Here's the thing about "Avant Garde." It literally means, "Advance Guard," or in other words, people at the current, cutting edge of new, usually artistic innovation. I mean, if you want to get technical about it, Beethoven was about as Avant Garde as it gets, back in his day. Haydyn's Symphony No. 94 was Avant Garde several decades earlier. Wagner was Avant Garde. So were the Beatles.
But none of that is at the forefront of new ideas, anymore. Some of it's still pretty cool, but it's all been done and done and done and sounds "Classic." Generally, to be avant garde, I'd say you still have to be ahead of the general body in terms of innovation.
Stockhausen certainly WAS Avante Garde back in the '50s, '60s, and even '70s, but I'm not sure that stuff really can be counted as contemporary Avant Garde, since people have been building on those "classics" for a few generations, now.
I suppose there's a case to be made for his later works up until his death a few years ago, but honestly, the stuff that was really innovative to most people was his early electronic work, when that kind of stuff just wasn't around.
That said, in a less rigorous sense, both "experimental" and "avant garde" are popularly used to signify "unusual," so...
I still kinda think he might fit best in 20th century, since I find him cropping up everywhere in "History of 20th Century Music" type stuff, and very little in "Cutting Edge of 21st Century Music" things.
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