Examples of European or American composers being influenced by non-Western cultures are many and well known, but it's important note that this exchange goes both ways. A great example is the Indian musician Kadri Gopalnath (1949-2019), who adapted the saxophone to the idioms of South Indian (Carnatic) music, with such devotion that, according to Evan Parker, the term "kadri" has been taken up as an alternate name for the instrument in parts of South India! Although he devoted most of his career to traditional Carnatic music, Gopalnath also undertook genre-bending collaborations with Rudresh Mahanthappa (Kinsmen, 2008) and James Newton (Southern Brothers, 1993).
"Kanakanaruchira" is one of the Pancharatna kritis (AKA "The Five Gems), a set of devotional songs by Tyagaraja (1767-1847), one of the three members of the hugely influential "Carnatic Trinity" of Indian composers. In these performances, the saxophone plays the part that is traditionally sung, and which includes many delicate nuances between and around the notes, recognized by Indian music theory as gamakam. In Gopalnath's hands, the melodic part sounds like it was conceived for saxophone, and in fact, he made several modifications to his instrument in order to make it better suited to the idiomatic gestures of Carnatic melody. (For comparison, listen to a vocal interpretation of the same piece by Nithyasree Mahadevan.)
In these recordings, Gopalnath's part is doubled by a violin (another Western instrument that Indian musicians have happily adopted) and a percussion trio of thavil, ghatam, and morsing (Indian jaw harp). The exchange of energy between melody and percussion in this music is absolutely staggering: from the dance of these two parts, the music radiates a prismatic array of color and feeling. As Lewis Rowell explains in his book Music and Musical Thought in Early India (p. 116):
"The polarity of melody and drumming is one of the deepest layers in the Indian musical tradition... The intrinsic complexity and equally complex interaction of these two dimensions partly explains why Indian musicians have never developed a system of harmony, [which] would have first required an unacceptable simplification of both the pitch and temporal dimensions."