The concerts on David Byrne’s tour for his recent album American Utopia, which includes a performance at the Shrine Auditorium on Saturday, Aug. 25, open in a most decidedly un–rock & roll fashion. Seated alone at a nondescript desk on a bare stage as the strands of a shimmering silver curtain rise slowly above him, the singer clutches a replica of the human brain as if he were Hamlet considering Yorick’s skull.

“Here is a region of abundant detail/Here is a region that is seldom used/Here is a region that continues living/Even when the other sections are removed,” Byrne intones reverentially within the gentle murmurs of the opening song, “Here,” while pointing to the cerebellum. “Here too many sounds for your brain to comprehend/Here the sound is organized into things that make some sense/Here there is something we call elucidation/Is it the truth? Or merely a description?”

“After wrapping up this album, I realized I don’t have many songs about girlfriends and boyfriends and breakups and a night at the club,” Byrne says by phone before a show in Boston. “There are really not a lot of people doing this. This is the area I’ve carved out for myself — it works for me.”

Byrne is performing a half-dozen songs from American Utopia at each concert, along with other solo material, and about eight tunes by Talking Heads, which are primarily drawn from the later, more commercially popular era of his influential art-punk band. Most nights, Byrne and his 11-piece ensemble close the show with a heavily percussive cover of Janelle Monáe’s “Hell You Talmbout,” with the lead singer exchanging call-and-response vocals with the other musicians.

As Byrne roams the stage, the musicians and backup vocalists — dressed like their leader in matching silvery gray suits — follow him and circle him while they play, marching and dancing in various choreographed patterns. Was it difficult to get his band to adapt to Annie-B Parson’s choreography while they’re playing? “It was a process,” Byrne admits. “Not every musician took to it as easily as others did. … Some had played in drum lines or had dance backgrounds, and the Brazilians [in his band] certainly knew what it was about.”

Byrne had previously worked with Parson as part of his concert collaborations with St. Vincent, but for this tour he had something different in mind. “I said, ‘Annie-B, I’m going to give you a completely bare stage — a choreographer’s dream — with no amps onstage.' It’s all about movement, stripping everything away, and becomes about us, how we move as individuals and as a group.”

The singer, who was born in Scotland and raised for a few years in Canada before his family relocated to Maryland, has long been fascinated by unusual rhythms, going back to the later days of Talking Heads, when he began incorporating disco, funk and West African and Brazilian beats into his songwriting. On the starkly percussive “This Is That,” from the new album, Byrne marvels about that magic moment “when the melody ends and the rhythm kicks in.”

When did his interest in infusing staid rock & roll with atypical rhythms begin? “It was very gradual, very incremental,” Byrne says. “In the late 1970s, I was hearing some African stuff. There used to be a lot more Latin clubs in New York and in the Village. All that percussion — the grooves were transcendent, no matter where it was coming from. Having a lot of groove doesn’t just mean everybody’s happy,” he adds about the clichés that such dance music is always celebratory. “There’s a lot of depth in there.”

Looking back on his past experiments and obsession with rhythm, Byrne says, “It’s always been there, sometimes more or less. The live show has elements of a drum line or a samba school with mobile drums.”

Byrne was exposed to a wider variety of music and challenged to think more experimentally when Talking Heads recorded three albums with producer Brian Eno — More Songs About Buildings and Food (1978), Fear of Music (1979) and Remain in Light (1980). A former synthesizer player with the early lineup of Roxy Music, Eno had evolved into an inventive producer through his work with David Bowie, Iggy Pop, Robert Fripp and others, and he worked so well with Byrne that the duo collaborated on two significant and disparate albums, My Life in the Bush of Ghosts (1981) and Everything That Happens Will Happen Today (2008). American Utopia is only the third official full-length release by the duo over the past few decades, but it turns out that Eno and Byrne get together more often than people realize.

“We’re lucky to be able to do that,” Byrne says about their less-publicized ongoing sonic explorations. “We can do it very quietly and see where things go. … We have a long history of working together. Each time is a little bit different. In this one, Brian had these drum tracks. It was like a kick-starter that got me going. I was so enthusiastic about the project that it became less of a 50-50 collaboration,” Byrne continues, adding that he had Eno’s blessing to go in his own direction.

But Eno’s contributions to American Utopia went beyond co-producing and creating some of the drum tracks. Eno also provided other instrumentation and was credited for manipulating a “robot rhythm guitar” on the funky, electronics-laced song “Everybody’s Coming to My House.”

“Brian loves messing with machines and algorithms, and sticking a wrench in it,” Byrne says. “I knew he had other guitar samples that he programs along with the drums, muted guitar parts that are actually played by a machine. Then Brian will mess with the program and algorithms to make it sound almost human.”

Is there any chance that the reclusive Eno might join Byrne onstage at one of the shows on the new tour, as the producer did once — albeit very briefly — on a previous tour? “He doesn’t do that,” Byrne says flatly.

Despite the current political environment, the album title American Utopia wasn’t intended as a kind of punk-rock sarcasm. “It’s not meant to be ironic. It’s not meant literally. It’s more about the eternal longing for something better,” he says, citing Alexis de Tocqueville’s writing about “the American project” as an inspiration. “People are sure there’s a better way of doing things. It’s not unique to America and goes on all over the world, but American Utopia had a nice ring to it.”

This sense of optimism and idealism not only permeates many of the tracks on the record but also courses through Byrne’s recent civic-minded project, Reasons to Be Cheerful (named after the Ian Dury song), which includes a website where the singer exchanges ideas about how to improve the environment and facilitate better transportation systems in large cities, among other topics. An avid biker, Byrne believes technology can be used to improve people’s lives, although most of the posts on the Reasons to Be Cheerful website generally contain common-sense advice and are more like conversation starters than in-depth analyses.

At various times on the new album, Byrne positions himself as a kind of tour guide, leading his listeners through the labyrinth of the modern American Dream and democratic process. On “Everybody’s Coming to My House,” Byrne recites a litany of lyrical slogans that are simultaneously poetic and uplifting: “I wish I was a camera … I’m pointing and describing … The skin is just a road map … We’re only tourists in this life.”

“In a sense, I think we all help one another,” Byrne says about the song. “We’re all staying in the same metaphorical house.”

David Byrne performs at the Shrine Auditorium, 665 W. Jefferson Blvd.; Sat., Aug. 25, 8 p.m.; $39.50-$149.50. (213) 748-5116,

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