Completely in line with Mahgister.
I would add that timber being a psychoacoustic personal construction, the key is probably to learn how to listen to what “works” for you and seek and tweak to deal with what doesn’t.
Personally, when testing to a system, I also pay a lot of attention to dynamics, transient, attacks, distinction in vibrato and the dissipation of a sound, the death of a note that remains distinctly audible among others…
harmonics and system induced coloration are also on my top list of stuff to pay attention to.
I am also very sensitive to sound staging, literally as I would be when attending a theater play or an opera.
I also have to admit that it has so far always been much more difficult for me to fully appreciate a sound system when “I don’t like” the piece being played to test it… That is a good feedback to self when it comes to trying to find scientific explanation to what works for me or not.
Finally, I try to always keep in mind that a sound system is made of a master signal which has always been designed (purposely or not, wisely or not), current, cables, electronics, speakers, a room, in the moment in the life (and the day) of an individual. So when the individual is me seeking for emotions listening to music, I very selfishly tend to consider it is the foundation of the system. I try and learn how to listen to the other components to gain in pleasure. Very easy to feel, a bit challenging to measure but so far very engaging and exciting, alone and with fellow passionate music lovers and audiophiles !