question about body size vs depth

[corlay]

Hello.

I'm wondering if someone could explain the general differences in tone one would get between two identically constructed guitars, with identical internal *volume*, but one guitar body is smaller/deeper and the other is larger/shallower.
(say a deep-body 00 vs. an 000/OM)

I'm guessing the smaller/deeper version would produce a stronger bass response and a mellower/more rounded tone, and the larger/shallower version would project a bit more with a sharper tone? But that's just a guess on my part.

Thank you!

[gitnoob]

Identical construction = same top thickness and bracing?

Then the smaller top will have a higher resonance frequency (probably perceived as brighter).

If you increase the box depth on the smaller guitar, you will lower the main air resonance a bit, but it doesn't seem to be as effective as making the top (and thus the box) larger. You've increased the distance between the top and back, so the "ping pong" between the two plates is weaker. Lower resonance, but weaker / more diffuse. Also can make the box sound a bit like an echo chamber (I guess because you've made it behave more like a signal delay by moving the back plate away from the top).

[Alan Carruth]

Actually, you have to deepen a box quite a lot to drop the 'main air' resonance enough to notice, assuming all else equal. This gets a little complicated...

The 'main air' resonance that you hear is actually the product of the interaction between the 'Helmholtz' resonance and the flexibility of the walls of the box. Technically, a 'Helmholtz' resonance hapens in a _rigid_ container, and the flexing of the walls, particularly the top, drops the 'air pitch below the expected 'Helmholtz' frequency.

The coupling between the 'air' and 'wood' is effected by pressure changes inside the box. As the top move inward the pressure rises a little, and pushes the walls of the box out, and the opposite happens as the top move out. For a given size outline (say, sticking with 00) the deeper the box the less pressure change there is for a given top displacement.

Most of the flexing in the walls is in the top, of course. The top has it's own resonances, and the one that has the biggest role in pumping air in and out of the box is the 'main top'; where the lower bout moves like a loudspeaker. On a backless box this might come in at around 160 Hz or so, while the 'Helmholtz' resonance on a rigid guitar shaped box will be at more like 125 Hz. These two are sort of far apart in pitch, but they are still pretty strongly coupled by the nature of things.

Any time you get two resonances with somewhat different pitches that are coupled, they tend to push each other apart in frequency. The higher pitched one shifts upward, and the lower downward in pitch. On many guitars the 'air' pitch is around 100 Hz, while the 'top' pitch is closer to 200, so the 'air' has been shifted down by about 25 Hz, and the top up by 40 or so.

Making the box deeper does drop the real 'Helmholtz' frequency: if the box was rigid, it would go down in pitch as you made it deeper. However, because the coupling is less, the drop from the 'Helmholtz' pitch to the observed 'air' pitch is less. It turns out that, if you don't change anything else, such as the top stiffness, deepening the box has almost no effect on the 'air' pitch unless you really deepen it a lot. Fred Dickens dis an experiment years ago where he cut down a classical guitar in stages from about 6" deep to something like 2", and saw a change in the 'air' pitch of only 7%: a little more than a semitone.

Not that thew sound of the guitar remains the same. As has been said, the 'air' mode peak in the output has a lower amplitude when the box is made deeper, but covers a somewhat wider pitch range. The timbre tends to get 'softer' in the low range, or that's how I'd characterize it. 'Fuller' might be another word.

The 'main top' resonance can also be effected. It's even possible that you could see the 'air' resonance unchanged, and the top resonance rise from cutting down the depth of the box. Fred didn't say anything about that when we talked about his experiment, and he may not have gotten that data.