Evaluating a system - what do you listen for?

The best is not to try and focus on any particular frequency or sounds at first. I am a mastering engineer, and the best technique I use is to almost not focus too much initially. It sounds counter intuitive, but this approach allows you to get an immediate first impression on the overall track, especially if it is one you know. It takes a while to get used to doing this, because you need to not think and you might feel you are being distracted. A good way to practice is to put the track on and do something else nearby, or simply look away from your speakers. Once you have done this for about 5 minutes, you can decide to zero in on various frequencies in a focussed manner. As a rule, vocal and piano are the hardest to get right, so I look for this to sound natural and musical, but not "live".

Try not to look for this "live" sound. Most live sound is amplified and through a distorted PA anyway, so doesn't mean anything by way of comparison unless you are comparing to acoustic live music. Only then is the live approach valid. Even then, many acoustic spaces are not great, so live sound is such a broad church. Better to go with your own subjective preference. 

Psychoacoustics make a big difference too. Looking at a beautiful high end system or listing to one in a glistening top studio where you are overwhelmed by the glamour will often make you want to think it sounds better, so clouds judgement. Simply close your eyes to overcome this problem.

Finally make sure you are in a good mood/same mood each time you listen. Nothing affects your judgment more than how you feel.

I would use the words, realism or holographic, as the essence of what I am now hearing. My last four years have been eye opening to me. I am now hearing very precise locational information, such as where all musicians are, in the case of piano solos even knowing where the high notes are in space, a real sense of ambience in the hall, bass reverb. In addition every note from 20 hz to immediate leading edge, and human noises of the musicians. Sibilants with no breakups and sounding real.

Frankly I never expected to hear what I'm hearing. It is a real thrill to hear performances that I could hear as the musicians are now dead.

I must say that this is all very fragile. Some records don't have this information and sometimes my system is not fully ready, such as having to be on for longer after being off for thunderstorms. But when it is right, wow!

I want an accurate timbre  recreation of what's on the recording. That and 3 demensionality,  as well as, the ability to handle dynamic swings.

Right On! bdp24-

after the Piano, the violin and cello, is next on the timbral scale of importance.