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Kallie

Does these tailpieces really "Enhance" tone?

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the force required to produce a given deflection (by plucking, bowing or stopping the string) depends on the total string length from peg to tailpiece. I assume this is what Jerry means by "flexibility".

John

I am not trying to be thick headed or confrontational about this but could you explain why a string stopped by the nut and bridge at it's respective ends will act differently because of the lengths beyond the stopping points? Other than small increased movement of the stopping points ( the dog on a leash) I don't see why this would make any difference.

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I would think that theoretics aside this would be easy enough to test with an apparatus like those the bow makers use for measuring the flexibility of sticks. I can say with some experience that it is a truism in the guitar world that the longer the afterlendth from the bridge to the tailpiece, the "softer" the "action" the player feels for the same note. Floyd Rose invented a locking devise at the nut that had players drilling holes through the neck of expensive guitars to supposedly increase the sustain. I never quite believed that one but many did.

 

I have made quite a few angled tailpieces for small violas, on request. And I have listened to quite a few arguments like these pro and con as to the effectiveness of this sort of tailpiece design. I can also tell you that it is not a new breakthrough as stated but has been tried many times in the development of instruments of all types. Jerry might know that Rene Morel thought it was bunk.     

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Add in the stick/slip of the bow and it relates to violin family instruments.

 

I think it is far more than that... guitars tend to have extremely low break angles over the nut and bridge, in the violin family it can get extremely high.  This makes for much higher normal force at the nut, thus much higher friction.  Even with graphite lubrication, I would imagine the friction coefficient of ebony is far higher than the hard plastic usually used on guitars.  I have been gluing in a tiny piece of guitar saddle plastic in my fiddle bridges lately under the E string, and it seems extremely slippery.

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I think it is far more than that... guitars tend to have extremely low break angles over the nut and bridge, in the violin family it can get extremely high.  This makes for much higher normal force at the nut, thus much higher friction.  Even with graphite lubrication, I would imagine the friction coefficient of ebony is far higher than the hard plastic usually used on guitars.  I have been gluing in a tiny piece of guitar saddle plastic in my fiddle bridges lately under the E string, and it seems extremely slippery.

No doubt. However the percentage of after length and peg box length is much higher than guitars, and I would propose that the stick/slip of the bow is much more sensitive than a plastic pick.

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John

I am not trying to be thick headed or confrontational about this but could you explain why a string stopped by the nut and bridge at it's respective ends will act differently because of the lengths beyond the stopping points? Other than small increased movement of the stopping points ( the dog on a leash) I don't see why this would make any difference.

Nathan, this is only a small correction to the force required to deflect a string. Most of the force is due to overcoming the transverse component of the tension in the string and this is independent of any length other than the vibrating string length. It's only when you consider the fact that when you deflect a string you also stretch it to a (usually very slightly) longer length that you have to consider the entire length of the string. I have no idea whether this very small correction affects the playing characteristics in any way. 

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My mind just keeps going back to the issue of pitch vs amplitude... if you can feel a compliance difference between one setup and another, using the same string, then the "stiffer" setup would just have to go sharp with strong bowing, picking, plucking, or whatever.  Logically, I don't see how you can have one difference without the other, unless your sensitivity to compliance is far finer that your sensitivity to pitch.

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This is what intrigues me.

I have to say I'm not really interested in the theoretical properties, only the ones one can hear or feel - and I concede that some people may be more attuned to this than others.

But wouldn't less compliance (feeling "looser") give greater pitch deviation?

I have a feeling that this may be a good quality (aesthetically) as long as it's not taken too far. It's perhaps the reason why some people find Eudoxas (very low tension) friendly where I find them unpleasantly pitchy!

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My mind just keeps going back to the issue of pitch vs amplitude... if you can feel a compliance difference between one setup and another, using the same string, then the "stiffer" setup would just have to go sharp with strong bowing, picking, plucking, or whatever. Logically, I don't see how you can have one difference without the other, unless your sensitivity to compliance is far finer that your sensitivity to pitch.

I do not disagree, in fact the example I used earlier with the bass and a digital tuner, you can see the pitch drift with more bow pressure.

We agree that the compliance increases with a longer after length right?

I do not know if all strings don't have some pitch drift at some level.

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compliance = pliability/elasticity?

think I got that back to front  :)

Then yes, more afterstring = more compliance. But is it perceptible on a violin string?

All strings have pitch drift, though bowing makes this a feature of the sustained note in a way that plucking doesn't.

