Mark Blanchard wrote:
"In my experience, figuring out which mode set is a good one and which is a bad one is best done by trial and error. Build guitars, keep records, and sort the good ones from the bad ones. "
The modes of the free plate are the modes of the free plate, the modes of the assembled guitar are not.
The two structures are related, but they are not the same, and going from one to the other mathematically is possible, but not easy even now. The weak link in all free plate tuning schemes, whether by tap tones or Chladni patterns, is that leap from the free to the bound plate, and we're really not much closer now to bridging that gap rigorously than we've ever been.
We do have a lot of tantalizing clues, though. I may have showed John the results of my 'matched pair' experiment that ended up making two classical guitars that sounded different. There was no difference I could measure at the time between the assembled boxes, but they did sound different. The one thing I could come up with was that the one people liked better had 'ring-type' modes that were more 'closed'.
Recently I loked at the records of all 15 of the 12-fret 000 style guitars I'd made. All of them had, of course, a 'ring' mode on the assembled top, but the free plates were quite a bit different from each other. You could imagine that, in sme way, the sides had to do some work to get the modes that were not 'naturally' closed or nicely shaped to close when the top went on the box. There's always a difference in pitch between the 'free' ring+ mode and the ring mode on the assembled top, and it makes some sort of intuitive sense to think that the more work the sides had to do to get the modes to close, the more pitch shift there might be. So I looked at the pitch shift and how it corresponded to the closure of the 'free' plate modes. The rersult was, as you might expect, more 'interesting' than I had thought.
It turned out that large pitch shifts correlate most with what you could call 'irregular' mode patterns. That is, a 'closed' 'ring+' mode that was not smooth, but had sharp 'spikes' on it, tended to shift pitch more than a smoother mode that might have been 'open' in one spot. In other words, the more parallel to the edge the node line of the lower 'ring' on the free plate were, the less pitch shift. This also seemed to correlate pretty well with the 'quality' of the guitars, although that's more subjective, of course.
I have thought of a simpler system I can use to test 'ring' mode closure and it's correlation with assembled modes, but have not had much time to work on the experiment. Preliminary results seem to indicate that the biggest difference in the output of the 'guitar' in this test is in the _high_ frequency range; the low-end spectrum is not much effected. This correlates with my own impressions of 'well-tuned' guitars: the low end doesn't get better, but the high end does (that was what happened on the 'matched' classicals, for example). This has me a little worried: it's the result I expected to see, so I wonder if I'm not fooling myself. I've got to try to prove myself wrong, and that's going to take a lot of time with the setups I have now.
Somebody on another list suggsted that we should be able to figure all of this out with 'only' a few million dollars of funding. In his world, that might be peanuts, but for us it's the moon. We just have to keep plugging along as best we can, with the realization that the answers may always be out of reach, simply because the system we're dealing with is more complicated than the funding we can get will suffice to figure out. I think of it as 'job security'.