Much of the music heard on Tortoise’s new album, The Catastrophist, began life as a sonic portrait of Chicago—but it’s the band’s own identity that comes through the clearest.

What eventually became the group’s seventh studio release grew out of a 2010 commission from Chicago’s Department of Cultural Affairs and Special Events. The idea was to create a suite of songs that would link Chicago’s historic jazz underground, as exemplified by artists such as Anthony Braxton and Roscoe Mitchell, to the indie-rock scene that, most notably, has given the world Wilco. Five pieces were duly created and performed with guest improvisers, but not readied for album release. Instead, Tortoise took those frameworks and then edited them so severely that, as guitarist Jeff Parker noted in an interview with Chicago magazine, “The songs are virtually unrecognizable.”

Most bands write songs and then improvise on them. Taking improvisations and then making fixed compositions out of them is so far from standard practice, as John McEntire admits in a telephone interview from the Windy City, that it’s almost perverse.

“Exactly,” says the keyboardist and percussionist, who’s also an acclaimed recording engineer. “I mean, we had pieces that were more open-form, based on the nature of the group that we had at the time, which included the guests. They were more like head-and-solo arrangements, but when we got into the studio and decided to try to figure something out with them, that improvisational aspect didn’t carry over at all.

“Except in very limited circumstances, we’re not really an improvising group,” he adds. “We’ve tried it, but with not much success. So when we’re working on something that we know is going to be recorded, we try to keep it pretty tight, compositionally.”

One example might be McEntire’s own “Gesceap”, named after the Old English word for “shape”. Opening with wheezing, harmonium-like keyboard arpeggios, it initially sounds like something from the early days of minimalist composition. (Steve Reich and Philip Glass are acknowledged influences on the band.) But once an attractively off-kilter drum pattern enters the mix, it soon opens out into something bigger and bolder, with what sounds like a fuzzed-out six-string bass providing textural interest.

Like Parker’s appropriately menacing “Shake Hands With Danger”, another album highlight, it finds the band sounding exceptionally muscular—an impression undercut considerably by Yo La Tengo’s Georgia Hubley’s singing on the soft-focus “Yonder Blue”, and by a surreal version of David Essex’s yob anthem “Rock On”, with U.S. Maple’s Todd Rittman at the microphone.

The latter sounds like it was knocked off as a studio lark, but McEntire begs to differ.

“No,” he says definitively. “If it conveys that sense that’s great, but for that we used the original as a template and stuck pretty close to it. We didn’t try to rework the form or anything: we just tried to make the sounds our own, and added a few little tweaks here and there. But obviously, the real breakthrough was when we figured out that we needed Todd to sing on it.”

Essex’s 1973 original climbed to the top of the pops worldwide. That’s probably not going to happen for Tortoise in 2016, but the band is clearly willing to try something different—as long as it doesn’t have to fly by the seat of its pants.

Tortoise plays the Imperial next Thursday (April 28).