In the fall of 1957, John Coltrane had suddenly overcome long and devastating addictions to heroin and alcohol, and was in the midst of a fascinating period of transition into a decade-long burst of creativity. Thelonious Monk, perhaps the greatest modern jazz pianist, had just regained his previously-revoked cabaret card, granting him access to New York clubs for the first time since 1951.

By their Nov. 29 gig at Carnegie Hall, Coltrane had worked for several months with Monk as his tenor saxophonist, learning to tap his reawakened talent from the mad architect of bebop. They had reached the apex of their collaboration, the extent of each artist’s understanding of the other allowing both to break new ground.

It was a seminal concert, the creative peak of a dynamic ensemble that for decades had only been documented in the minds of the audience and now long-dead performers. This February, an acetate tape marked “Carnegie Hall Jazz 1957” turned up in the archives of the Library of Congress — accompanied by a hand-scrawled set list that includes just about every highlight of the Monk canon. This week it was released as an impeccably cleaned-up CD by Blue Note, Monk’s original label.

It was worth the wait.

The album opens with the somber “Monk’s Mood.” The band’s performance showcases Monk’s usual, sparse elegance and fun-house mirror rhythms. Two minutes into the song, Coltrane slides in so smoothly that it’s barely perceptible. But the two begin to weave confidently around each other, comfortable after months of collaboration. The degree of their mutual influence is movingly apparent — Monk, known as madly deaf to the world around him, stunningly echoes Coltrane’s effusive, storming arpeggios.

The transition from “Mood” to “Evidence,” another Monk classic, is deceptively seamless. The band gives just a few staccato notes before plunging face-first into the challenging and idiosyncratic song. It is a thrilling experience; Coltrane clambers down scales with beautiful, almost awkward dissonance. He changes keys on a whim, while Monk’s contorted hammering follows within heartbeats. The result is haphazard, unsettling, and yet breathtakingly controlled.

“Crepuscule with Nellie,” “Nutty” and “Epistrophy” round out the early set, each song rife with the intersection and divergence in artistic sensibility. Ahmed Abdul-Malik’s baseline at the end of “Epistrophy” is nothing short of intoxicating. He profoundly changes the feel of the song right at its end, yet he distorts nothing but the downbeat.

The late show begins with the casual “Bye-Ya” and “Sweet and Lovely.” The latter boasts a staggering introduction by Monk, setting the stage for the delirious nine minutes that follow. In what could be the best performance of the evening, Monk plays with a curiously light touch, nonetheless holding down the structure of the song. Coltrane, meanwhile, plunges into double-time with ecstatic abandon.

“Blue Monk” and a second rendition of “Epistrophy” complete the night. The band-leader lets his soloist take off, and Coltrane doesn’t disappoint. He bravely experiments with the hell-bent runs that would lead to the “sheets of sound” approach, which has since become synonymous with his name.

Coltrane and Monk may share an instinct for underlying logic and structure, but you can hear on these tracks that Monk gravitates towards the stark and broken-down while Coltrane is expansive and fluid, especially when soloing. Listening to the two artists push each other in new directions, and mirroring each other’s insights, is a true pleasure.

It is easy to hear why Monk and Coltrane’s collaboration has been called one of the most important in jazz history. And yet, by the time the recording was made, Coltrane had already rejoined Miles Davis’s ensemble (which he had left during the darkest days of his heroin addiction), where he would record “Kind of Blue” two years later. And in 1959, Coltrane would leave to make “Giant Steps,” his solo masterpiece.

So we’re left with this recording, the most beautiful of souvenirs from a dynamic and crucial period in the development of the two. Nearly half a century has gone by, but the sense of possibility, the sheer excitement of the evening, is still in the air.