redir wrote:
"I have a hard time understanding what the pitch of a free, or even braced, plate has to do with an assembled instrument."
The short answer is; 'not much', but.....
The problem is that there are so many variables involved. I've been doing 'free' plate tuning using the Chladni method for a long time. If you make 'identical' tops and backs, using 'the same' wood, and assemble them to matched rims, the finished boxes will have their lowest 'signature' resonant modes (such as the 'main top' and 'main back' at the same pitches, within a very small range, depending on how careful you are to match things. However, the instruments will probably not sound 'the same', although they will be very similar.
The problem seems to be that any piece of wood will have some local variation in density and stiffness, which will perturb the shapes and pitches of the higher order modes on the assembled instrument. Since normal hearing is so sensitive in the 2-4 kHz range, where these differences tend to become more pronounced, listeners can readily distinguish the guitars. I suspect this will be the case so long as you work with wood.
OTOH, if you have fairly complete information about the assembled modes of a given guitar it's possible to produce a 'tonal copy' that will be 'arbitrarily close' to the original, even though it's unlikely to be 'identical'. If the one you want to copy is one of your own, and you have the 'free' plate information along with data on the wood properties, you could most likely make a reasonable stab at a match using the 'free' plate modes.
Again, I feel that 'identical' sound is probably not possible, but the more information you have, and the further back in the process you can start to match things, the more likely you are to have a satisfactory outcome.
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