The news media have consistently cast Mr. Rattle as the one who got away: a putative candidate for the position of music director in Philadelphia before Berlin snapped him up. Watching him work with the Philadelphia players during their latest visit to Carnegie Hall on Friday evening, you sensed an enduring mutual admiration.

As important, you heard it. At a glance the program looked like standard business: symphonies by Brahms and Schumann bookending Webern’s Six Pieces for Orchestra (Op. 6). A vital advocate for modern music, Mr. Rattle has been more wayward in canonic Classical and Romantic repertory. Some critics have suggested that while working with the Berlin Philharmonic he has absorbed as much about tradition as he has imparted about curiosity and progress.

That same effect applied here. The sound the Philadelphia players mustered from the heroic opening bars of Brahms’s Third Symphony was the orchestra’s own, showing the richness and refulgence that are this institution’s legacy. But the way the music breathed and flowed was Mr. Rattle’s doing. His deft balances in the second movement brought out mild, melancholy dissonances; likewise a glorious account of the heavenly third movement seemed flecked with seraphic light.

After an intermission awkwardly prolonged by a few dozen audience members returning to their seats for the Webern with the alacrity of children facing a dentist’s chair, Mr. Rattle and the orchestra presented the most exactingly voiced, intensely characterized account of the Six Pieces I have ever heard. Each facet of these gemlike miniatures glistened distinctly within a seductive span; Mr. Rattle’s careful calibration made palpable the work’s core sensations of dread, shock, loss and ache.

Schumann’s Symphony No. 3 (“Rhenish”), less a coherent statement than a themed grouping of felicitous evocations of German life, opened with an impetuous thrust that initially seemed to sacrifice nobility for buoyancy. But here again a subtle elasticity in Mr. Rattle’s phrasing gave the music teeming inner life.

The Philadelphia players were infectiously blithe and vivacious for Mr. Rattle in the symphony’s airy second, third and fifth movements. The fourth, Schumann’s rendering of a Gothic cathedral, was perfectly German in its weighty solemnity and perfectly conveyed by this happy combination of conductor, ensemble and hall.