JoshMc

Jazz is just as complex as classical music but often in different ways. You can do what you've said and just follow around some basic chords with predictable scales and whatnot but that's just the basics. If you start trying to really figure out what's going on you'd find a ridiculous amount of chord substitutions, voice leading that's possibly even more complex than you'll find in classical music especially since it's usually figured out on the fly, crazy polyrhythms and syncopation, etc. Honestly, I'm having trouble summing up all the things that go into the music as there's too much to list really.

Maybe it would be easiest if you just listened to some of the better jazz artists or checked out their lead sheets. For instance, Coltrane had some really complex chord progressions going on. Thelonious Monk figured out how to use phrasing to make progressions that shouldn't work sound wonderful. Ornette Coleman took improvisation to it's limits by using some creative aleatoric tricks. You also have people like Chick Corea who is pretty much an amalgamation of jazz from the last century with a lot of classical aspects thrown in. Joe Pass would be a good place to look to understand how jazz musicians use chord substitutions to morph a tune into something completely different as it progresses.

Ok, this is starting to seem impossible. I don't know how to sum complexity up. How about this. What do you think makes classical music so complex? If you tell us that then I can pretty much guarantee you that we could list jazz music that contains these same elements and sometimes these ideas probably even came from jazz.