLE, violin setups from Andrea Amati have never even approached this equal angle theory of yours.

2. Forget about your bridge wedge of 3º - the angle over the bridge is split at the point where the bridge makes contact with the strings. As I've said before, you could have a bridge with a wedge width of 30º if you like - it will still make no difference. If you deduct 3º from the front angle, you are FUDGING your numbers, plain and simple.

3. As others have mentioned, you "baseline" is meaningless.

 

You, like the rest of us, will have to learn to live with a back angle of around 77º, and a front angle of around 81º - at best (from your point of view).

 

It will be salutory experience for you to read Roger Hargrave's recent (February and March) two-part article on Baroque neck sets. You will see that the parameters you are mentioning were IDENTICAL on original Stradivari violins - fingerboard projection, bridge height, string angle, split of front and back angle.

 

Dude, you are wasting too much energy on mental wild goose chases.

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PS - your "baseline" should be from the nut apex to the saddle apex. Nothing else makes any sense whatsoever.

 

For some obscure reason you derive the baseline from the rib surface - how on earth do you get to that? It's the next best (worst) thing to saying the earth is flat.

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Peter I just thought I would also point out that a right angle will not bisect a triangle unless that triangle is isoceles. (Both sides are the same length.)

That being said you have got me looking into this subject with more care so I owe you a big thanks.

 

Cheers.

 

r.

 

 

:)  It's not easy to get the all the terms right for a non mathematician.

 

 

Hi Peter,

 

I do not understand why you eliminated both the saddle height and the thickness of the tailgut in your calculation as both contribute to diminishing the string angle at the bridge. I also agree with Melvin that the Lady Blunt is not a completely modern setup and probably should not be used as an example.

 

Bruce

 

The thickness of the sadle and tailgut are not elimineted:

 

bridge = 32 mm

top arch = 15 mm

sadle + gut = 9 mm

tan(θ) = opposite/adjacent

θ = tan-1(160/(32+15-9))

θ = 76,64 °

 

The tailpiece side angle is not calulated from the yellow baseline, but from the blue baseline, because it's unknown where the yellow baselin will cross the tailpiece line.

 

The violin is only there as an illustration, so it's easier to picture the whole thing in our minds

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Jacob,

 

My point is;

They are not equal and it's almost impossible to get them equal!

That's what I have learned and what the illustration is all about  (I have not gone over to the dark side) :)

 

I will read Rogers article and looking forward to it because one other thing that is starting to develop is exactly that:

Was there even a difference between old and new setup/projection?

 

This is very interesting because it goes to the fundamentals of the violin sound

 

Peter

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PS - your "baseline" should be from the nut apex to the saddle apex. Nothing else makes any sense whatsoever.

 

For some obscure reason you derive the baseline from the rib surface - how on earth do you get to that? It's the next best (worst) thing to saying the earth is flat.

 

I see now that the purpose of your "baseline" is to determine a vertical stance for the bridge in relation to the rib (or perhaps top) surface.

 

Be that as it may, the baselin, whatever or wherever it is, won't affect a given angle for the strings over the bridge. What you need to do is, working with your baseline, accept that the angle of the strings over the bridge happens at ONE POINT, and that two triangles created by that split have a COMMON BORDER, TOP TO BOTTOM. The big red herring remains the incorporation of some sort of bridge wedge thickness in delimiting the two triangles.

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This may be a trivial and irrelevant observation for what's going on here, but that 330 vibrating string length, to middle of bridge, is a bit on the long side, by about 1 or 2 mm, judging from the modern fiddles I have with 130 and195 neck and stop lengths. 

 

While that 330 (as opposed to 328, + or - a mm) number may make no difference in the calculations being done here (I don't know that one way or the other), I would worry that someone might think that 330 should be a standard and start leaning a bridge way back, too far back, or start shuffling bridge feet around to come up with that 330 number.

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Was there even a difference between old and new setup/projection?

 

 

According to Roger, very little if any (talking SPECIFICALLY about Cremonese/Strad setups.

 

As for it being about the "fundamentals of sound": a violin is a very unnatural instrument, and playing it is a very unnatural physical procedure. For me it is about compromises to make the best of a bad case. Forget about optical, ergonomic or mathematical ideals.

 

An ideal scenario would be where there is no more than just the barest amount of pressure on the top, like a guitar, in which case the strings then can't be bowed, both because the strings are strung over a flat bridge, unreachable by a bow, and because strings with that little upward pressure from the bridge can't take bow pressure - etc, etc.

 

Making a violin work is like having a guy in intensive care on breathing aparatus, while being 100 meters under sea  dressed only in a raincoat, but still  productively catching fish at the same time.

