Ian wrote:
"Are you suggesting dampening in certain areas to make the sound, say, "thinner"? In which case I think putting a large mass on the top would help. "
First: I tend to learn best by 'getting the feel of it' too. People who start out by writing equations bug me. What I was talking about there was the notion of 'impedance', which is a little tricky. Basically, it has to do with how easy it is to move something at a given frequency. It's not that hard to get something of a feel for it, though.
Imagine you've got something like a ruler that you've clamped to the edge of the bench, with most of it standing out sideways and free to vibrate. Stick a lump of something fairly heavy on the end. Now you've got a pretty good 'spring and mass system': most of the mass is in the lump on the end, and most of the 'springyness' is in the ruler. If you pull it aside and let go it will 'twang', and we all know that the stiffer the ruler is the higher the pitch will be, while more mass will make the pitch lower.
Now, push the mass aside and hold it. You've got to do some work (apply a force through a distance) to get it moved aside, and you've got to keep exerting force to hold it there. You're working against the stiffness of the ruler here. If you push the mass slowly back and forth, the stiffness is what's 'impeding' the motion: so that's the 'stiffness impedance'.
If you try to move the mass at a higher frequency you've still got to work against the stiffness to move the mass off center, but as it's swinging back you can allow the spring to do some of that, so as the frequency goes up you have to fight the stiffness impedance less and less. On the other hand if you are always trying to keep the same amplitude of motion the mass has to move faster at higher frequencies, so you've got to do work more to overcome the inertia of the mass; that is, more mass will 'impede' the motion at higher frequencies, but not so much at low ones.
There will be some frequency at which the energy stored in the displacement of the spring when it's all the way over will be the same as the energy stored in the inertia of the mass when it's in the center and moving it's fastest. The spring and the mass will trade that energy back and forth, and you'll be able to get a lot of amplitude by just feeding in enough power to overcome the friction in the system. This is the 'resonant frequency'. The physics types would say that the 'capacitative (stiffness) reactance cancels the inductive (mass) reactance, leaving only the resistive (loss) reactance'. But I wouldn't.
The point here is that the impedance of stiffness is high at low frequcies, and falls off at higher ones, while the impedance of mass is low at low frequencies and rises as you go up.
The bridge and top of your instrument have stiffness and mass, so there's an impedance there. The same holds for the strings, although with them it's 'tension' rather than 'stiffness'. It turns out that when the impdeance of two things, like a string and a bridge, that are hooked together is the same, the energy can pass from one to the other easily. You want _some_ of that on your instrument , but not _too_ much, or you'd have no sustain.
But remember, impedance varies with frequency. A light stiff bridge is likely to have an impedance that more or less closely matches that of the strings at high frequencies, so that energy gets out and into the top easily. Making the bridge heavier will raise the impedance, but most especially at high frequencies, so you won't get quite as much treble in the sound.
Luckily, it's easy to check this out and get a feel for it. Get some poster adhesive ('Blu-Tac' and 'Fun-Tac' are a couple of brands) and stick a wad of it onto the bridge. Don't use modeling clay; it has oil in it that can get into the wood. With the poster adhesive it's pretty easy to home in on the amount of mass that will just be enough to take some of the edge off.
One of my students got a little carried away a couple of years ago when carving her bridge, and ended up with a 'sharper' sound than she wanted. We ended up adding about 3-5 grams of weight to the bridge to get it to sound about right. Later, when we had time to get some finish on it, we were able to remove the weight, as the added mass and damping of the finish did the trick.