What did, and do, we see in him? Both a steward of music’s traditions and an explorer of the future. A vibrant interpreter of the music of others and a creator of his own. An artist who can star more than plausibly in an Apple commercial without seeming a sellout — one who’s thoughtful, even analytical, without ever seeming to try too hard.

Almost no one else in classical music so completely satisfies our polarized demands for old and new, innovation and tradition, head and heart. As Mr. Salonen prepared to leave Los Angeles, Alex Ross wrote in The New Yorker that he’d become “a fixed point of cerebral cool in a city of spectacle and flux.”

But if his persona has a certain wry distance to it, there is heat in his presence on the podium, and in his effect on orchestras. His connection to the San Francisco Symphony seemed close, confident and charged on Friday, just his fourth time leading the ensemble. (Classical marriages can be shotgun.) If his feet were bothering him, there was no betraying it in the music-making.

That he was able to come here for a visit so soon after the announcement last month was happenstance. This weekend of concerts at Davies Symphony Hall was supposed to be conducted by Mirga Grazinyte-Tyla, who has canceled a spread of dates this season (including her debut with the New York Philharmonic) after giving birth in August.

Mr. Salonen, who happened to be free, kept the second half of her program — Sibelius’s “Four Legends from the Kalevala” — and preceded it with Anna Thorvaldsdottir’s “Metacosmos” and Strauss’s “Also Sprach Zarathustra.”