Okay, here it is according to Guitarist mag;
"There is a good reason for it. People like Billy Gibbons and Duane Allman figured out that if you screw the tailpiece down hard on the body then wrap the strings back over the tailpiece, not only did you get the perfect downward force on the bridge, but it also seemed to increase sustain and tone. Also, many people say it reduces tension, making the guitar feel spongy and easier to play."
Alright Muttley, do your worst!!!
OK here's the deal again.
There are two things to consider, the direction in which the forces are acting as a result of the string tension and how they are overcome. Regarding the sustain you need to consider how the energy in the string is transfered to sound waves.
The forces thing first. The machine head and the stop tailpiece anchor the string. Both will take a hugely greater force before they fail. The fores of the string under tension act longitudinally along the length of the string. The tension is rigidly maintained by the tailpiece and machine head. If it wasn't the string would not hold in tune. The bridge introduces a third force to the equation which acts directly down through the bridge. This force is overcome by the rigidity of the body. This force is Dependant on the break angle at the bridge. The greater the angle the larger the downward force. Think of it like a bow and arrow, the further you draw the bow the further the arrow flies. With a bow and arrow when you draw it back you increase the force at either fixed end. With a guitar string you don't the tension has to be what it is for the given note or frequency. From this you can establish that the force at each point has to be the same to stay in tune.
Now no matter how you fix the string, over under through etc, the force will act in exactly the same direction for a given break angle. The method that is used to fix the tailpiece or machine head is irrelevant because it is capable of withstanding much greater forces than the string imparts. It has to. It doesn't matter that the post holding the tailpiece in place is a few more turns into the body the same amount of energy is going to be transfered at least in so far as we are concerned. There will be a slight increase in the amount of energy lost to the body when there is more contact between the threads on the tailpiece. This will actually decrease sustain not Increase it. However the amount is so small it will have virtually no noticeable effect on the tone or the decay rate. So if anything screwing the tailpiece down will have the opposite effect. With both systems there is a single point at which the string contacts the tailpiece and energy is transfered, if this wasn't the case you would get buzzing when the string vibrates against adjacent material.
The string energy and tension in the string and the materials fixing the string to the body and the material of the body dictate the tone and the rate of decay. When you pluck the string you impart a finite amount of energy into the string. This energy is lost in several ways, Most important to us are, via the air as sound waves, through the body via the bridge, and as heat resulting from internal damping of the materials (impedance) a good deal of energy is reflected back down the string. The tone is governed by the upper partials or harmonic overtones that the material of the bridge and body impart as the energy is reflected. A small amount of energy is lost to the tailpiece as well but not a lot. Pick a string and then damp behind the bridge with your finger it wont make a hell of a lot of difference. Most of that energy will be permanently lost via the tailpiece. same goes for the string between the nut and machine head. Some will be reflected but not enough to give a noticeable increase in sustain or amplitude.
So in short the forces act in the same direction for any given break angle and are overcome by the method used to fix the string. To change the timbre, decay or amplitude you have to change either the break angle or the material or material properties of the instrument. Over wrapping does none of those. The minute amount of change in energy transfer as a result of overwrapping is undetectable to our ears it really is that small.
The break angle is critical on archtops however but that is because the top is designed to be efficient when it comes to absorbing and reflecting energy. A solid body is not it is what it is.
