Paul Simon and his nine-piece band at Bass Concert Hall on May 10, 2016. Photo by Suzanne Cordeiro for American-Statesman

Could Paul Simon have become an icon of American popular music if he’d stuck to the lyrics-focused folk-rock that made Simon & Garfunkel a household name in the 1960s? Probably, because so many of his early songs left such an indelible impression that crowds still sing along with them nearly half a century later, as they did Tuesday night at Bass Concert Hall.

» See more photos of Paul Simon at Bass Concert Hall

But it was his push toward polyrhythms after he went solo in the 1970s that ultimately gave Simon the broader legacy he enjoys today. At 74, he still has a magic way with words that can make the mind reel and the heart feel, even as the body is grooving to the endlessly creative beats of his tunes.

Paul Simon at Bass Concert Hall on May 10, 2016. Photo by Suzanne Cordeiro for American-Statesman

Simon’s current tour, which includes a second show at Bass Concert Hall on Wednesday along with his first-ever taping of “Austin City Limits” at ACL Live on Thursday, partly allows a sneak peek at some songs from his upcoming album “Stranger to Stranger,” due out June 3. New tunes such as the eerily dramatic “Werewolf” and the hip-hop-influenced “Wristband” show Simon’s continued insistence on pushing himself into uncharted territory.

But he also traveled far into his past for many longtime favorites. Those passages yielded mixed results. “Mother and Child Reunion” and “50 Ways to Leave Your Lover” felt a bit like going through the motions, but “Me and Julio Down By the Schoolyard” kicked up the pace mid-set, and the Simon & Garfunkel-era “Homeward Bound” sparkled in its stripped-down simplicity.

The most rewarding moments, though, came from back-catalog songs that weren’t among Simon’s biggest hits. On “Obvious Child,” a standout from 1990’s “The Rhythm of the Saints,” march-style drums propelled some of Simon’s most inspiring lyrics (“These songs are true/These days are ours/These tears are free”). And an instrumental snippet of Simon & Garfunkel’s Peruvian staple “El Condor Pasa” brilliantly led into the early-career marvel “Duncan,” a hauntingly reflective tune that has grown more poignant with the passing years: “I was playing my guitar, lying underneath the stars/ Just thanking the Lord for my fingers.”

There were moments during the show when Simon seemed to disappear amid all of the music swirling around him, and that’s probably just the way he likes it. His worldly nine-piece band included multiple multi-instrumentalists who helped cover bases ranging from guitars and percussion to horns and accordion to piano and organ, and more.

At the very end, though, the spotlight rested on the songwriter alone. As full-band echoes of “Late in the Evening” and “The Boxer” faded from a five-song encore, Simon serenaded the crowd with one last classic, just him and his guitar: “The Sound of Silence,” complete with a mesmerizing extended guitar intro. His playing was so lyrical that it almost seemed like he could have played the whole song as an instrumental, without even uttering any of its immortal words. Such silence, in that moment, seemed golden.