Complex 20th-century scores like Stravinsky’s 1946 Symphony in Three Movements held no terrors for him. A 2022 recording with the BBC Philharmonic demonstrates his mastery of the work’s turbulent polyphony. When he was a student at Cambridge, he was casually asked if he wanted to conduct Schoenberg’s fearsome Five Pieces for Orchestra; he blithely accepted, and it was only “years later you realize how fiendishly difficult it is,” he remembered, laughing at himself, in an interview with Peter Sagal of NPR two years ago.

“Whenever he comes to conduct, you can just see his love of the music, He’s so excited. It just sort of pours out of his body,” Abbey Edlin, a French horn player in the Melbourne orchestra, said in a video tribute.

The British opera critic Alan Blyth, writing in The Grove Dictionary of Music and Musicians, described Mr. Davis as a “conductor whose technical skill was enhanced by an inborn enthusiasm for and dedication to the task in hand that he was able to transfer to the forces before him.” in the Grove Dictionary of Music and Musicians.

Yet his early-career move into conducting — he was a prestigious Organ Scholar at King’s College, Cambridge — was, in his understated telling, almost an afterthought. “I got interested in conducting sort of by accident,” he told Mr. Sagal. He had been invited to conduct a Haydn divertimento, he recalled, and “I thought, well, I rather like this.”

“I liked being able to bring a group together,” he explained. “I suppose the basis of my conducting technique, such as it is, started early.”

His instinctual approach to conducting served him well in opera. At the Lyric Opera of Chicago, he led almost 700 performances of 62 operas, by 22 composers. There were also many performances at La Scala in Milan, the Metropolitan Opera in New York, the Royal Opera House in Covent Garden, the Bayreuth Festival and elsewhere.