Really interesting

My own take comes from the analyses (mathematical and measured) of the sound, and a physical understanding of it's production.  I agree with @Fiddlerman and @AndrewH and @Gordon Shumway  - well - OK I agree with everyone....  it's such a subjective subject (and indeed terminology)

The produced sound comes, in the first instance, from the "grip-and-slip" of the bow-hair and rosin, the bow speed and pressure, and the "engagement" of the rosined hair to the strings.   You end up with a sort of saw-tooth ( not triangular ) waveform when you look at the audio waveform. Now, some strings, and bows, and hair, and rosin, and instrument resonances and deadening-effects (from mass of the chin and shoulder rests, and physical holding, and etc.....) will ALL affect the sound production, and take the produced waveform away from the mathematically ideal sawtooth shape.

So, in playing, this "sawtooth waveform" I mention is not a "perfect" sawtooth wave - like /| where the '/' is the grip and the '|' is the slip - it is not perfect in real life ( I mean, the ideal "slip" is instantaneous - and of course it is not - because of the inertia of the strings - nor is the / ( the leading slope ) a perfect straight line as it is being accelerated as it catches the the bow-hair.

When you take a step further, and look at the actual audio spectrum (as distinct from the waveform) - for a sawtooth waveform - it will, for a "perfect" (mathematical - but real-life impossible) sawtooth waveform - have all harmonics of the fundamental frequency, in decreasing amplitude, going on forever.

However, in real-life situations, there are going to be effects due to the inertia of the string, the loss of energy by both projection of the sound into the air from the moving (vibrating) string, absorption by the bridge and body and so on, and the "mathematically ideal" waveform spectrum is NOT what you'll see from the analyses of a violin tone.  But - it is close - you can clearly see it if you just take a few minutes to record an open string (or stopped, doesn't matter) using Audacity, then look at its spectrum - yup - all harmonics are there, 1st (the fundamental - say 440 for an open A), the second (880) the third and so on... decreasing in amplitude up to around the 10th or 12th harmonic

Now - yes - I am not ignoring the instrument itself - like how "dead" or "lively" it is - yes, indeed, these characteristics all come into the equation - but - in general - as an overall description of what sounds "dark" or "bright" to me (and, well, both are good in their own place - and - for me - well - that's fine - and to some extent could be changed on a specific instrument by the choice of strings) comes down to the relative presence of the higher harmonics.  A "seriously bright" instrument and strings might be somewhat "edgy" for me - not overly pleasant to listen to, or indeed play (unless you are a David Garrett with a feel and touch that accommodates the instrument).  A "super dark" instrument and strings can sometimes sound somewhat "labored" in playing (unless, once again, you have the technique) - like where the strings just DONT RESPOND as rapidly as you want - (so, go on, fit steels LOL) but again - the tonal quality (of a dark instrument) can be quite magnificent for certain pieces.

But, that's just my personal take on this whole scenario of bright and dark ( and other associated terms, like "lively", "dull", "wooden", "shrill" and so on )

It's how I see it, and I know, many players have asked me "so just exactly what has math to do with music?"  Personally, I think it has everything to do with music - and I'm not saying players should know this, in the same way, as a driver, you don't need to know how your engine management system and petrol injection systems work.   

It's just the way I see it, right or wrong, doesn't matter either way - just wanted to throw in my tuppence-worth !    so you'll all notice how I have gracefully side-stepped @FortyNothing 's original post by not really giving an answer !!!

Even more ( OK, this was/is specific to mentioning G2 ) -

G2 is not far away from 100Hz.   In the UK our mains frequency is 50Hz.   You ( well I, and most folks ) can easily hear a 50 Hz mains hum - ( 100Hz in USA ?  not sure... )

And - (well while not hearing it at the same time) the G2 is close enough to 100Hz, which for me here, is an octave up from the "ingrained 50Hz UK hummmm" we never escape from, for me to "imagine" it at half of that ( because the 50Hz is "always there, somewhere in the background" - and even in the mind if not actually an audible hum)  

OK, just kidding - my reference to hearing G2 when a G3 was played in my earlier post was just a "for example" - I experience a similar thing on many of the lower frequency home notes / key tonics...   I should perhaps stop listening to so much solo cello music...  (it's evidently destroying my aural perception)