Originally Posted by OccultHawk

I don't think of it as avant garde but it's a fine place to start.

Get high. Put on your headphones. Walk at night in the woods, through the city, or ride a subway. Blast Miles Runs the Voodoo Down. If for any reason you feel inclined to turn it off turn it up instead.

Late period Coltrane is a progression. Some people might feel at home with it right away and jump in. If you don't feel like that first get to know A Love Supreme and African Brass. Late period Coltrane might not seem like it at first but it's very deeply connected to his earlier works. He keeps bending and bending and reorganizing the notes in more and more complicated patterns. Follow the path of My Favorite Things. Take your time about it. Learn the Sound of Music version. Take your time with early versions. Move at your own pace. Just that one song is decades of work. I also suggest going back to Schoenberg's early piano pieces. Take your time listening to how following composers dealt with his 12 tone ideas and how they worked with atonality through both dissonance and ambiguity. Also take note of how previously radical ideas are now mainstream. You're probably already far more connected with the avant garde than you realize.