Inspiration struck Joseph Alessi, the New York Philharmonic’s principal trombonist, when he heard the pianist Makoto Ozone and the vibraphonist Gary Burton perform Chick Corea’s “Brasilia” at Birdland, the midtown jazz club, in 2017. “Something came over me,” Alessi recently recalled. “I just love the music so much.” He asked Ozone, who also had performed with the Philharmonic, to broker an introduction to Corea to discuss a commission. The resulting Trombone Concerto—which Alessi describes as a fusion of Latin rhythms and the impressionism of Erik Satie—became the last piece Corea completed before he died, in 2021; now the Philharmonic gives its U.S. première, at David Geffen Hall (May 25-27). Originally, each movement ended quietly, so Alessi summoned the courage to ask Corea for a new finale. Now a balmy tango flows into a fistful of dangerously high F-sharps on the last page. “Be careful what you wish for,” Alessi said.