Music suffuses the films of Jim Jarmusch, sometimes not so much complementing as completing them. He has prominently cast Tom WaitsIggy PopRZAGZAMeg WhiteJohn Lurie, and Screamin’ Jay Hawkins. Briefly, he played no wave at peak CBGB. And he’s always looked the part of the art rocker, his dandelion dome of hair and Terminator shades still in place at 70. In the 2010s, as a softly growling guitarist, he conjured a razed Renaissance in several albums with the lutist Jozef van Wissem. And, working with instrumentalist and producer Carter Logan as SQÜRL, he began to score many of his own movies. A great new Jarmusch interview in The Guardian frames this turn toward music as a reaction to the sorry state of the film industry, which seems a bit like leaping from the Hindenburg and landing on the Titanic, but never mind.

Silver Haze is SQÜRL’s first album outside of cinema, yet it still feels tightly scripted, especially on “She Don’t Wanna Talk About It,” where Jarmusch and the British-German singer Anika talk past each other in a long, dark corridor of guitar. And the sets are well-dressed. “Berlin ’87” uses Super 8 footage from Europe shortly after the fall of the Berlin Wall to coat a standard mood-setter—overtone-capped drone rock in the manner of Boris and Earth, both prior collaborators of producer Randall Dunn—with Cold War-era grit. On “The End of the World,” the riff is a podium at which Jarmusch, in a pleasing baritone reminiscent of John Cale, recites a postapocalyptic short story about “an older man, approaching 70” who watches “feral teenagers” doing donuts and dancing to sad pop in the concrete plaza below the prison of his apartment. This leads into a guest-laden middle run that shows off Jarmusch’s knack for casting as the focus tightens on the romance of 20th-century New York.

It’s no slight to Jarmusch and Carter that the guitar playing gets considerably more interesting when Marc Ribot shows up, as he’s one of the most distinctive, widely traveled American guitarists of his generation. Ribot started by helping Tom Waits redefine himself as a clangorous visionary in the ’80s and has cut a vast swath across art and pop music since. On “Garden of Glass Flowers,” churning riffs finally break apart into dancing, dewy angles that gradually fill with light. Ribot also plays on “Il Deserto Rosso,” which seems less imaginative than the album’s highlights, simply pairing desert rock with the title of a 1964 film by Michelangelo Antonioni. Perhaps it’s just that I haven’t seen it.

But I have read the influential American poet who gets a wonderful tribute in “John Ashbery Takes a Walk,” which features actor and musician Charlotte Gainsbourg almost whispering his experimental but accessible verses, in her musical English-French accent, over a wide, glimmering groove that explodes in slow motion. The title also brings to mind Frank O’Hara’s “Lana Turner Has Collapsed,” another beacon of the New York School of which Ashbery was an original part. Its urbane yet playful influence resonates not just here but throughout Jarmusch’s work.

It’s hard to think of Jarmusch’s musical trajectory without also thinking of David Lynch’s: two legends of American independent cinema since the 1980s who both leaned into music in their 60s. While Lynch’s bond with Angelo Badalamenti and unforgettable song scenes made his leap from film a short one, Jarmusch has perhaps an even stronger claim to be the most musical director of his cohort. In some ways, SQÜRL’s stacked delays and synths and strings are as in-the-lines as Lynch’s music is off the map. But something enriches even the most formulaic trudge-rock passages of Silver Haze. That something is Jarmusch, who brings a rich history to the proceedings, experimenting with passerelle bridges, cigar box guitars, and radio static. Just as in his films, he spins strange yet strangely familiar stories from everyday stuff.

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Sqürl: Silver Haze