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Assuming you've made all of your bridges to a standard size, the pitch of the main resonance is telling you something about the ratio of stiffness to weight of the bridge. A wood with higher density and low stiffness will give a low tap pitch, and low density and high stiffness goes the other way. Since this pitch is determined by a _ratio_, it does not say anything much about the absolute stiffness or mass, but, of course, if you know what all of the bridges weigh and have the tap pitches you can figure out the ranking there, too.
The bridge does two things on the guitar: it tells the string how long it is, and it's also the heaviest, and one of the stiffest, braces on the top, so it has an effect on the way the top vibrates. Since these two functions work at cross purposes to some extent, you're looking more at a balance of things than at some absolute definition. You want the bridge to be massive enough and stiff enough to define the string length pretty well, so you don't end up with 'wolf' notes, for example. However, the heavier and stiffer the bridge is, the more it's going to restrict the top movement, and particularly the 'monopole' modes.
(The nomenclature that Trevor uses is pretty common, and is often used even in the violin world when talking about some modes of the assembled instrument. Since fiddles are pretty standardized, they do normally use numerical designations, as 'mode #1' and 'mode #2, for the _free_ plate modes, which usually occur in the same order. Guitars are more variable that way.
What Trevor calls the T(1,1)1 is often referred to as the 'main air' resonance, and the T(1,1)2 is the so-called 'main top' mode. These are actually the two halves of a 'bass reflex couple', where the 'Helmholtz' air resonance and the top 'monopole' mode interact strongly. The result is two resonances that _both_ involve air motion in and out of the soundhole [like the Helmholtz' mode], and the entire lower bout of the top moving like a loudspeaker cone and producing sound [the isolated T(1,1)]. In what we term the 'main air' resonance most of the energy in the mode is tied up in air motion, and the top and air are 'out of phase', so the top is moving inward as the air is coming out of the soundhole. In the 'main top' mode, the situation is reversed: most of the energy is in the top and the air and top are 'in phase', both moving outward at the same time. Due to the 'phase cancellation' the main air mode tends to produce less output in front of the guitar.
All of this can get confusing. The rule with resonances is that you can get two or more resonant mode shapes at a given frequency in a simple system, but you'll never see the same mode at two different frequencies unless there are two different oscillators involved that are coupling. Using the top mode shape to talk about both parts of the bass reflex couple is accurate enough, but might obscure the fact that there are two potentially independent vibrating systems working. I think it helps to keep that in mind.
If you think that's confusing take a peek at the violin world sometimes. Between the somewhat more complicated structure, and the way the terminology has evolved, they have all sorts of terms for modes that are hard to see, and may or may not affect the timbre; things like the 'CBR' [corner block resonance], and the' B1+'and 'B1-' modes. There's a lot of discussion about just what the relationships between these mode does to the sound, and not a lot of agreement. We're a lot better off that way.)
Anyway, since the top 'monopole' mode bends a lot in the center, a stiff bridge can restrict that motion, and cost a lot of sound. Similarly, since the top moves the most in the middle for that mode, too much mass can cut down on power as well. You need enough combined mass and stiffness to get the end of string to be more or less stationary, so that it will make the right note, but either high mass with low stiffness, or high stiffness with low mass, can potentially work well.
A light, stiff, structure will, of course, tend to have relatively high resonant pitches, and guitars with light,stiff tops tend to be more 'treble balanced'. I'ts more complicated than that, though: since the 'bass reflex' action is in the low range of the guitar making a light, mobile top can give very high output in the bass range, often as 'punch' in the attack. This is part of the characteristic sound of a Dread with scalloped braces. The dense ebony bridges they often use make a lot of sense there, using mass rather than stiffness to 'nail down' the end of the string, and lowering the resonant pitch too. Some of the 'lattice' and 'sandwich' top guitars have a sound to my ear that speaks of a light and stiff structure.
This all can get very complicated, and tends especially to do so on good guitars. Ultimately, each design exists as a system where all the parts have been balanced to get a desired result. On my own guitars, which tend to be fairly, but not totally, 'traditional', I've found that using bridges that are as light as Trevor likes tends to give a sound that is too 'sharp' and 'trebly'. I have not noted any particular trend in the sound related to the damping factor of the bridge wood, as some have. No doubt altering one or another property of the bridge will have a predictable effect on the tone that will be similar from one design to another: mare mass> less power and a larger drop in the treble range than the bass, for example. However, this is likely to sort out differently for different designs, and you need to work out how it's all going to work for _your_ system.
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