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compliance = pliability/elasticity?

think I got that back to front :)

Then yes, more afterstring = more compliance. But is it perceptible on a violin string?

The compliance changes the stick/slip of the bow. As the compliance increases the deflection or "stick" before the "slip" changes, at the same point on the vibrating string length everything else remaining the same.

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compliance = pliability/elasticity?

think I got that back to front  :)

Then yes, more afterstring = more compliance. But is it perceptible on a violin string?

All strings have pitch drift, though bowing makes this a feature of the sustained note in a way that plucking doesn't.

good question.

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Martin,

There are two major sources of compliance that are distinctly different.

 

1 - That due to nominal tension of the string.  This provides most of the resistance to deflection, but in a linear way that does not affect pitch.  Think of an extremely stretchy string (like Evah A's).

 

2 - That due to the longitudinal stiffness of the string, such that deflection actually increases the tension, making it non-linear and out of pitch when played hard.  Steel strings are generally stiff in this way... but it depends on how much the string has been stretched to reach nominal pitch.

 

You can have a high-tension, stretchy string (like the Evah A) which will have a low compliance but stay in tune, or a low-tension string with a non-stretchy core (think of a low-tension steel string, if such things exist), which would have a high (but non-linear) compliance and be pitchy.  Added stretchiness at the pegbox or afterlength won't do much for the Evahs, but would have an effect on the second example.

 

Bending stiffness of the string can also enter theoretically, but I think that's negligible for what we've been discussing.  It might be important for the higher harmonics of the string, though.

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I think of string tension similar to systolic and diastolic blood pressure.  You have the tension at rest, and the tension under bow pressure.  At least it helps me to think of it that way.  I imagine that some of the flexibility of the bowed string comes from the string pivoting over the bridge and nut more than pulling back and forth past it, although it's surely some of both.  Imagining the bridge as a pivot point, and the tailpiece as a counterbalance might help in thinking how the components are interacting.  I think we want the maximum string tension of the bowed string to fall within a certain range, which is dependent on the flexibility of the string, as well as the instrument and it's setup.  As such, tailpiece choice is dependent on the sum of other factors.  

 

I've never tried the compensated after length tailpieces, but they've been around long enough that if there was some real merit they would probably be more widely adopted.  I tend to think that when there is a very strong preference for a specific measurement such as after length there is probably good reason even if we can't explain it.  I could imagine, though, that there may be a specific circumstance where the tailpiece would be ideal.  Perhaps where a more flexible lower string is desirable.  If your low strings are temperamental as bow pressure increases it may be worth trying this sort of tailpiece or perhaps a lighter tailpiece.  I think this is more or less in agreement with Jerry's earlier comments on viola C strings and sounding point.

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I did a quick calculation for a plain steel violin E string deflected by a distance of 3mm at its midpoint.

Ignoring string stretching I get the force required to be about 2.5N. Including string stretching requires a maximum extra force of 0.05N. This is the case for zero after length. Increasing the after length decreases the force required by about 1.6mN per cm.. So i reckon the "compliance" changes produced by after length changes are on the scale of 0.1% per cm. It's pretty linear as long as the after length is small compared with the total string length. Very small effect i would say.

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Hi Don,

I'm still struggling to understand the two forms of compliance - can you make that idiot-proof?

Are these two types of compliance present in all strings, or are you saying that some behave one way and others another?

If the former,I suppose I don't understand how the nominal tension and the longitudinal stiffness can act separately or be perceived separately.

Am I right that one is purely to do with the pitch assigned to the string, and the other is purely to do with the material of the string? If so, these are theoretical properties, not individual qualities which could be perceived separately ...

confused  :blink:

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I did a quick calculation for a plain steel violin E string deflected by a distance of 3mm at its midpoint.

Ignoring string stretching I get the force required to be about 2.5N. Including string stretching requires a maximum extra force of 0.05N. This is the case for zero after length. Increasing the after length decreases the force required by about 1.6mN per cm.. So i reckon the "compliance" changes produced by after length changes are on the scale of 0.1% per cm. It's pretty linear as long as the after length is small compared with the total string length. Very small effect i would say.

A quick experiment would be:

Set up a cello with a 1/6 after length and play it, then change the after length to 1/5 and play it.

Do you feel a difference in the compliance?

Do the same thing with a player and pay close attention to her/his bowing between the two, did it change? Did she/he tighten the bow?

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Hi Don,

I'm still struggling to understand the two forms of compliance - can you make that idiot-proof?

