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Double Bass String Tension and Angle Across the Bridge

jmlee

jmlee

Catgut? Not funny.
Supporting Member
Jun 16, 2005
5,788
14,999
Halifax, Nova Scotia
bme.medicine.dal.ca
#1
Tonight my new Bass Player magazine came. Kind of makes me look forward to going to the bathroom. But that's another story...

In this issue, Ed Friedland reviewed a new King-type plywood upright optimized in a bunch of ways for slap playing. He noted that the angle made by the strings going over the bridge was shallower (closer to flat, I guess) than is typically the case and he suggested that this resulted in lower tension in the strings.

Now call me a crotchety old physicist, but where I come from string tension is completely determined by frequency (pitch), mass/length of the string, and string length. The angle a string might make coming over the nut or bridge don't enter into it. (Although I do buy his other point that it might influence the likelihood of breaking a string while wailing away on it in a slapping frenzy.)

Have I missed something here?
 
#3
I have a theory on this, but i dont feel like starting a flame war. Heres the bottom line of it: For more than redundant reasons the flatter angle creates less tension. I'll try to come up with an educated paragraph on my theory in a bit.
 
#4
The tension on the strings is the same, regardless (a string in-tune is always the same tension). What changes is the tension on the bridge. This rages from 0 if the strings are simply passing over with little/no contact, to the same tension as the strings if the force is completely in line with the bridge (parallel).

Bridge tension and string tension are related, but operate separately. You cannot alter the string tension without changing the tune.
 
#5
Jay, that's the first bit of sense I've ever read on this classic question.
So the next question is... If the bridge tension is lower, how might the strings feel easier to play?
Thorny physics questions are often easiest solved if you think about energy. I guess there's a fixed amount of stored energy in the tension of the string. Plus variable stored energy in compressed bridge, depending on angle. Perhaps these two energy stores combine to create the feel of playability in a string?
Not a complete theory, but it's a start.
 
#6
jayscheuerle said:
The tension on the strings is the same, regardless (a string in-tune is always the same tension). What changes is the tension on the bridge. This rages from 0 if the strings are simply passing over with little/no contact, to the same tension as the strings if the force is completely in line with the bridge (parallel).

Bridge tension and string tension are related, but operate separately. You cannot alter the string tension without changing the tune.
Click to expand...

I had a higher saddle put on my bass for just this reason. The top on my Arvi is gradually settling, and my luthier wanted to reduce the pressure. It's easy to understand why this works by imagining the extremes.

First, think of the case where the bridge is below the level of the nut and the saddle - no tension on the bridge, no downward tension on the top. Now, imagine that the bridge is extremely tall - the string tension is almost all directed downwards onto the top.

Of course, making a change like this affects other things, too. For instance, with less downward pressure on the bridge, things might ring more freely. But they might also reduce the extent to which the vibration of the strings drives the top.

My bass didn't come out sounding appreciably different, at least not to my uninformed ear, so whatever changes seem to have more or less cancelled each other out.
 
#7
There's another factor here: the friction between the string and the bridge. Like any physicist, I imagine extreme cases.

Extreme Case 1: Infinite friction between the string and the bridge. In that case, the tension in the string between the bridge and nut will be independent of the tension on the string between the bridge and the tailpiece.

Extreme Case 2: Zero friction between the string and the bridge. In that case, the tension in the string between the bridge and the tailpiece must be exactly the same as that between the bridge and the nut.

In the real world, no matter how much graphite I put in the notches on my bridge, there is some friction there, and the string will have higher tension beyond the bridge than in the playing area. Since both static and sliding friction have a dependency on the normal force acting down on the the bridge, the shallower the angle made by the string (tailpiece-bridge-nut), the lower the normal force, the lower the friction, and the lower the string tension between the bridge and tailpiece when the bass is tune to pitch. I don't think there's much impact on the tension where we're playing or how we perceive the resistance of the string to flexure; however, we all know that a shallower angle means less pressure on the top of the bass and less transmission of vibration from the string through to the top.

I still don't get where Ed was going, even presuming that he was referring to the tension between the bridge and tailpiece, not the tension between the bridge and nut.
 
#8
jmlee said:
In the real world, no matter how much graphite I put in the notches on my bridge, there is some friction there, and the string will have higher tension beyond the bridge than in the playing area.
Click to expand...

I believe it is equally likely to be the other way around, given your stated conditions.

jmlee said:
...however, we all know that a shallower angle means less pressure on the top of the bass
Click to expand...

Indeed.
 
