"Floored by Four" (Chimera Records), the new album released last week by the quartet of the same name, is New York avant-garde music down to its raw, improvisational core. Band members Nels Cline, Yuka Honda and Dougie Bowne deliver four new compositions by Mike Watt that call to mind the work of Sonny Sharrock, James Blood Ulmer and early '70s Miles Davis, as well as Captain Beefheart and other musicians who took an off-the-beaten-path approach to rock.

"Me and Nels left our Cali thing behind," the affable Mr. Watt said by phone recently. The bassist lives in San Pedro, Calif., while Mr. Cline, who has an apartment in the West Village, was born in Los Angeles.

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Floored by Four, left to right: Nels Cline, Dougie Bowne, Mike Watt and Yuka Honda. Chimera Records

Mr. Cline, a guitarist who seems to release a new recording every month, is committed to Wilco and his own Nels Cline Singers, an ensemble without a vocalist. Mr. Watt, noted for his contributions to several punk groups beginning in the 1980s, especially the Minutemen, has been with Iggy and the Stooges since 2003 and in countless other projects, including at least one with Mr. Cline. Ms. Honda, a keyboardist who co-founded Cibo Matto, and Mr. Bowne, a drummer for the Lounge Lizards in their heyday, are in-demand musicians with long résumés; the two were once married to each other, and continue to collaborate on projects together.

A busy lot, the quartet carved out a brief slice of time to collaborate last year at Mr. Bowne's studio on Ludlow Street. How they came together is a twisty tale that reflects the serendipitous life of independent musicians clamoring to keep doing what they love.

It began with the Stooges in late July 2009, when Mr. Watt was invited to perform at Central Park's SummerStage. Finding Mr. Cline available, Mr. Watt asked him to join in; Ms. Honda and Mr. Bowne soon followed. It was for this project that Mr. Cline met Ms. Honda for the first time, suggesting a new dynamic.

Three days before the show, Mr. Watt presented the group with compositions written to suit their musical personalities. Written on the bass, Mr. Watt's songs suggested a mood and direction, but not much more. "My feeling is, if the bass player knows the song, anybody can know it pretty quickly," Mr. Watt said. "The bass is like grout, you know? Most people look at the tile." He didn't need to finish the metaphor: With nothing to hold it together, tile falls apart.

"The bass doesn't have harmonic content," he continued. "A lot of people don't think there's enough information there—you know, it's like writing something on a kick drum."

Speaking about his bandmates, he said, "I gave them a lot of freedom there so it wouldn't turn into 'Whippin' Post' for three hours," referring to the Allman Brothers Band jam standard.

The SummerStage concert was a success. Floored by Four promptly entered the studio and worked rapidly, giving the music a spark of spontaneity.

Each of the four songs on the album is named after the person for whom it was written, and in each case that musician drives the performance, though Mr. Cline, by the nature of his instrument and skill set, is the dominant voice. After kicking off with a variety of raspy, spacey guitar sounds, the track "Nels" settles into a bit of modal funk with a wah-wah, invoking the free-jazz of Sharrock as well as Miles Davis's "A Tribute to Jack Johnson." "Yuka" is a mini-suite with Captain Beefheart touches as Mr. Watt provides preacher-like vocals over Mr. Cline's squeals and squalls. Clocking in at close to 20 minutes, "Dougie" is a down-tempo number that Mr. Bowne controls with brushes and mallets. And "Watt" rises from a funky soul riff to which Mr. Cline provides a bit of surf guitar while Ms. Honda solos on what sounds like a cheesy old organ. "My Jamerson bit," said Mr. Watt of his part, referring to Motown bassist James Jamerson.

Mr. Watt conceded that it's unlikely, at least for now, that Floored by Four will tour or even record together again. "It's kind of tough, with Nels's thing with Wilco, and me with the Stooges."

But in addition to the album, there will be another testimonial to Floored by Four's brief existence. Ms. Honda and Mr. Cline are to be married on Nov. 13 in Tokyo.

"It's trippy, isn't it?" said Mr. Watt with apparent glee.

—Mr. Fusilli is the Journal's rock and pop music critic. Email him at jfusilli@wsj.com or follow him on Twitter: @wsjrock.