NoNoise- No doubt. Musicians can get the gist of a recorded performance over a crappy boombox, because they are listening to the song or performance for artistic reasons, and not the fidelity of reproduction. (Not to say a musician or songwriter can't appreciate a good system, but for artistic purposes, i think they are listening to something different).
Likewise, there are folks who are willing to trade off bandwidth for tonality- i am thinking here of single driver systems or some of the positively ancient designs that come from theatres. (I can accept this trade-off myself, one of the reasons I lived with old Quads, and even traded off dynamics as well for so many years).
There was a little experiment a few of us did on another site, listening over a lo-fi computer set up to a few tracks with the EQ set to max on 1khz and setting everything else down as low as it could go. You could get the gist- the gestalt as you refer to it- even though it was not a 'good' sounding reproduction- things were missing, but the performance was still 'enough' there to be able to go with the music in a non-critical sense.
You are right that we analyze parts, rather than the whole, when trying to capture the fidelity at a higher level. The analytical part of the brain is like the 'specs' in the sense that it is looking for explanations for why something sounds the way it does. When I am in that mode, I am not listening to the music, but it is, I suppose, a necessary evil- there are times when the system is just 'right' sounding and you can relax and enjoy it without dissecting it. For me, it's not easy to switch between the analytical and the more 'relaxed' mode- if I am trying something new in the system, my brain is often in analytical mode. Sometimes (usually with help, it is harder to do by yourself, i think), you can make a change and listen to the difference and change back and listen again, and based on your 'gut' impressions, decide what sounds more natural or more akin to what you think a real musical performance sounds like. I think, sometimes, listening late at night is good, not just because the electrical system may be less 'noisy,' but because you are a little fatigued- your defenses are down- you (or maybe it's just me), are more inclined to just absorb, without thinking.
I think i have pretty 'quick' ears in hearing differences that way (but the analytical part of the brain is kicking again). It's deciding what's better or 'more right' that's often the hard part. And, to complicate things, what works for one piece of program material may not work so well on another. So, rather than changing preamps or cartridges or speakers on a recording by recording basis (perhaps, at least in the case of cartridges, this is practical if you have multiple tonearms already set up), you (or I) try to strike a balance- what works across the board, on as wide a variety of program material as possible.
None of the above is meant to provide an answer to the 'magic' part, just echoing what you said about the 'gestalt' and how my brain- or what's left of it- seems to work in listening to music over a hi-fi system.
