This thread is fascinating to me. When it comes to luthiery, in general I lurk and learn quietly. When we're talking measurement and science, well, my big mouth can't stay shut.
Arnold referred to "psycho-acoustics" in his first post, and now we're talking about ways of "objectively" analyzing the tonal quality of a bass. There's no way one can sensibly think about and model the bass "process" without the psycho-acoustic component. Humans like music, they make all kinds of intruments to play music, and when the sounds are made they go into a human brain for processing and appreciation. The psycho-acoustic part is the critical component here, IMHO.
Problem is, human subjects make lousy objects of scientific investigation. They change their minds. They lie. They are socialized into cultures that pre-condition their thinking. Yada yada yada. Does that mean you can't investigate sensibly what they think? No. Just makes it much harder to do careful science. A lot of people look at that problem and don't want to have anything to do with it; others have made some headway over the last century or so.
As someone who has committed a fair amount of science in this general area (people, not acoustics), I would look at the problem like this:
1) What about this effect players and luthiers have been talking about for centuries? Is there something to it? That is, can knowledgeable human beings (remember, we're talking bass players here -- thank God we're not talking about differences between drums or banjos) reliably distinguish between new instuments and aged intstruments? If such an effect can be observed, you might then want to explore its attributes. How "big" a tonal difference is noted? What are the qualitative characteristics of the difference? How widespread is the ability to discriminate in the bass-player population? The whole point of this is to confront this psycho-acoustic thing head-on.
As for how to do this, first let's assume that practicality and expense aren't a problem. As Arnold points out, there are way too many factors that influence tonal quality for a classic controlled experiment to work here. I won't give a big methodological justification, but I would want to pursue a design where there is a small number of expert "ears" -- that's the panel. The panel evaluates a LARGE POOL of basses (somewhere around 50 would be a good starting point). These basses have all variation in them that the world of basses produces. Given all that variation (and I would expect us to come up with some ways of describing and measuring these other factors), we add one more experimental factor: vibration dedampening. To cut to the chase, there are very good statistical methods (provided there is enough high-quality data) for assessing the influence of a single factor among many. What we'd be looking for here is a very strong influence of vibration dedampening that is independent of those other factors.
Even without the vibration dampening thing, I'd be interested to find out whether the discrimination effect is widely and consistently present in the population. This would addresss Arnold's sneaking suspicion that it's all in people's heads. You can never forget about those sneaky human subjects, though. The whole study would be absolutely founded on the careful use of language (carefully pre-tested and calibrated measurement instruments) to express and measure tonal characteristics.
2) I'd like some non-human assessment of the vibration dedampening effect. The spectrum analyzer could help here. Just because it doesn't "measure" a difference though, doesn't necessarily mean that people don't hear a difference. The first study tells me whether people hear a difference. What we're looking for here is some form of corroboration of the discrimation effect coming from a method that DOES exclude the psyco-acoustic aspect. Makes me more comfy when completely different methods arrive at the same result. Makes me more confident that I am, in fact, going to a place that is an actual place.
3) I wouldn't even begin to hypothesize reasons for the discrimation effect until I know more about it through the first study. The micro-crack thing sounds like it might have legs and is an excellent example of a good, testable hypothesis. The fact that Bob frames it as a testable hypothesis offered up in service of old-bass theory is a sign that Bob's a very clear thinker; lots of people skip the testing and move right to religion. Trouble is, the testing and subsequent theorizing is not relevant here in the absence of knowledge on the discrimation effect in general.
To me, the whole thing is fascinating. As an experienced woodworker new to viol lutherie, I love the long line of traditional knowledge and methods borne from experience. But we don't know everything, and it's entirely possible that some of the things we "know" might be illusory or "mis-known". Careful thinking and experimenting -- the hallmarks of good science -- surely can only add to the mix. It's true at the same time that most of the good stuff has been discovered and mapped already.
To finish, I'm really interested in that laser, Arnold! I assume you use it for assessing longitudinal straightness of fingerboards? What's the advantage over a really good straightedge? I've got good straightedges (one of them plus/minus .0002" per foot); feeler gauges and light shining through cracks have always worked for me. You have to hold that straightedge with one hand, though. Be nice to free up that hand...
It started off as my two cents worth. Looking at it now, I'd say it's about two bits. I'll shut up and go back to learning mode now.