All them tests and comparisons are done with the wrong strings. Few violin players have the guts to use the real strings
http://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1235&context=ppr
period instruments are still made and are tuned differently. A = 415 Hz
ralph, the point is that there is no need to attempt to explain the sound of Strads and other old violins. Over the years there’s been various hypotheses - the varnish, the wood (including whether tree growth during the little ice age produced a different kind of wood), mere age, etc., etc. But the reality is that despite being amazing instruments, they have been surpassed by modern makers.
Heh.
Which can be really annoying. My wife sings in an early music ensemble that performs in 415. But our piano is in 440, which means she either has to transpose at sight as she’s plunking notes (which is incredibly tedious) or just practice in 440. She doesn’t have perfect pitch, but her innate pitch memory is good enough that she has to concentrate really hard in rehearsals to not go sharp (also she’s an mezzo/alto and in 415 some things go low.)
Bumped.
The Strad of NPR’s Nina Totenberg’s violinst dad, stolen in 1980, has just been recovered: A Rarity Reclaimed: Stolen Stradivarius Recovered After 35 Years : NPR
I know! I just read that. I was processing the name Roman Totenberg and they mentioned Nina and I went Whoa!! Who knew?
Sad story that some twit stole it and stashed it for decades because…twit.
An article in the New York Times about the recovered violin says, “After the theft, Mr. Totenberg, who had owned the violin for 38 years, told CBS News in 1981 that it had taken two decades of playing the instrument before it reached its potential. ‘It took some time to wake it up,’ he said, ‘to work it out, find all the things that it needed, the right kind of strings and so on and so on.’” In another article, he said that after the theft, he bought a Guarneri to replace it, but needed to relearn the fingerings.
That’s interesting. Earlier I think I linked to a blind comparison of Stradivarius and other older violins and high-end new ones. The results were that even experts weren’t able to tell the difference. But what Roman Totenberg is saying is that you need time with a fine instrument before you can use it to its full potential.
I was recently at a violinmakers’ dinner where the featured speaker was Joe Curtain, from Oberlin. Fascinating - and really nice - guy. A quick Google showed this NG article which has some graphics he used in his talk.
I’d suggest if you are interested in whether old instruments are better, reading up on his work would at least give you some info. His bottomline was that there was no way to jigger the results in a way that showed old or new fiddles were better than the other. However, there were some instruments that players and listeners pretty consistently liked better than others. So he tried to assess the acoustics of those. Looked like soloists preferred loud instruments. (Duh!) Also, IIRC, they preferred instruments with a strong bottom end, and a relatively even top and bottom. So then he said, if there are characteristics that people prefer, how can the traditional construction be tweaked to maximize those. Of course when he got into specifics of construction, it was WAY over my head.
He says one huge issue with testing old instruments is that their owners are really resistant to letting you change the set up, and really don’t want to risk having their fiddle identified as one of the poorer performers. So you can’ t really set up all of the instruments so that they have the same strings, same string height, etc.
I also had a recent discussion with a professional bluegrass bassist. He said when he was in business school, he wanted to study the effect of branding. He had a very nice, reasonably expensive carved bass, and a pretty mediocre plywood bass. (Probably $20 K vs $2K. Even the nice one cost a fraction of what a top professional concert bassist plays.) He recorded identical scales and passages, and played them for as many bassists of various styles as he could. But the kicker is, for one group he did not say which bass was which, for another he correctly told which was which, and for the third, he incorrectly identified them as the opposite of what they were. You can guess the result - an alarming number of folk swore the misidentified cheap bass sounded superior, whereas next to no one had any difficulty correctly identifying them when unlabelled.
I’m currently looking into buying a new bass, and I find this kind of stuff fascinating. I bought my current - pretty cheap - bass about 5 years ago. Emotionally, I want to buy the more expensive older bass I should have bought back then, but the more basses I play, the more I like how my bass feels and sounds. Of course, I have to try to figure out to what extent I am preferring what I am accustomed to. And, I’ve got to admit that it isn’t the quality of the axe that is holding me back as much as a lack of talent! 
There’s the woods, varnishes, and glues that Stradivarius used. Some are not available now. Or no one knows what exactly he used. And nowadays, there’s a lot of Headology involved too.
Re: Gibson PAFs… the PAFs were inconsistant. Some were great, some weren’t. They didn’t have the equipment to wind the coils as consistently as they have now. So some PAFs have coils that bulge at the top, bottom, or middle. And some of those might sound better to some than the evenly wound ones. But folks will pay top dollar for an authentic PAF and swear it sounds better than anything else. Headology.
Yes. Learning how to get a top-tier instrument to respond can take time - and you have to decide you think it is worth it. That’s a long investment to get a violin to open up, but he thought it worth it.
