Overall string length and tension.

Myth.

There are four interrelated factors.

The pitch produced is a result of: the vibrating length, the tension, and the mass per unit length (the linear density).

Another way to look at it is that the required tension is a result of the desired pitch, the vibrating length, and the mass per unit length (the linear density).

There are also two more ways to look at it-- in each case, if you fix three of the factors, this determines the requirement for the fourth.


You can also easily demonstrate that changing one factor, while holding two constant, will result in a change in the fourth.

If you hold the string density (ordinarily determined by your string gauge) and the vibrating length constant, and increase the tension, the pitch goes up. This is what happens when you tune up.

If you hold the string density (ordinarily determined by your string gauge) and the tension constant, and decrease the vibrating length, the pitch goes up. This is what happens when you fret a note.

If you held the tension and vibrating length constant, but increase the mass density (made it heavier) by adding lots of little clip -on weights along the string, the pitch would go down. Or conversely, if you stripped off the outer wrap (changing, say, your .100 to a .080), lightening the string, (but without releasing any tension), the pitch would go up

But - all of this is dependent only on the vibrating string! The string could continue one inch or ten beyond the nut or bridge, but at one tension, at one vibrating length, at one "weight", it can only produce one pitch. I think this is fairly intuitive to a lot of people. What might be slightly less intuitive, but is just is true, is to simply (and properly) turn the logic around-- one particular pitch, at one vibrating length, at one "weight", can only result from one tension.



The one wrinkle to this, is that if the string is allowed to slip over the bridge or nut, then the longer the extra length beyond these points, the softer the string can feel while you're plucking it because some string will slip over into the vibrating area, and so will offer less resistance to your finger pulling it sideways.

And even with that being said, if you're fretting at, say, the seventh fret, then you've already got about 11" inches of "extra" length between your finger and the nut, so whether there's 1.5" or 2" between the nut and the tuner is essentially meaningless.


If you're interested in doing the math, there are a few simple string tension calculators available on the web. I've also got a fairly involved one posted here on TB.

The one thing you'll find in all of them, as well as in every single physics text on the planet, is that non-vibrating length does not enter into the equation.

Here's the related wikipedia page. You'll see the basic governing equation down under "Frequency of the wave".

You'll see the same equation on the D'Addario Strings site, in the pdf document that gives the linear density of all their strings so you can calculate tensions.

pilotjones said:

Myth.
The one wrinkle to this, is that if the string is allowed to slip over the bridge or nut, then the longer the extra length beyond these points, the softer the string can feel while you're plucking it because some string will slip over into the vibrating area, and so will offer less resistance to your finger pulling it sideways.

Click to expand...

A wrinkle on the wrinkle....this will also depend on the break angles across the bridge and nut. A more severe break angle will exert more downward pressure on the nut/saddle, increasing the resistance to sliding across.

This will make everything feel ever so slightly tighter. I think that's the effect you're referring to with a string-thru bridge.

Except for one thing: (dramatic pause): if there is significant extra length beyond the speaking string, and if this length does slip over the bridge or nut during plucking, this will then cause the string to feel looser, not tighter.

And, BTW, while additional downforce is produced by increasing the break angle of a string going over a bridge saddle, this does not necessarily increase the "stickiness" of the string at that point. It is also very much related to the geometry of the saddle: the simplest condition would be a knife-edge saddle, where the increased downforce would result in directly proportionally greater pressure, and result in roughly proportionally greater friction. But when you bend the string around a barrel shape, it changes things, increasing the contact area and decreasing the contact pressure.

Yes, increased break angle over something resembling a knife-edge would increase force, increasing the pressure, increasing the friction, so it sticks better without slipping.

Increased angle wrapped over a barrel increases the total force, which is then spread over a larger area, resulting in roughly the contact same pressure. Friction could go either way depending on the materials and finishes involved.

[edited for clarity]

Damn, it is fantastic that we've got a resident engineering division to help us with this stuff.

I've said it to you before Peter - if you EVER need anything for your first build that I can supply - you only have to ask. It's the least I could do for the service you supply this forum.

One of these days... I may need a lot of help.

pilotjones said:

One of these days... I may need a lot of help.

Click to expand...

Give some, get some.


And vice versa.

In short(?): TB Luthiers forum.