Like Bauhaus architecture or a Charles Eames chair, Stereolab is retro yet refreshingly new. Beneath the surface of their shiny, polished pop, the lilting melodies of ’60s lounge music, the drone of German progressive rock and the lightest hint of dance-floor beats coexist in a controlled upheaval.

On an early Friday morning in South London, upheaval also describes the household of singer Laetitia Sadier and guitarist Tim Gane, the group’s core members (along with drummer Andy Ramsay and second vocalist and guitarist Mary Hansen). The roof has caved in. While Sadier juggles the roofers and the couple’s young son, Gane has settled amid the chaos for a morning of interviews to support the group’s (or “groop’s,” as they like to call themselves) upcoming tour of Japan.

“I see our music . . . as a selection of many elements . . . the relationships of which create a structure that doesn’t seem to work but actually does,” says Gane.

This approach comes to the fore on Stereolab’s latest album, “Sound-Dust.” The prog-rock-derived wave of sound that characterized their earlier work has been deconstructed into bits and pieces that twist and tumble around each other. The instrumentation is almost baroque in its polyphony. Horns come into the mix from seemingly nowhere to be subsumed in a rush of rhythms. The involved melodies threaten to spin apart at any moment.

As if mirroring the constrained chaos of Stereolab’s music, when Gane talks, words and ideas tumble out at lightning speed. He is a self-confessed information omnivore, reading five books at a time, frustrated that he can’t absorb the information at a faster rate.

Asked to describe his recent top musical faves, he says he only needs to look around the room. Yesterday’s playlist — the first few Wire LPs and discs by film composer Bernard Herrman, Chicago avant-jazz musician Rob Mazurek, Fela Kuti and proto-rapper Gil Scott Heron — cover many of the available surfaces.

Gane’s musical eclectism, which makes Stereolab one of the most postmodern of groups, is perfectly matched by Sadier’s brainy, stream-of-consciousness lyrics. They are more akin to Situationist slogans than typical rock odes of teenage passion or depression. This is, after all, a band that tried to delineate the Marxist take on economic cycles (“bigger slump and bigger wars and a smaller recovery”) within the three-minute space of a pop song (1994’s “Ping Pong.”)

“Guy the Mynah Bird” from the new album, with its lyrics about “a military regime . . . that lies in all impunity,” sounds like a prediction of the world order post-Sept. 11.

“It’s a difficult subject to write a song about politics in an artistic way,” says Gane. “I think it works [for us] because it’s not contrived. I’ve had many people say, ‘Why don’t you say the things simply?’ But we aren’t missionaries.”

Stereolab’s composing process is equally cerebral. “Strumming a guitar, I’ve never written a song like that!” says Gane. “I’m interested in ideas rather than instruments.”

Instead of starting with a chord structure or a melody, he starts with an abstraction. He’ll try to replicate the effect, for example, of listening to a Messaien composition or looking at Minimalist art. This gives him “something to aim for.”

“I like the mechanism [of songwriting] but . . . still think of it as a wonderful thing despite the mechanism,” he explains. “People tend to cover up how things are done. They have this idea that music is born of genius, that it’s more mundane to think about a person coming to an idea through a logical process.”

Part of this deliberate approach has been to choose the right producers. For “Sound-Dust,” Stereolab returned to the Chicago studio of Tortoise’s John McEntire. As with their last record, McEntire produced half of the record, while Chicago’s other wunderkind, Jim O’Rourke, produced the rest.

“I like the ongoing process of building up [a relationship], much like film directors will use the same cameraman, the same editor. You can start again at a higher level of understanding. A lot of things are unsaid,” says Gane.

“I really want our records to be about the personalities that make them,” he says. Thus, though Gane provides the skeleton of each song, the final product is the result of hours of improvisation in the studio.

Both producers were a part of the process. The tightly structured rhythms and melodies of “Space Moth,” off the new album, are a result of McEntire’s “architectural” technique, while the surprising, C&W guitar break on the album’s first single, “Captain Easychord,” is an example of O’Rourke’s “more disheveled” approach.

“We got to this part of the song and thought ‘What do we do here?’ ” Gane recalls. “And there was a steel guitar lying around in a bucket and Jim just picked it up.”

This reliance on chance is brought to the fore during the group’s dynamic concerts. While Stereolab’s recordings are often classified with other lounge or pop-electronica groups, their live performances are more akin to recent Sonic Youth, with whom they recently toured. Though Sonic Youth’s rough edges would seem a far cry from Stereolab’s polish, both groups rely on improvisation and exploit the tension between structure and chaos on stage.

“I’m always looking for the unknown X factor, the unforeseen result of a series of things happening,” says Gane. “The interaction of real instruments . . . is more entertaining. Anything can happen. For lack of a better word, it’s dangerous.”

In line with COVID-19 guidelines, the government is strongly requesting that residents and visitors exercise caution if they choose to visit bars, restaurants, music venues and other public spaces.

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