#10
My experience has been that reducing the breakover angle at the bridge usually results in the player reporting a lowering of the perceived tension in the strings. I wonder if this is a by-product of the different way the top table is driven by the bridge. Or perhaps when the top table is under more pressure it takes more energy to excite the soundboard...perceived by the player as tension, or tightness. Think of the extra tension you'd get with a very high bridge as a weight on the vibrating top. It would take more energy to get that top to vibrate. There are a few tweaks (like tailpiece position/weight) that seem to also have a small effect on perceived tension. (I use "perceived tension" because as jmlee stated in the OP, you can't change the actual tension without changing the pitch or string length.)
 
#12
The arching of the top and the neck and body all form a spring. When you stop a string, the top of the bridge moves down and toward the nut very slightly; it has to because of the geometry and force distribution. If the downforce on the bridge is lower, then the arching is less loaded up, which will mean that it takes a bit less stop pressure because the bridge will move down further. This is, of course, a small effect, but would you notice? Maybe.
 
#15
nicechuck said:
If the bridge height is raised, it also raises the string height over the fingerboard
Click to expand...
No, we're talking about a theoretically higher bridge with the neck angled in such a way that the string height off the fingerboard would be the same. We're not talking about string height off the fingerboard, but rather the geometry of the entire unit (and how it might affect tension).
 
#16
Andrew McGregor said:
The arching of the top and the neck and body all form a spring. When you stop a string, the top of the bridge moves down and toward the nut very slightly; it has to because of the geometry and force distribution. If the downforce on the bridge is lower, then the arching is less loaded up, which will mean that it takes a bit less stop pressure because the bridge will move down further. This is, of course, a small effect, but would you notice? Maybe.
Click to expand...

I like this
 
#17
PaulKing said:
I like this
Click to expand...

I think that is barking up the right tree. Also think about this: if you have a string of x length at some fixed tension (to get pitch) it will take y amount of pressure to depress the string a fixed amount (to reach the fingerboard). If you make that string longer, say 2x, at the same tension it will take less pressure (say, what, cosine(x)? ) to depress it the same amount.

A high breakover angle at the nut and bridge will increase friction at those points and allow only the speaking length of the string to deflect freely. A minimal breakover angle (or maybe use of some friction reducing technique from graphite to rollers) will allow the entire length of the string to stretch, reducing the pressure needed to deflect a portion of it. So, it's entirely possible that the player will notice a difference in effort when reducing the friction (either from graphite or shallower breakover) in the system. A more flexible tailpiece/cable and/or longer string length past the bridge will do the same thing.

A downside is that with the momentary reduction in tension on the string as more length is pulled past the bridge will lower the pitch, so the intonation will not be as accurate. I'd imagine that players might compensate by stopping the string further up the neck without even thinking about it.

It occurs to me that players with high action will notice the effects more easily, as they have to use more pressure in the first place.

Just my thoughts anyway.
 
#18
Just to throw in something different too:

If the bridge is lowered and the position on the top is not changed and the bridge is still perpendicular to the top the scale will get a bit shorter, so the tension to get to the same pitch is a bit lower.
I know it is not much, but it might have an effect too.

Another thing:
The more the string is angled over the bridge, the more the string is clamped (and not so much hinged), which means that less energy is transfered due to stiffness to the afterlength.
(Of course also the movement of the bridge itself transfers energy to the afterlength, but with the opposite phase, I think.)
 
#19
grisezd said:
I think that is barking up the right tree. Also think about this: if you have a string of x length at some fixed tension (to get pitch) it will take y amount of pressure to depress the string a fixed amount (to reach the fingerboard). If you make that string longer, say 2x, at the same tension it will take less pressure (say, what, cosine(x)? ) to depress it the same amount.

A high breakover angle at the nut and bridge will increase friction at those points and allow only the speaking length of the string to deflect freely. A minimal breakover angle (or maybe use of some friction reducing technique from graphite to rollers) will allow the entire length of the string to stretch, reducing the pressure needed to deflect a portion of it. So, it's entirely possible that the player will notice a difference in effort when reducing the friction (either from graphite or shallower breakover) in the system. A more flexible tailpiece/cable and/or longer string length past the bridge will do the same thing.

A downside is that with the momentary reduction in tension on the string as more length is pulled past the bridge will lower the pitch, so the intonation will not be as accurate. I'd imagine that players might compensate by stopping the string further up the neck without even thinking about it.

It occurs to me that players with high action will notice the effects more easily, as they have to use more pressure in the first place.

Just my thoughts anyway.
Click to expand...

I like this too.
 

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