Fred Dickens did some interesting experiments on this, and I've done a few myself. As is often the case, some of the results are pretty clear and logical, and some others can seem just weird until you think it through a bit.
Fred's big experiment was to make a classical guitar that was very deep, and cut it down successively until it was very shallow, measuring the changes. What he found was that cutting the height of the sides in half, from say 6" to 3", raised the pitch of the 'main air' resonance by (drum roll) 7%. La de dah.
THe reason seems to be that the 'main air' resonance that you hear is actually the lower part of the 'bass reflex couple' between the 'Helmholtz' air resonance and the 'main top' mode. The Helmholtz resonance is what you get when you blow across the neck of a wine bottle: it's a 'breathing' mode, with air flowing in and out of the hole and changing the pressure inside the whole box. The 'main top' mode has the lower bout area (more or less) going in and out like a loudspeaker cone. The pressure changes in the Helmholtz mode push on the top, and the top pushes on the air, so the two have to work together, even though they are 'naturally' pretty far apart in pitch. The result is that they sort of elbow each other aside, with the lower pitched Helmholtz mode being shoved downward a bit, and the higher ''main top' resonance pushed up in frequency. The increase in the seperation from the 'expected' values is a measure of how tightly coupled the two modes are.
Of course, for a very deep body, a given amount of air flowing into the soundhole will make less of a pressure change to push on the top. By the same token, a given amount of top motion will produce less pressure change in the body. Thus, a guitar with a deep body will tend to have the two modes closer together in pitch than the same box cut down would. If that were all that was happening, you'd expect the 'main air' mode to be higher in pitch, and the 'main top' to be lower with a deeper body.
Of course, it's not all that's happening. The deeper the body is, for a given soundhole size and location, the lower the pitch of the 'real' Helmholtz air resonance. It's not shoved down as much by the coupling with the top as it would be with a shallower body, but it starts out lower in the first place, so that, for small changes in body depth, the 'main air' mode will hardly move at all. What does move is the 'main top' mode: since that started out in the same place, and doesn't get shoved up so much with a deep body, it tends to be a little lower. Again, the change might not be much: the top pitch doesn't change as much as the air, owing, I think, to the fact that the top weighs more, although, no doubt, the math enters into it too (it's a 'least square' thing).
There is one other outcome. If you look at the spectrum of the guitar the 'main air' peak will be lower for the deeper body: there's less output. Again, that's because there is less pressure change for a given amount of top motion, and less pressure moves less air through the hole.
The deeper body might have a 'stronger' low end, depending on how the balance between the possibly lower pitch and smaller output works out. It is likely to be 'more even' in the low end, with less of a tendancy for that 'low G wolf'. It will be less 'punchy', and that might come across as less 'bright'. Very shallow bodies are often percieved as 'forward' or 'harsh' for the same reason, I think.
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