Mason J. answered • 08/19/21
Creative and Inventive Producer with 5 Years' Experience
This is a fun one!
I don't have much of an academic background in ethnomusicology but what I can say based on past study is this:
In the late 19th to early 20th century, European composers started to incorporate non-Western musical tropes into their work. You can hear this in pieces like Rimsky-Korsakov's "Scheherazade", Tchaikovsky's "The Nutcracker", Mahler's "Das Lied von der Erde", and others. However in many such pieces those non-Western tropes were used as novelty or not taken seriously--effectively it was cultural appropriation.
There were a few phenomena at the start of the 20th century that changed the public perception of non-Western music in Europe. One was Bela Bartok, who travelled around the world recording traditional folk music from various cultures and incorporated it into his music, basically inventing the entire field of ethnomusicology. Another was, quite arguably, the induction of blues & jazz into the mainstream of American culture in the 20's. Both events heavily influenced the creative output of composers such as Ravel, Gershwin, Stravinsky, Shostakovich, & countless others throughout the 20th century; and helped reshape the perspective of the listening public regarding music with non-Western roots.
Another important event to note is Philip Glass's work with Ravi Shankar in the 60's, a result of which being that Glass was so influenced by Indian classical music that he helped jump-start the minimalist musical movement in the West, along with La Monte Young and Terry Riley.
Again, I'm no musicologist, but this is what I've learned about this topic through my academic studies thus far. I hope this was useful!