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This may be a trivial and irrelevant observation for what's going on here, but that 330 vibrating string length, to middle of bridge, is a bit on the long side, by about 1 or 2 mm, judging from the modern fiddles I have with 130 and195 neck and stop lengths. 

 

While that 330 (as opposed to 328, + or - a mm) number may make no difference in the calculations being done here (I don't know that one way or the other), I would worry that someone might think that 330 should be a standard and start leaning a bridge way back, too far back, or start shuffling bridge feet around to come up with that 330 number.

 

It is not trivial and irrelevant, because that's how it is practice. This will make the angles about 82/76

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PSS - you might as well draw your baseline from the top of the overstand to the top of saddle, it will give you a clearer idea of what what's going on. If a violin were a theorbo/chittarone (4' neck), you would need an extra page for your version of the "baseline". In other words, it doesn't need to originate from the nut. Your baseline is sort of parallel to the rib surface, so it's immaterial how low you decide to start. Your starting points are the string angle, and the rib surface. But leave out the bridge "wedge" in your calculations, it's not applicable.

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It is not trivial and irrelevant, because that's how it is practice. This will make the angles about 82/76

 

Peter,

 

What I'm saying (and I could be wrong) is that in practice, in actual, well set-up violins with 130 and 195 neck and stop lengths, the vibrating string length (from where the string leaves the nut to middle of bridge measuring along the G string) is about 328, maybe 329, but seldom 330.

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It is not trivial and irrelevant, because that's how it is practice. This will make the angles about 82/76

 

It is indeed trivial and irrelavent (see my previous post). Your theory/ideal rests upon two elements - and overall string angle, and what happens when they are split in a violin setup context.

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:)  It's not easy to get the all the terms right for a non mathematician.

 

 

 

The thickness of the sadle and tailgut are not elimineted:

 

bridge = 32 mm

top arch = 15 mm

sadle + gut = 9 mm

tan(θ) = opposite/adjacent

θ = tan-1(160/(32+15-9))

θ = 76,64 °

 

The tailpiece side angle is not calulated from the yellow baseline, but from the blue baseline, because it's unknown where the yellow baselin will cross the tailpiece line.

 

The violin is only there as an illustration, so it's easier to picture the whole thing in our minds

I can now see how you are calculating by subtracting edge thickness, saddle height and tailgut thickness. I didn't see your thin blue line. Nonetheless you are speaking of an ideal situation where both of your yellow right triangles would have to be the same size (330 x 325 x 57.2) in order to obtain equal angles on either side of the bridge. A situation that in real violins is going to be an extremely rare occurrence.

 

I also agree with skiingfiddler that the vibrating string length is usually around 328 mm. I know Paganini's Cannon is 330 mm but the neck is short and the body stop is long, increasing even more the difference between the two angles.

 

Most bridge warp is from the musician not checking the position on a regular basis.

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PSS - you might as well draw your baseline from the top of the overstand to the top of saddle, it will give you a clearer idea of what what's going on. If a violin were a theorbo/chittarone (4' neck), you would need an extra page for your version of the "baseline". In other words, it doesn't need to originate from the nut. Your baseline is sort of parallel to the rib surface, so it's immaterial how low you decide to start. Your starting points are the string angle, and the rib surface. But leave out the bridge "wedge" in your calculations, it's not applicable.

 

 

It is indeed trivial and irrelavent (see my previous post). Your theory/ideal rests upon two elements - and overall string angle, and what happens when they are split in a violin setup context.

 

I don't understand Jacob, are you trying to argue, when I'm saying all the time YOU ARE RIGHT :)

But I'm proving it from a different viewpoint that is very simple:

 

sin(θ) = opposite/hypotenuse

=> θ = sin-1(325/330)

θ = 80 °

sin(θ) = opposite/hypotenuse

=> θ = sin-1(325/328)

θ = 82 °

 

The tailpiece angle is almost allways 76 °

 

Peter

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OK Peter, sorry, if I seem like I'm arguing. It's just that you use too many parameters and too many calculations for something which is about as simple as cracking an egg.

 

But, just for the record - have you been able to let go of your bridge wedge yet? Hopefully you understand by now why I call it "mathematical alchemy".

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The two givens which we are all working with here is (a) the string angle over the bridge, and the pointS at which the bridge splits this angle, and where it contacts the top (this is a POINT, not a range, in other words, forget the "wedge").

 

 

 

Jepp, and the drawing is not the same as in the other topic. This new updated illustration divides the angle over the bridge straight through the bridge. The -1 degree only shows that it makes hardly no difference even if someone wants to add the bridge in the calculations to force/fabricate an equal split (as I did in the other topic)

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