Evaluating a system - what do you listen for?


I have been in this hobby a long time and my opinion of what I want to hear in reproduced music continues to evolve. Having owned many systems - and critically listened to many, many more - I am now looking for an overall sound that as accurately as possible captures the tone and tempo of the music with enough of a bass foundation to convincingly portray an orchestra at full tilt or club beats while still nailing the timbre of an upright bass. Decent portrayal of leading and trailing edges is nice, and a high end that’s fully present and balanced without stridency is a big plus. Detail’s good, but hyper detail without musical flow can be distracting. Airy treble and pinpoint or large soundstage are also nice to have, but if what’s coming out of the speakers doesn’t make me want to tap my toe or cry a little bit when a vocalist holds a note just so, then what’s the point? That’s what I’m looking for these days - what about you?
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@b, on the emotional connection imparted by a particular component. I wonder if Art Dudley is admitting that even he doesn't have the Audio vocabulary to capture or summarize the full effect of adding or subtracting a particular component from the chain. Perhaps the effect was too profound in one or many ways, and it just resonated in his listening experience to create a personal reaction beyond rationalization. This may sound too "woo woo" for some, but I think I can relate.
@bdp24 I don't know how they do it, but when you hook up certain amps to speakers they just seem to have better timing than others (One brand comes to mind).  Good speakers do what they are told.  Source material and electronics (and turntables) do the telling.
Power amps DO interact with the speakers they are hooked up to, (particularly at high and low frequencies), different drivers in different ways. Dynamic woofers are well-known to send a signal back to the power amp, though I forget what that phenomenon is called. Electro-magnetic feedback, perhaps. And some tweeters (especially ESL and ribbon) can cause slightly unstable circuits to oscillate. That interaction definitely can affect the timing of music.
I remembered the term! Back EMF, or electro-magnetic force. That’s what the woofer sends back to the power amp, different amps responding to it in different ways. I believe amps employing a lot of negative feedback have a more difficult time dealing with it.