I've always been interested in early East-West relations like the Silk Road and Marco Polo's accounts of the East. Studying classical music history there were definitely points in time where Western musicians would be influenced by east (Debussy, Mozart, Rimsky-Korsakov). What did Easterners who had never heard of Western music think? Was it generally aesthetically pleasing to them or did it sound unpleasant?
I don't know about further east, but the Ottomans were aware of European classical music as it was being developed. They didn't like it, they felt it was too busy with too much going on. Ottoman classical music, developed at a similar time, was all about a very small ensemble playing very few notes to back up a solo vocalist. They called it "thin music." There is an Ottoman History Podcast on the subject, I believe.