What music is good music?

I like to abide by Duke Ellington's mantra that "There are two kinds of music: good music and bad music."  But what defines good music?  Let's consider some pieces of "new" music--are they good or not? 

I am an Elliot Carter neophyte.  In 2008, I found myself reading a lot about his 100th birthday, and reading reviews of concerts comprised completely of his music.  My preconceived notion of his music is that I don't like it, but I do try to sincerely investigate different musics before I truly pass judgement on them.  I've decided to set off on an investigation of Carter's work to learn more about it, and find out what all the fuss (on both sides of the good-or-not debate) is all about.  So while I'm still deciding if I enjoy Carter's music, I'm incredibly interested in finding out why other people love his stuff or hate it.  Here are some samples: 

My first judgement is that I don't like the first, but I like the second two.  But, I only listened to these pieces once before passing judgment on them.  The first, to me, is simply too challenging to grasp--there just is not enough for my ear to grab onto and connect with.  I have complete admiration for the performer, and for the mathematical process Carter followed to assemble the piece, but I get no pleasure out of listening to the piece.  The second is pleasing to me simply because of its unique instrumentation, and because I know a little backgroud about the piece.  I think the transmutation of time and rhythm in that piece is incredibly interesting, and--again, to me--draws the listener right in.  The third piece suits my ears well, and it is the interaction of the two instruments that catches my attention.  While listening to this third sample, I found myself sitting back and letting the performance unfold in the same manner as watching a good movie--it kept my interest and kept me guessing.

So: is Elliot Carter's work "good" music?  Is it "bad" music?  Why?  I'm still investigating, but I want to know why you would or would not go to a concert with Elliot Carter listed on the program.