Cecil Taylor (1929-2018) is the most influential jazz pianist of the late 20th century. Some of today’s leading keyboard masters, including Kris Davis, Vijay Iyer, Matthew Shipp and Craig Taborn, cite him as a cornerstone influence. Yet some of the major early, evolutionary chapters of Taylor’s unique style—which could switch gears from thunderous bombast to sublime elegance with lightning speed and breathtaking virtuosity—are poorly documented. He was recorded only sporadically in the ’50s and ’60s, and barely at all in...

Cecil Taylor (1929-2018) is the most influential jazz pianist of the late 20th century. Some of today’s leading keyboard masters, including Kris Davis, Vijay Iyer, Matthew Shipp and Craig Taborn, cite him as a cornerstone influence. Yet some of the major early, evolutionary chapters of Taylor’s unique style—which could switch gears from thunderous bombast to sublime elegance with lightning speed and breathtaking virtuosity—are poorly documented. He was recorded only sporadically in the ’50s and ’60s, and barely at all in the early ‘70s, before re-emerging almost fully formed in the mid-’70s, from which time he was recorded often and won numerous accolades for his work.

Now “The Complete, Legendary, Live Return Concert” (Oblivion), a performance of Taylor’s quartet recorded at New York’s Town Hall in November 1973, is out now on select streaming platforms. In the years leading up to the show, Taylor had been teaching at Antioch College and the University of Wisconsin-Madison. Even though the jazz avant garde, of which he is a founding father, was thriving, Taylor was creating recordings on his own Unit Core label in only limited editions. He released the second half of this concert in 1974 as “Spring of Two Blue-J’s,” pressing only 2,000 copies.

“The Return Concert” features that music plus the first half, a previously unreleased 88-minute opus called “Autumn/Parade” that is one of the most remarkable performances of his band, and it displays Taylor’s distinctive approach coming to fruition.

Unlike his peers of the new jazz of the late ’50s and early ’60s—most notably, Ornette Coleman, John Coltrane and Albert Ayler —who expanded and revised the familiar bebop form, Taylor was creating entirely new structures. In his early recordings, he played compositions by Thelonious Monk, Cole Porter and Billy Strayhorn, but even in those renditions, there was a rumbling of a new style trying to break out. By the ’60s—especially on his live album “Nefertiti, the Beautiful One Has Come” (which was recorded in Denmark in November 1962) and on “Unit Structures” and “Conquistador!” (two albums for Blue Note Records that were recorded in 1966)—it was beginning to take shape. He would introduce clusters of notes, and then he and the band would expand and revise those figures in individual and collective improvisations. But there is little official documentation of what happened after “Conquistador!” was released in 1968.

“The Return Concert” fills in the blanks and showcases a master reaching his peak. Taylor’s music doesn’t aim to entertain its listeners; it seeks to excite or even exhilarate them. It requires devoted attention, however, lest one get lost in the overwhelming cascades of sound.

The highlight of the release is “Autumn/Parade,” and it’s a stunner. At the outset, Taylor introduces several figures, adding to them with extraordinary speed and alarming dexterity; it is as if he has three, even four hands darting around the keyboard. When alto saxophonist Jimmy Lyons enters, Taylor invokes a bit of call and response, one of the few easily recognizable signposts in his music. Lyons, who played with Taylor for more than two decades, is adept at building on the momentum. Neither bassist Sirone nor drummer Andrew Cyrille are properly represented in the mix, but it is possible to hear their rumbling support of Taylor, and occasionally Mr. Cyrille’s accents on cymbals offer useful punctuation to the music. The piece hurtles along at a breathtaking tempo. It’s a reminder that Taylor considered both classical and popular dancers as crucial influences. When I interviewed him in 1990, he couldn’t stop marveling at the techno dancers in Berlin where he was giving concerts. In this music, it’s easy to imagine both balletic leaps and dance-floor euphoria.

Still, the brilliance of “Autumn/Parade” doesn’t overshadow the wonders of the two parts of “Spring of Two Blue-J’s.” The first is a dazzling solo recital and the second features the band with Mr. Cyrille’s placement in the mix improved, so that his dialogues with Taylor are clearer. Drumming is essential to Taylor’s music; in her book “As Serious as Your Life,” author Val Wilmer referred to Taylor’s piano as “88 tuned drums.”

The rest of the ’70s were Taylor’s breakout years. He recorded two excellent ensemble recordings, “Cecil Taylor Unit” and “3 Phasis,” for the contemporary classical label New World. In 1979, he collaborated with ballet greats Mikhail Baryshnikov and Heather Watts, and he began a series of exceptional duets with drummer Max Roach.

Taylor was named an NEA Jazz Master in 1990; he won a MacArthur Fellowship in 1991, and in 2013 he won the Kyoto Prize. “The Return Concert” marks the beginning of Taylor’s halcyon days.

—Mr. Johnson writes about jazz for the Journal.