That assertion is probably based on a PhD thesis done by Howard Wright at UWales/Cardiff in '96, in which he used a computer model to generate guitar sounds and asked people if they could hear the differences when he made various changes. The thing that had the most effect on the tone was the ratio of vibrating area to mass of the top resonance modes, and particularly the 'main top' mode, which is the one that acts like a loudspeaker. Wright's thesis advisor, Bernard Richardson, later used those results, and some other data, to argue (in an article in the Catgut 'Journal' entitled 'Simple Models of Guitar Design') that small guitars can, indeed, be as loud as bigger ones.
There's one absolute requirement that every guitar top has to meet: it has to be stiff enough to not fold up too fast. Anybody who's worked on a house knows that as you increase the span of the floor you have to use heavier joists to keep it from being too bouncy. Richardson showed that, for a given top structure, increasing the span beyond a certain point increases the weight faster than the area: the A/m ratio goes down and the power suffers.
Of course, you can't always lighten up a smaller instrument all that much either. There are absolute minimum limits to the thickness of the top, below which you'll be putting your finger through it.
So, if you start with that minimum thickness, which gives you _some_ stiffness automatically, you can increase the size for a while without having to make the structure heavier. But, at some point, you will have to start beefing things up, and shortly after that the weight will be rising faster than the area, so you're losing ground. For any structure there seems to be an optimum size.
It's interesting to look at a book that has lots of pictures of old guitars with this in mind. The early, ladder braced ones were small and narrow. As soon as the more efficient fan bracing came along they started making the lower bouts wider, until you get up to Torres and the 'modern' designs, and the growth pretty well stops. Meanwhile, on this side of the pond, when X bracing came into use, the guitars grew again until the Dread and Jumbo, and stopped pretty much. You see an occasional bigger one, but they are not common. Archtops were built that were wider than Dreads and Jumbos, but there is a limit to what you can tuck under your arm, too.
Anyway, a larger box will tend to give off low frequency sound more effectively, so that effects the bass balance of the tone. In terms of tone production it seems to me that length is far more important than width. This may have to do with the way the lower air resonance modes couple with the top, or it could be more related to precession of the equinoxes....
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