So much this. People are told that the reference point for classical music is Eine kleine Nachtmusik or some other iddly-twiddly Mozart, but in fifty years of exposure to classical music I’ve never got Mozart (with the possible exception of the Requiem). Shostakovich on the other hand…
If you want to give your ear for harmony a workout, I’m going to suggest string quartets - the Debussy is gorgeous, Shostakovich no. 8 is heart-rending. The best way to experience any of them is to be in the same room as the string quartet, but I guess the next best way is through good headphones.