Are these two types of compliance present in all strings, or are you saying that some behave one way and others another?

If the former,I suppose I don't understand how the nominal tension and the longitudinal stiffness can act separately or be perceived separately.

Am I right that one is purely to do with the pitch assigned to the string, and the other is purely to do with the material of the string? If so, these are theoretical properties, not individual qualities which could be perceived separately ...

confused  :blink:

 

Not really two forms, better to think of it as two contributions.

To understand why there are two contributions, bear in mind that when you deflect a string by a given amount you also increase its length slightly.

 

To a first approximation, the string is treated as perfectly flexible (i.e. the increase in length requires no force). The force required to deflect the string is then just given by the component of the string tension in the direction of deflection. It's the same maths that's used to determine string downforce on bridge, if that's helpful.

 

If the string is not perfectly flexible (i.e. has finite stiffness), then stretching it to the new, displaced total length requires an extra force (=cross sectional area of string X Elastic modulus of string X fractional change in length). This is the term that includes the after length, since the fractional change in string length = change in length/total string length (including after length). 

 

The second term is only a small correction, as I said before. Does that help?

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Don, I'm not understanding how string length from nut to bridge would change due to nut slippage.  Again, guitars are the only thing I know about, but when you increase tension on a string, it stretches.  On a guitar, the distance from the nut to the saddle of the bridge cannot change.  The slippage at the nut allows this extra length to be taken up on the tuning machine.  One popular retrofit for steel string guitars is a nut made of a Teflon composite to allow easier slippage.  With a violin, I don't know.  The problem with a violin is that the bridge is not hard fixed like on a guitar.  Also, I imagine that the bridge material with it's slots might be more binding.  If that were the case, I can imagine that the bridge could tilt slightly one way or another due to the stretching of the strings.  In that case, the length would change but if the string slips over the bridge then the length would remain fixed.  That little plastic sleeve over the e string used to protect it from digging into the bridge should allow slippage on that particular string.

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Hi Don,

I'm still struggling to understand the two forms of compliance - can you make that idiot-proof?

 

Try this thought experiment, and see if it helps:

 

Instead of the usual setup, imagine the nut is replaced by a frictionless bearing, and the string tension is provided by a weight and gravity.  Then, no matter how far you deflect the string, the tension will remain constant in the string, and the weight will just rise and fall accordingly, so that the total string length remains constant.

 

Now, take the above example, and weld the string and bearing solid.  Now when you deflect the string, there will be the original force from the pre-tension, PLUS some extra tension due to the fact that you are now stretching the string when you deflect it.  How much extra tension you get depends on the longitudinal stiffness of the string... if it was steel, the increase could be considerable; if it was rubber, not so much (actually, it depends on how much the string was stretched elastically to get to the pre-tension value, but that might be too much information).

 

Don, I'm not understanding how string length from nut to bridge would change due to nut slippage. 

 

I'm not sure I understand the question.  I think the basic concept is that when you deflect a string, you change the length, you change the tension (however slightly)... and since that will be different from the tension in the forelength and afterlength, there must be some slippage to equalize the tension, or friction must be high enough to prevent slippage. (edit:  or the bridge can deflect too, without slippage)

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I think the basic concept is that when you deflect a string, you change the length, you change the tension (however slightly)... and since that will be different from the tension in the forelength and afterlength, there must be some slippage to equalize the tension, or friction must be high enough to prevent slippage.

 

Or the bridge moves. I think it's the flexible bridge on a violin that makes the afterlength affect how the strings feel. Think of when you first string up a violin. As you tune the instrument up to pitch the bridge will lean forward. Even with the strings not fully to pitch the bridge will move before the friction in the string grooves is overcome. 

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To further prove my point I just did a little experiment. If you pluck the d-string on a violin then press down on the string behind the bridge you can simulate a faint vibrato (with the note going sharp). I think this is because the bridge is moving. If you do the same again and pull sideways on the string in the pegbox the pitch doesn't change, because the string isn't moving in the groove at the nut.

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As far as I understood, the more tension of the E string will pull the tailpiece, the pivot is on the endpin, and the tailpiece will twist slightly towards the G string. To alleviate some tension on the E string you could make a longer afterlength, placing the E hole further (and the fine adjustment), which is exactly the opposite of what you see in the Frirsz tailpiece. But at the same time, in the Frirsz, the G hole is closer to the belly plate, making the angle more acute at the bridge, increasing the pressure on the G side, and this maybe can balance the tailpiece, but how much, I don't know.

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