OK, when it comes to bass shapes, I actually have a little bit to contribute...
Some years ago I got heavy into this subject. It meshed well with some interests I have in history and in the sociology of knowledge, so I went kinda deep down the hole...
Here are these two images of basses. One of 'em (the second one attached here) belonged at one point to our own Don Higdon, the other is a Bob Ross bass. Over top of the images I've overlaid a grid work and some circles. The thing I was trying to get across (to myself -- I've never really let this out of the lab very much, so to speak) is that these two basses seem to have shapes that consist of modular circles. That is, these circles all have a radius that is an even multiple of some number. So, for example, the circles are 4 modules, 2 modules, 5 modules, etc. Some of 'em aren't even, but they're close: 1/2 module. I've never pursued this too much, but my thinking is that "the number" comes from some other proportion -- mostly likely some kind of golden proportion type ratio involving aspects of the scale length.
Other people from the violin world have gotten heavy into this stuff. Too heavy, some of them.
What's the practical import? Well, back in the renaissance days it wasn't too common to find tradespeople -- even architects and engineers -- who had today's kind of competency at math and mechanical drawing. Measurement systems, too, were multitudinous and extremely local. You couldn't give an apprentice a bunch of formulae and have him lay out a complicated piece of work. But you could develop a layout method that used modular geometry and you could easily assemble good-looking (and holy) designs and layouts for almost any size instrument.
Modular design and construction methods were invented by the Romans -- it's how they built so many awesome structures using less-than-sophisticated labour. I think the Rennaissance craftsmen must have revived or reanimated a bunch of these concepts.
Anyway, my working hypothesis is that instruments that adhere to the modular concept are the "most pleasing" to look at. I certainly saw some ugly ones that weren't close. But I looked at a lot of instruments and there's likely something there.
Some people who are into this type of thing want to say that classically-designed instruments sound better, but I'm not touching that one with a ten foot pole.
I think all that stuff about f-hole placement in really old instruments probably works on those old modular principles, too.