Have a listen to it, for a piece of contemporary classical music it's pretty nice to listen to and easy on the ears too. In fact, I'd say most of the pieces he composed were gorgeous.
I had the luck to come across a concert and go in for free when I was in Heidelberg, Germany. They performed 4 pieces in the concert - one from Beethoven, another from Mozart, while the other two were compositions from featured young composers in the whole music festival.
Honestly, I was a bit apprehensive before actually listening to the piece, as the 2nd performance, also modern classical music, was crap (to me). I mean, I know you can argue that the composer knows the piece best and everything, but who writes a piece of music and insists on playing the solo himself? Especially for a composer - don't you have to make sure that other people are able to understand and perform your piece? Most of our applause were just given out of politeness (compare the polite clapping with the enthusiastic cheers and whistles given to the others), and even so, I think most part of the applause belonged to the orchestra who worked so hard to play your piece, the concert master to the extent of breaking his E string. And after the concert, when someone praised your composition, you had the nerve to go and say 'Yeah, I know (it's good).' Well, these are just the thoughts (and rants) from my puny, insignificant self who's unable to appreciate 'too elite' contemporary music.
Now, Carter's piece is a different story all together. The people playing it, the Szymanowski Quartet, already looked happy when they were seated on stage, even before playing the piece. The piece itself has a nice ring to it. Although there's still heavy use of dissonance and high pitches, it doesn't hurt the ears as everything converges beautifully together in the end between the four instruments. And the guy wasn't such a show off too. He didn't blow flying kisses to the players nor fake humbleness.
Anyway, I'm just saying - don't blow your own trumpet and praise it.