Originally Posted by robobass
As I alluded to before, this is a Creationist vs. Darwinist arguement which I think will never be settled. On one side you have the godless, evidence based fools, who insist that afterlength and the size and geometry of the tailpiece do not affect string tension or downforce. They have a false and shallow belief that tension and downforce are calculable solely from break angle over the bridge, active string length, and bridge height. I was one of them for most of my life, but now I pray for their souls.
Anyone here measure this - actual string tension ? I have. And there's Mottola who has looked into this in detail. He does suggest that there's a difference in actual tension and "perceived tension", but that difference is not defined. After communicating with Liutaio, I have embarked on a controlled study of the element he describes as 'compliance'. If there is interest here I will post my findings. If not I won't bother.
What you have going on are two different forces. You have tension in the strings, which is going to remain the same as long as the strings and the length from nut to bridge remain the same. The tension in the particular string determines its being in tune.
Then you have the tension on the bridge, both vertical and lateral. Let's say you have 25 lbs. of tension on the string for it to be in tune. When your bridge is in the center, just underneath the string, it has 0 lbs of tension on it. As you move it upward, the tension increases, both on the bridge AND on the string. If your endpoints are fixed, your string would have to get longer to accomodate this higher bridge, but you'd add that length from the tailpiece side, keeping the 25 lbs. of tension and distance from nut to bridge the same. This increase in length on the tailpiece side affects how the shorter string lengths resonate.
What you're working with are force vectors that can be visualized by perpendiculars to the string faces. A low, centered bridge splits the force into mostly vertical components, slightly tilted in towards the bridge. A higher bridge turns more of those forces toward the bridge. If you split the strings with unequal angles on each side of the bridge, you get two different force vectors. The lesser angle pushes downwards more, the sharper angle pushes more to the side. This leads to instability. Imagine a bridge being all the way to one end of two string connection points (creating a right-angle with the strings). As you tightened the string, it would immediately pull the bridge over.
So, you have two different tensions that you're talking about. The string tension is always going to be the same for a given string and given string length if it is in tune. The tension on the bridge in both strength and direction can vary depending on its height and the relative angles of the strings on either side of it. AND string tension includes the tailpiece. Regardless of which side of the bridge it's all on, the total tension of the string system doesn't change. What you can change is the length of the exposed string on the tailpiece side, which can affect the sound quality. Technically, you could customize each string length on tailpiece side so that they produced desired harmonics. You wouldn't want to adjust their tone via tuners, but via moveable mini-bridges, because tuners would create additional tension and throw off the tuning on the other side of the bridge.
It IS all physics, but it's not simple. And just like the Darwinist/Creationist argument, it IS settled if you willing to give up long held, heartfelt beliefs in favor of reproducible, measurable experiments. And that's asking a lot for a lot of people.
...but what about the elasticity of the string itself? If the string can stretch, lengthwise, a given amount per inch of string - then if you increase the length (even though the "speaking length" would remain the same) would you not increase the amount the string could be easily stretched, and therefore make it easier to stop a note or pull with one's right hand.
