Aside from the successful arrangements for concert band of "Rydeen" in Season 1 and "Takarajima"（宝島）for Season 2, the Kitauji High School Band has become known for its orchestral pop theme song, "Mikazuki no Mai" (Crescent Moon Dance) that it played to success at the end of the first season. At first, I thought it had been created long ago by some American composer but it was actually composed by Akito Matsuda（松田彬人）who was in charge for the soundtrack for "Hibike! Euphonium". In-universe, the credit for the piece has gone to Namie Horikawa（堀川奈美恵）.
Listening to it in full, I couldn't help but feel that there was some tribute to the Gershwins' "Rhapsody in Blue" in that I felt a certain early 20th-century hustle and bustle of urban living. According to the write-up for "Hibike! Euphonium" on J-Wiki, excerpts from British composer Nigel Hess' "East Coast Pictures" was also used in the show, and after listening to the 2nd and 3rd movements of "The Catskills" and "New York" respectively, I could also imagine that there was some influence from them as well.
In any case, it will be interesting talking with my anime buddy when he does come back about "Hibike! Euphonium". I have a feeling though that he will be much more praising of it than I am but that's cool. I don't think there will be any more sequels to the franchise aside from a condensed cinematic version of Season 2 but it might be interesting to have a spin-off based on the complicated character of Asuka.