I'd like to add that predicting the exact pitches of tap tones may not be all that necessary anyway. Most of the people who've done experiments on this say that 'small' changes in these pitches don't effect our perception of the tone of the guitar much, with a couple of exceptions.
One thing is that notes that are very close to a strong resonant pitch will sound different. Shifting the 'main air' resonant mode from F to G will alter the sounds of those two notes, at least. The overall timbre of the guitar might not be effected much, though.
The other thing is that there are lots of resonant modes of the different parts of the structure, and the air in the box, and these interact in complicated ways. Altering the pitch of one or another of them could change a whole web of relationships, and that could change the general impression of the sound in some ways.
All of this is pretty fuzzy in many respects. It's _very_ difficult to make two guitars that are alike, and sound it, and the thought of making two that are alike except for one thing is close to absurd. (Ive' made 'almost matched pairs', and learned things from them, but you really have to keep in mind that the margin of error in thse tests is huge. There's always a chance that what you 'learned' isn't really true) To 'prove' that that one thing had a certain effect you'd need to do that sort of matched pair experiment some number of times, and probably a large number of times. The only approaches we have, then, are:
1) make an instrument that can be easily and quickly modified in some way, like my 'corker' guitar. This can allow for the testing of a number of different configurations, but, of course, there are only so many plausible tests of this kind that can be done. There's no way, for example, to easily and quickly swap out a back so that you can A/B the sound in a few seconds.
2) use a computer model that allows for easy changes of almost anything. One such model was produced by Howard Wright back in '96, and it was very productive. Of course, a computer model is not a guitar: limitations of computing power and model sophistication limit the aplicablilty of the results. These things are improving, of course, but they're out of the reach of us luthiers for the most part for now.
3) build lots of guitars, with the best possible quality control, and look for common elements. At present the biggest QC problem is with wood: any species of wood varies a lot, and the folks who are set up to make lots of guitars with otherwise good QC, like Martin and Taylor, can't afford the time to test wood before building guitars from it. Some enterprising researcher could learn a lot if they could convince one of the big factories to make a run of guitars with 'known' wood, and submit them for testing before they went out to be sold. The factory would probably reap some benefits as well.
The big problem with all of these: who's going to pay to get them done? Most of the computer modeling is done by students who are learning how to use the tools on their way to engineering jobs. Big guitar factories are more interested in applied than basic research: finding a decent substitute for mahogany before it goes on the CITES list is more important than 'Quantifying the exact tonal consequences of altered T(0,0) /T(1,0) mode spacing on the perception of bass-range 'punch' in spruce/rosewood Dreadnoughts'. They already have a good enough feel for that for their purposes. That leaves a bunch of us 'left-brain' luthiers putzing around and wasting time when we should be building stuff. No wonder progress is slow.
