Matthew and Eleanor Friedberger, the brother-sister duo known as Fiery Furnaces, have become the standard bearers of underground progressive rock by reviving the idea that albums can be complete, integrated pop works unto themselves. In this age of institutionalized short attention spans and the iPod Shuffle, such an approach might sound regressive, if not downright quaint.

The Furnaces’ second album, “Blueberry Boat,” released last year on Rough Trade, was a true test case: an ambitious work of art whose derived pleasures greatly depend on how willing you are to give yourself over to the album form. Critics were sharply divided, with some claiming that listeners who didn’t lend it the full attention it deserved were simply lazy, while others dismissed it as turgid self-indulgence.

But while the cuts on the band’s first album, “Gallowsbird’s Bark,” are more conventionally structured, the manic energy and surfeit of musical ideas they contained made it clear that the Furnaces were interested in much more than songs. “Blueberry Boat,” which is over 70 minutes long and is essentially an extended suite of disparate and sometimes repeated melodic and lyrical ideas, represents the siblings’ sensibility more faithfully.

Or, at least Matthew’s. In a phone conversation from a New York recording studio, the older Friedberger said that the Furnaces will release two records before autumn, one of which will feature their 83-year-old grandmother, Olga Sarantos.

“It’s kind of a period thing,” he says in a relaxed, confident tone that indicates he’s used to being interviewed. “The lyrics are inspired by anecdotes surrounding my grandmother in Chicago in the ’30s and ’50s — not necessarily things that happened to her, though some things did.”

The record will feature “a lot of narration” by both Olga and Eleanor. “It’s like a talking book,” he elaborates. “The songs go back and forth into one another. They aren’t standard songs, but the subject matter is specific and the music is conventionally tuneful, so hopefully it will be interesting.”

Matthew is quick to point out, however, that it is structurally dissimilar to “Blueberry Boat,” which even he concedes “was often confusing.”

“This one may be confusing at first. There’s nothing obscure on it, but there are things that people won’t be familiar with, especially about Chicago.”

Though the Furnaces are sometimes too expansive for their own good, Matthew is a details man all the way. “I like listening to things that are specific — people discussing their neighborhoods, that sort of thing — even if I don’t have any idea what they’re talking about. I hope people will be equally indulgent in our case.”

The other record will be more song-based, but since they’re still working on it Matthew won’t say what it will probably end up like. Eleanor is supposedly in the studio as we talk, struggling with her brother’s knotty compositions. Though the Friedbergers are equal creative partners, in past interviews Matthew has come across as the Furnaces’ sole conceptualizer. Does that make him Richard to Eleanor’s Karen Carpenter? Or is he, as some writers have implied, a kind of Svengali?

“That’s from Eleanor,” he says dismissively. “It’s because I make more stuff up, arrange everything. But it’s also because I’m the older brother and I’m always manipulating things in strange ways. She’s nervous about what I try to do, but it’s just sisterly suspicion.”

It seems unfair to discuss such matters without Eleanor present to corroborate them (interviews with the pair often descend into verbal pillow fights), but in any case it was Matthew who convinced Eleanor to become a rock musician.

“When we were both younger I tried to talk her into it. ‘You’re a music fan, you could be a good singer. I’ll write songs for you.’ She was like, ‘Yeah, OK,’ but never really felt it.”

Then in November 2000 Matthew left Chicago and followed Eleanor, who had moved to New York the previous April, and there she finally agreed to form a rock band with him. If there’s a sibling rivalry, it seems to be a fruitful one. “We’re used to being suspicious of each other, so it’s not a problem when I’m trying to get her to sing a 10-minute song about chipmunks and bears.” He laughs and adds, “She feels superior to me. I own more books than she does, but she probably thinks of me as a failure.”

It’s obvious that Matthew doesn’t fear failure because he doesn’t even find criticism disturbing. He understands that a lot of people found “Blueberry Boat” annoying because he rarely followed a melody through to its natural conclusion. The same goes for their live shows, in which the songs are cut up and rearranged so that they form an unbroken suite.

“Some people don’t like it,” he admits. ” ‘Why don’t you play the songs? What’s all this nonsense? Why’d you play it so fast?’ And sometimes they’re right. It was different, but not necessarily better.”

In any case, it’s a rush. The Furnaces appeared at last year’s Fuji Rock Festival, where they played at 10:20 in the morning before a handful of curious people who stood spellbound while Eleanor banged fitfully on her guitar, barking out manic folk-rock songs about animals and the sewers of London in her androgynous voice, with Matthew frantically running around behind her switching between guitar and keyboards as their two bandmates kept it all from flying to pieces. They played a 35-minute set without stopping.

“Tone is everything,” Matthew says about the usual rock show expectations. “The quality of the playing or the arrangement is not as important as whether the person poses or conducts himself in the right way. For some people those performance aspects are just as important if not more important than the music. We don’t think that way. We think more about these songs and how we’re going to take them apart and put them back together in an interesting way. And if we like it, we figure other people might like it, too.”

Is that what we should expect when they come to Japan?

“Yeah, but we’ll play an hour this time,” he says. “Another big medley.”

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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