Elegant, urbane and impossibly smooth, jazz giant Ahmad Jamal and his quartet brought a sense of purpose and order to an otherwise frantic and chaotic game day in Ann Arbor on Saturday.

Playing to an adoring, if disappointingly undersold, Hill Auditorium audience, Jamal delivered a measured, austere performance that surveyed his legendary career, while proving that, at 81, he’s far from finished.

“My memory is short, but it’s good,” Jamal deadpanned as he settled in to his 90-minute set, which kicked off the University Musical Society's 133rd remarkable season.

Jamal remains a nimble and jaunty pianist, and on Saturday, he displayed an easy, low-key approach that allowed his compositions to breathe in the more-than-capable hands of his quartet. Songs began in an almost startlingly nonchalant fashion, usually with Jamal tinkling on his Steinway, before easing into arrangements.

Once the tunes got rolling, Jamal took control, acting as his own conductor, steering the band at his whim, directing solos and, essentially, directing traffic, as he’d point to a player when he wanted to hear him solo. If he wanted to hear something different, the gesture would change ever so slightly. When he’d heard enough, he would wave his hand in a single calm swipe and bring everything to a perfect, fluid conclusion.

The result was jazz as it’s meant to be played: in the moment and open to the possibilities that those moments offer.

And these moments offered plenty of variety. “Aftermath" was a rhythm-heavy, almost funk-tinged bop number, featuring percussionist Manolo Badrena, who was the secret weapon throughout the show, augmenting the compositions with seemingly effortless and ever-changing percussion touches. He didn't necessarily carry the show—that honor belonged, rightfully, to the leader—but his vivid playing kept some of the more traditional numbers from ever getting to sleepy or from sliding into rote piano trio style.

In spite of Badrena, the band sputtered occasionally during ill-fitting forays into Latin-flavored grooves and some oddly structured numbers that proved less than the sum of their parts.

The rhythm section of James Cammack on bass and drummer Herlin Riley was simpatico, and the two clearly enjoyed playing off one another, whether trading solos or simply interacting within a the compostions.

Jamal, though clearly slowed some by age, remains a showman, exuding an easy, breezy vibe throughout entire set. Sometimes he would get up and amble around the stage or just sit, arms folded, watching his bandmates do their thing. The effect was that of a grandfather giving the kids a hard time, even though he was having a blast in the company of the youngsters.

The overall effect wasn’t that of a band of hungry players burning through a set, but rather a quartet with no question about its ability to bring Jamal’s compositions fully to life, even as they found ways to keep them fresh and inviting.