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Do any of you guys use pinless bridges? The kind where the string stays flat and slides through a slot in the bridge until the end catches. Wouldn't this change the way the strings drive the top? Wouldn't it also put more pressure on the bridge since the strings are anchored right behind the saddle instead of going down under the bridge patch?

Did an OLF search on "pinless bridge" and here are the results. You will have to wade through the less than relevant stuff to get to the good stuff but there is good stuff in here:

http://luthiersforum.com/forum/search.php?keywords=pinless+bridge&terms=all&author=&sc=1&sf=all&sk=t&sd=d&sr=posts&st=0&ch=300&t=0&submit=Search

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Ann Arbor Guitars

I have built with pinless bridges for years. As far as the physics go on how the top moves, I'm not the guy to ask. I have my hunches and I have an experiment I want to eventually do, but nothing at this point. I suspect it does move the top in a slightly different manner.

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ELEVATE || Next Level Lutherie
http://elevatelutherie.com
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http://ensorguitars.com

As far as I can tell, any 'stop' type bridge, including Classical tieblock types, as well as steel string pinned and pinless bridges work the same way. Things are a little different when there's a tailpiece taking the string tension, but not as much as most folks seem to think. Basically all of the signal stops at the top of the saddle if things are working right, and what happens behind that is pretty much moot. Pretty much...

Again, as you look closely at any of this it gets a bit more complicated than it 'ought' to be. Changing the break angle alters the static loads on the bridge a bit, which alters the way the top distorts. This can change the way it vibrates a bit. I suspect that on most guitars most of the time the change would be inaudible, but there's always a chance that it won't be.

Tailpiece setups take up the tension change that rocks the bridge fore and aft twice per cycle of the string vibration. This is a small force, and not very effective at producing sound, so the actual output power of the guitar is not changed, as far as I can tell. A 'stop' bridge guitar will tend to have a little more of it's output in the second partial of the strings than a tailpiece one, so the timbre can be slightly different. A lot depends on the geometry there, too, particularly the string height off the top.