Let me copy a post that I just wrote on another thread, because it's really the same topic. The question was about whether adding extra string length between the bridge saddles and the tailpiece on a short scale bass will increase the "tension" on the strings:
Well, yes and no. The actual tension in the string is the same. The tension is determined by the scale length (the distance between the bridge saddle and the nut), the gauge/construction of the string, and the note that it is tuned to. Adding extra length at either end, between the saddle and the anchor point/tailpiece, or between the nut and the tuner, does not change the tension of the string.
However, adding that extra length at either end does change the sound and feel of the string. It's a factor I call the "snap" of the string, which is often confused with the tension. It works like this: When you pull sideways on the string, as you are plucking it, the string is stretching like a long spring. Then you release it, and it snaps back to straight, overshoots it, and goes into the back and forth oscillation.
When you add extra length to the string at either end, you are making that spring longer. So, you have to pull it farther sideways to get the same feel on your fingertip, because the string stretches easier.
For example, suppose you have two basses, same scale length, same string, tuned to the same note. One has the standard short distance between the bridge saddle and the anchor point. The other has an extra 3" of length back to the anchor point. Again, the actual tension in both strings will be the same.
But, if you pull the string sideways with a force of, say, 1 pound on your fingertip, there will be a difference. With the extended string, you have to pull the string a longer distance to the side to reach that 1 pound load. It's because there's more length of string to stretch.
Now, when you release the strings of these two basses, the extended string has a longer distance to travel to get back to center. The physics of it is that they will both accelerate at the same rate, because the tension is the same. The extended string will take longer to reach center, but it crosses over center at higher velocity and goes farther to the other side before rebounding. This is the effect that I call "snap". Increasing the overall length of the string increases the snap, regardless of the scale length.
How does this affect the sound? Increasing the snap mainly changes the attack curve of the note. It increases the pulse at the beginning of the note, which is why I call it snap. Think of the percussive sound of upright basses. They have a huge amount of snap because of the very long overall string length. The increased pulse can be heard through the amp, and also unplugged.
The funny thing about increasing the snap is that players will describe it in opposite ways. Some will say that the tension is higher, because they hear that extra pop on the note. Others will say that the tension is lower, because the string feels softer to their fingertip. But actually, the tension is exactly the same.
It's the same factor in all those long arguments about reverse headstocks, and how increasing the length between the nut and the tuner of the B string will increase the "tension" of the string to improve the sound, etc. It doesn't actually increase the tension, but it increases the snap. Which may make the B string sound more like the other strings.
Etc.
So, a reverse headstock increases the "snap" on the lower strings, the most on the B, while reducing the snap on the upper strings. That may add more balance to the feel and sound across the strings. But, it's not actually increasing the tension.