But…but…dude! It was a scatterwound PAF!!! (to Ranger Jeff’s point, those old pickups were wound by hand. At one point, a particular example that sounded good was repaired and discovered to have been “scatterwound,” i.e., the copper wire was not wrapped in an organized way. The person at the manual winder just appeared to have let the machine run. For a few years “scatterwound” PAF replicas were the rage. So it goes.)
Having said that, I have played a bunch of PAF pickups, in 50’s Les Pauls, 335’s, ES-175’s, etc. I agree with RJ that they can be hit or miss - the misses only sound like a great humbucker. But the special ones deserve the reputation. They give amazing feedback (as in information; not a squealing amp) that help you dial in your playing and tone. Simply wonderful.
As an Oberlin alum, I’m always glad to hear about other grads and faculty.
Sounds fishy to me.
I am surprised nobody seems to have mentioned “projection” as a factor in the superiority of Strads. Not volume, “projection”.
For whatever reason (and I am not a violinist or a violin maker so I am not going to hazard a guess as to why), a concert violinist playing a Strad will be heard loud and clear by the people furthest away from the stage … much more so than if he or she were to play a lesser instrument. Obviously, in the days before electrical amplification, this was a most important attribute of a violin.
Nowadays, this projective quality is perhaps not quite as important as it once was.
Interestingly, the same quality can be found in acoustic guitars, both steel string and nylon. A handbuilt guitar by Romanillos is going be heard (unamplified) at the back of the hall much more clearly than any Pacific Rim import built with similar solid woods.
Projective quality aside, the difference in “tone” of a top quality handbuilt guitar can be instantly heard (and felt) by the player … whether the same applies to handbuilt violins v. factory instruments, I have no idea.
Hmm, projection doesn’t seem to be a quantifiable quality. It’s a mix of the volume and tone of an instrument intersected with how it sounds in a particular setting. Certainly some instruments have a lot of projection, but put it next to a group of instruments that have a similar volume and tonality, and it’ll get lost.
I think I mentioned upthread: a guy who posts on vintage guitar websites, has an amazing collection of old guitars and was an acoustics engineer and professor for his career - he calls this “cut.” Meaning: It may or may not be louder but more of its energy is focused on the frequencies you want, and less on the ones you don’t, so the good frequencies cut through the mix and project better.
In my experience, new and old excellent guitars do have better Cut, and an older, excellent guitar may get a bit more as it is played in. As I have said all along, I don’t think a Strad has this quality in such abundance vs. other excellent instruments that it is in a whole 'nother category.
Well, and one instrument that cuts appropriately in one setting won’t necessarily work in another. I can’t think of a handheld, stringed, acoustic instrument with more cut, projection or volume than a banjo. It’s far from appropriate for many types of music, though.
Of course, any high end instrument has a trade-off between volume and tone ( yep even a banjo, you haters 
). Most of what makes a Strad (or an early electric guitar) so unique at this point is that it’s one of an early group that was an excellent example of the art. It’s special because it was one of the first, not because it’s a unique instrument that can never be reproduced.
TLDR;
Math…
It could be that the growth rings in the wood and how it is cut/sliced, resonate with the most equal frequency response.
A sudo-side view of growth rings. “lolloolllooolllooololooolloloolllool”
Or, could be just plain ol’ SORCERY.
Yep. Guitars started to get modified in the 20’s simply to compete with banjos. The guitars were more versatile, but the banjos had more loudness AND cut. So they tried F-Holes on archtops, resonators and forms of amplification - as well as modifying flat tops to take steel strings and project. In bluegrass circles a loud flattop that can compete is called a Banjo Killer.
Just yesterday I was playing right next to a guy flatpicking a National resonator. Good LORD was that thing loud when he pointed it in my direction. Meanwhile, thumping away on my bass I often lose a good sense of how it is projecting down there. We play outside often, and folk regularly say when they arrived the first - and only - thing they heard was the bass. Makes it really hard to compare different basses when playing them, as you don’t get a true sense of how they sound.
Curtain mentioned volume, observing that you could only go so loud in an instrument positioned right under the player’s ear.
Have you considered buying a folding Chadwick bass? Charlie Muench of the Stray Birds plays one, and he showed me how it folded away compactly … very cool.
You can see him play it on this video https://www.youtube.com/watch?v=U3XUzdlOoUk.
He’s bowing it on this tune but it sounds just as good plucked.
So, if I buy a Chadwick, I’ll be able to do THAT?! 
Yeah, I’ve played - and played with - them. Really neat - especially if you tour as I imagine those guys do. But the Chadwick is a modified Shen - which (IMO) isn’t too terribly different from my current Englehardt.
I imagine I’m going to end up with an old Kay.