Though it’s hard to tell by listening, the first two albums by Captain Beefheart (aka Don Van Vliet) found him creatively frustrated. Safe as Milk from 1967 and Strictly Personal from the following year were inventive blues-rock records, but Beefheart had bigger ambitions. At that point, his group the Magic Band were a mostly democratic collective, and since Beefheart had less musical expertise than his colleagues, his odder suggestions were vetoed as too unconventional. “That really pissed him off,” said bassist Gary Marker. “[Because] he had all these ideas in his head and he had no way of getting them across to people.”

To gain the control he needed to express his vision, Beefheart morphed the Magic Band into a kind of musical cult. In mid-1968, he replaced some members of the group with younger, more impressionable players (guitarist Bill Harkleroad and bassist Mark Boston were each just 19), gave everyone a nickname to match his own, and holed up with them in a house on the outskirts of Los Angeles. The sessions in the house have since become a crucial part of rock legend, the subject of contradictory stories and much myth-making. By many accounts, Beefheart imposed weird lifestyle rules and played mind games that bordered on brainwashing. Some claim the musicians couldn’t leave the premises save for a weekly grocery trip, and drummer John “Drumbo” French said he spent one month eating only a cup of soybeans every day.

Beefheart put a piano in the house—despite not knowing how to play it—and banged out ideas, which French transcribed and assembled into tunes. The resulting pieces were more like puzzles than songs, giving different instruments conflicting time signatures and varying part lengths that had to somehow meet at specific points. French compared it to building a solid wall with bricks of unequal size. This unorthodox complexity forced the Magic Band to rehearse 12 hours or more a day, usually without Beefheart. Often they would sleep right where they had just practiced, and immediately continue upon waking.

After six months of this bunkered mania, the Magic Band entered a studio with Beefheart’s friend Frank Zappa, who “produced” them by staying out of the way. Riding the adrenaline of their intense woodshedding, the group recorded 20 songs in less than six hours. Beefheart added vocals separately, syncing uncannily with the music despite rarely having rehearsed with the band and eschewing headphones during takes. In less than a week, after adding two tracks from an earlier session and a few more made at the group’s house, Trout Mask Replica was born. As Third Man’s new reissue makes clear, this 28-song double album might be the strangest record in major-label rock history. Beefheart made more accessible music before and after, but his most difficult work is still his most famous, defining his musical legacy and the sound of the Magic Band for going on five decades.

Its enduring place in the canon is due in part to the allure of Trout Mask Replica’s singular logic. Like life in a cult, the music seems crazy to an outside observer but makes perfect sense once you’re inside. In a 1993 BBC documentary, “The Simpsons” creator Matt Groening said it took him just seven listens to go from hating the album to deciding it was the greatest of all time. Few records lend themselves to such a transformation, where they eventually click into place while still sounding so thrillingly wrong. The rules that Trout Mask Replica shattered haven’t been reassembled in quite this way by anyone since. After all, capturing its sound would mean somehow retracing the steps from Beefheart’s enigmatic brain to French’s devout hands to the Magic Band’s inhuman toil.

The thrill of Trout Mask Replica also lies in the boggling assemblage of stylistic and thematic strands. There are shards of rock and blues in the band’s deconstructed grooves; free jazz in Beefheart’s primitive, Ornette Coleman-inspired saxophone playing; literary surrealism in his obscure yet oddly resonant lyrics; outsider folk in his growled a capella songs; and postmodern collage in the album’s diverse sound sources, which include field recordings, spoken skits, studio banter, and even vocals recorded over the phone. Though the songs seem to reject convention, there are references to musical history scattered throughout Trout Mask Replica, from snippets of melody borrowed from traditional tunes to lyrical quotes like Beefheart’s chant of “Come out to show them” in “Moonlight in Vermont,” taken from Steve Reich’s tape experiment from two years earlier. Though Beefheart’s lyrics were mostly oblique conundrums, he could also be bluntly topical, singing boldly about the Holocaust and the Vietnam War.

And though Beefheart could be pathologically controlling with his bandmates, he was surprisingly open to chance and accident throughout Trout Mask Replica. He left in the sounds of the tape player pausing in his acapella songs, inserted recordings of himself wandering the weeds into others, included mistakes and under-breath commentary in pre-song skits, and created one spontaneous track, “The Blimp,” by having guitarist Jeff “Antennae Jimmy Semens” Cotton call Zappa and read him a poem, which Zappa recorded while his own band, the Mothers of Invention, played in the background.

Perhaps most surprising is how catchy Trout Mask Replica’s jagged songs turn out to be. Some even have verses and choruses, albeit filtered through the band’s sonic contradictions and Beefheart’s skewed timing. The rushing climaxes of “Ella Guru,” the building swing of “Pachuco Cadaver,” and the swaying blues of “She’s Too Much for My Mirror” are all earworm inducers, as their multiple sonic elements coagulate into melody, like filaments spastically aligned by a magnet.

Over five decades, Trout Mask Replica has proven incredibly durable, still sounding as bracing and radical as any rock music since. That’s even clearer in this remaster, sourced not from the decayed original masters but from less-worn backups. But was the music worth what Beefheart put the Magic Band through? French and Harkleroad have both said that though they wouldn’t want to endure it all again, they were thrilled to have created such a landmark. They certainly deserve more credit than they got from Beefheart, who often claimed to be the sole songwriter (he even left French off the original album credits completely, apparently as punishment for leaving the band before it was released). But luckily each member’s vital contribution is loud and clear in every note, beat, and weird and wonderful turn. Captain Beefheart might have led this cult, but Trout Mask Replica is the work of a collective—a serendipitous line of charged neurons that wired together to make something truly magical.