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One of my students built a deep-body OM for his first guitar. The objective was to get a 'fuller' low end, and it worked. _How_ it works is a bit complicated, though.
First; resonance frequencies. Most of the sounsd output of the guitar comes from the 'bass reflex couple' between the top and the air, with the back getting into the act sometimes as well. The lowest top resonant mode works like a loudspeaker cone, with the lower bout moving in and out as a unit, usually somewhere near the open G string pitch. This both produces sound out front, and pumps air thruogh the soundhole. About an octave lower you've got the 'main air' resonance, which is just like what happens when you blow across the mouth of a wine bottle. The air moving in and out of the hole pushes on the top. Thus you have the top pushing the air, and the air pushing the top, and the two have to work together, even though they are pretty far apart in pitch.
Actually, if the body were rigid, the 'main air' mode would be higher in pitch, probably around A# or B. By the same token, without the push from the air in the box, the 'main top' resonance would be lower in pitch; prbably nearer E or F. It's the interaction between the two that shifts the pitches further apart. So, with a weaker interaction, you get less pitch shift. Making the body deeper is one way to weaken the coupling between the two modes. There is a smaller pressure change for a given motion of the top when the body is deeper, so less air is pumped from the hole, and there is less push on the top. Thus from this standpoint, you'd expect a deeper body to yeild a slightly higher 'main air' pitch, and a lower 'main top' one, all else equal.
At the same time, making the body deeper does drop the pitch of what we could call the 'real' main air mode; the one that you'd have if the body were rigid. Putting it all together, the result is that the deeper body shifts the 'real' air pitch down, but the further downward shift caused by the coupling with the top is less, so it tends to end up about where it would be on a shallower box. However, the upward pitch shift of the 'main top' resonance is less on the deeper body, so that tends to end up lower than it would have otherwise. Thus, in terms of resonant pitches, the somewhat paradoxical outcome is that the top pitch tends to drop, rather than the air pitch.
The lessened pressure change inside the box from the deeper back has the outcome of making the 'main air' peak in the output spectrum a bit lower in level, but it may also spread it out in terms of frequency. Instead of having one strong note, you might end up with two that are a bit less strong. This is one thing that seems to contribute to the 'fullness' of the tone.
It's really hard to say whether the deeper guitar will be 'louder': loudness is a subjective term. A deep body tends to have a less 'edgy' tone, as the 'attack transient' takes a bit longer to build up. Sometimes that loss of 'edge' can sound less loud. OTOH, it's possible that the extra 'fullness' can make it sound more 'powerful' or 'solid'. This is one of those cases where there are a lot of variables, and you just have to get some experinece building them in different ways so you can make up your mind what you like.
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