Best CD Player for Classical Music?

I realize that a CD player that is good for classical is good for anything, but the reason I was specific is because the classical section of my CD collection is the fastest growing section. And not being very familiar with classical music I rarely heard it live. But now I'm going to more concerts and I'm looking for a CD player that can get me close to what I'm hearing live.

To be more specific, most of my classical listening has been through my system and not live. But when I hear it live it sounds softer, smoother, and flows more naturally. It sounds effortless, unforced, more relaxed. I then realize how "hard" sounding classical music sounds through my system. It may be that it's digital that makes it sound hard, but I'm not going analog right now so please stick with the CD player recs : )

I'm looking for something for my headphone system. My headphone amp, a Grace 901, is a highly resolving amp so a quality source really shines through. My favorite instruments are the cello, violin and piano and I would prefer to find a CD player that excels at making these sound natural. I'd also like something that is not too forward.

Maybe I'm crazy thinking I can find what I'm looking for in a CD player, but please let me know if you have any recommendations. I'd like to find it if possible. Thanks.