Possibly the Damned Trilogy by Alan Dean Foster:
Two major alien civilizations, the Amplitur (a squid-like species with telepathic and mind-controlling abilities - which they couch as "suggestions") and The Weave (a confederacy of more or less equal species), have been fighting a war for several millennia. The Amplitur are attempting to join all sentient species in what they call the "Purpose", an alliance which they "guide" to some unknown (even to them) end. The Weave is a group of species allied in opposition to the Purpose.
From the first book, Call to Arms, at the start of chapter 3:
Chichuntu was a sublimely beautiful world, elegant and refined as its inhabitants. The Wais were ornithorps: tall, quiet, manicured of manner and appearance, rarely flustered, and always comfortable no matter what their surroundings
The musician is Will Dulac. However he's not a jazz musician. Rather he's actively trying to avoid jazz in his compositions. From chapter 7:
Dammit, Ravel had found the effect he wanted! So had Debussy, and Griffes. If a bunch of
early-twentieth-century Frenchmen and a sickly American could create the sound he needed, why couldn’t an experienced academic from New Orleans? Maybe he’d subconsciously avoided use of the saxophone all along because the last thing he wanted was any jazz overtones. Coming from that part of the country, it was something he’d had to fight in his work all his life. ”Oh, yeah, you’re that composer from New Orleans. Your work must be, has to be, cannot be anything but jazz-oriented. Right?”