A classically trained pianist who writes songs that are sometimes playfully quirky and sometimes complexly arty, Regina Spektor has a habit of going on the road to open for rock-and-roll dudes. In 2003, she opened for the Strokes on her first tour, which included a stop at the Tower Theatre, where she will headline Saturday. She just wrapped up a stint opening for Tom Petty and the Heartbreakers.

"I feel like since [the tour began in] Denver, I've just gone to the University of Awesome for a few weeks," she said from Austin, Texas, on the last date of the Heartbreakers' tour. "I enrolled in their values, how much they care about music, how hard they work, how talented they are, how nice they are. It's just a beautiful thing to be surrounded by."

Although Spektor and Petty contrast in style and genre, they both are students of song: They take pride in melody and arrangements, and they're mindful of history. But while Petty has been a model of consistency since the '70s, Spektor has been unpredictable throughout her decadelong career.

On the coming What We Saw From the Cheap Seats, her fourth major-label album, Spektor downplays the perkiness found in some of her best-known songs, such as "On the Radio" and "Fidelity," in favor of darker and more adventurous compositions.

"I think the key to everything is just not to do the same thing over and over again, so you have to be in new situations," she said. "That's why travel is so important, or reading new kinds of books, or just having new experiences that stretch you."

The new album stretches, in its first three tracks, from "Small Town Moon," a dramatic, shape-shifting tune about the quandaries of leaving home behind, to "Oh Marcello," a dichotomous song that jumps abruptly between fast-talking verses and choruses lifted from "Don't Let Me Be Misunderstood," to "Don't Leave Me (Ne Me Quitte Pas)," the album's bounciest and brightest track, and another with a playful allusion. "Don't Let Me Be Misunderstood" and "Ne Me Quitte Pas" are both associated with jazz great Nina Simone.

"One of the things that I really loved when discovering jazz is that they would always be quoting," Spektor said. "You would be listening to 'All of Me' and then somehow the bass would just for a second play 'My Favorite Things' from The Sound of Music. They would get into a certain thing that would make them think of another thing, and they would segue through a little medley, and just travel through songs as if they were underground tunnels or shortcuts to other things. I loved that. Obviously, in classical music it's there, too; people use variations, or they use inside jokes. To me, it's a beautiful shorthand to have in anything."

The occasional allusions are part of the charm of Spektor's songs, but what's most impressive is their range and artful construction.

"I really value a contrast," she said. "It makes a much more interesting trip."