I think string length tension from tailpiece to bridge really affects the sound
Yes it does, in a subtle way. Increasing the length of string between the bridge and tailpiece
does not change the overall tension on the string. The actual string tension is determined by the string's construction and mass, the scale length between the bridge and nut, and the note it is tuned to.
Adding extra string length behind the bridge (or up at the headstock) increases what I call the
snap of the string. It's the acceleration rate of the string when you let go of it. Think of it this way: the extra length of string is like having a longer length spring. There is more length of string to stretch when you pull on it. If you have two springs, a long one and a short one, and you pull on them with the same number of pounds of force, the longer spring will stretch farther before you reach that level of force. When you let go of them, the longer spring will accelerate through a longer distance and reach a higher speed. It will make a louder snap.
And that's what happens when you pluck the string. Compare, say, a Fender style bridge, which has about an inch of string length between the saddle and the tailblock, and an Ampeg AEB-1, which has about 4" of string between the saddles and the tailpiece. Assuming that the strings are the same, and the scale lengths are the same, the actual tension in the strings will be the same. When you pull sideways on the string, you'll find that, with the same amount of force on your fingertip, the Ampeg string will be pulled farther to the side, in distance. This is because the extra length of string behind the bridge is allowing the string to stretch farther. Even though the string tension and the fingertip force is the same. So, when you release the Ampeg string, it has a harder louder snap.
You can feel this increased snap when you release the string, and it also gets picked up by the pickup and sent to the amp. It exaggerates the attack curve of the note, putting a larger pulse on the beginning of the note. That's the change in the sound. Now, if you play with a very light touch, and play fast notes, you may not hear any difference between the Fender and the Ampeg. You may not care. But, if you play old school style, with heavy plucking and longer notes, that pulse can be an important part of the sound.
There's a funny psychological angle to this too, in terms of how the string feels when you increase the snap. Some players will describe it as "higher tension", because they feel the extra pop. Others will describe it as "lower tension" because the string feels softer to pull on. But, the actual tension is the same.
That's why, whenever this subject comes up on the main TB threads, it usually ends up in a long bar fight argument. Because nobody can agree what "tension" means.
Anyway, that's why Ampeg put the extra string length back there. They wanted that extra snap, similar to the Baby Basses. And that's why I use the extra string length on my Scroll Basses too. At least, up until now. My upcoming new AEB-2 has a new improved version of the mechanical percussive pickup, and will not require the special super-duper long strings. In my twisted engineering brain, I've come up with a better way of creating that pulse in the attack curve. No electronics involved......
