Think about the guitar as if it was a xylophone bar. There are several ways the whole body+neck system can vibrate, and the lowest pitched 'mode', in particular, can effect the tone.
It's easy to find this. Hold the guitar up, pinching the neck at the first fret between the thumb and first finger of one hand just lightly enough to damp the strings and keep it from falling. Allow it to hang freely. Tap on the back of the headstock right up at the top, and listen carefully with your ear as close to the headstock as you can get it without sticking a string end in your earlobe. You should hear a fairly clear, low pitched sound. What's happening is that the entire guitar is bending and vibrating. As the headstock and tail block are moving toward you, the heel is moving away.
When the guitar is bending that way it is putting pressure along the length of the soundboard. Since most tops are made bellied out a little this pressure tends to push the top up, and sucks a little air in through the soundhole. When the guitar bends the other way, the air is pushed out.
This is just what's happening with the 'main air' resonance; air is moving in and out of the soundhole at a particular pitch. It's just like the sound you hear when you blow across the top of a bottle. On a guitar, this air mode is often around the pitch of G on the low E string. You can hear it by singing the note into the soundhole, but keep your face at least 5 or 6 inches away from the hole, as having it too close can alter the pitch.
Since the body and air vibrations are doing the same thing they can work together. In practice they will only do that if the natural pitches match very closely. Since the neck is bending a lot in this body vibration the flexibility of the neck will effect the pitch a lot. Similarly, since the headstock is moving a lot, the mass of the head matters. Usually this so-called 'neck mode' pitch is too low to work well with the main air mode. however, if the neck is light and stiff, and the headstock light, it can happen. I even made one short-scale classical where the 'neck mode' was too high!
When the 'neck mode' and 'air mode' pitches match the usual air resonant peak in the output spectrum is spread out into a broader peak with two humps and a valley in between. The frequency response is more even in the bass range, and more powerful. The tone can be 'gutsy' and 'rich'.
Using a light wood, like cedro, helps. Deep V necks are stiffer than shallow ones. 12-fret necks have a higher pitch, all else equal, since they are shorter. The weight of the machines can be critical; even swapping out metal tuner buttons for wood can do it. A tapered neck that is deeper at the body end helps. This is not something I've learned to control reliably, darn it, but it's nice when you get it.
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