Trevor Gore wrote:
" Most of us have found that free plate frequencies are not a good predictor of closed box frequencies, if those are what you're interested in. "
Yup. Several years ago I dug up the data on about twenty guitars of the same size and shape, looking for any sort of correlation between the 'free' top ring+ mode pitch and the frequency of the 'main top' mode on the assembled instrument. There was none. However, there was a correlation between the mode shape and the frequency shift between the 'free' and assembled mode pitches: the 'better' the free plate shape the less of a pitch shift there was. It seemed to me that there was also a correlation between the mode shapes and the quality of sound of the assembled instruments, but:
a) I'm biased, and
b) what's 'quality'?
Some years back I made what was supposed to be a matched pair of Classical guitars. After a lot of effort to control everything as closely as possible, they ended up not sounding the same. They were both good guitars, and very similar, but everybody who tried them preferred one over the other. The one they liked had the better mode shapes. Since they didn't know which was which, this is a reasonably good test, although, of course, one would like to repeat it. Up until then I had been controlling for frequencies, and those matched well. Since then I've been looking at mode shapes more, and getting better results.
I'll note that 'better' mode shapes tend to give 'better' tap tones; ones that are clearer and have lower loss.
A short digression. The Ford Model T car used magnetos in the ignition system. There was a separate capacitor for each cylinder, with a set of points that worked like a buzzer to produce an AC current that could be stepped up to fire the plug. To set the gap on the points you rotated the engine to the correct position and listened to the buzz, adjusting the setting until you got a specific note. I had read years ago that the cars actually came with a 'C' tuning fork, and a recently referenced article on line suggested C# as the correct pitch. At any rate, the pitch was just an indicator of the gap, which was what you were really trying to adjust. I strongly suspect that this is where the phrase 'tuning up a car' came from.
Back when we started looking at Chladni patterns we thought that the pitch might be a useful indicator, and 'tuning' the plate seemed a good term for what we were doing. At this point we know the 'free' plate pitch doesn't convey a lot, but we're sort of stuck with the term.
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I can roll with that!
. Thanks for helping to get me into this!