Monk was the master of the single note, perfectly selected, timed, and struck so that it would have a symphonic amplitude. Photograph: Burt Glinn/Magnum

A treasure chest of jazz is being rereleased this week: “The Complete Riverside Recordings” of Thelonious Monk, a fifteen-disk set of his recording sessions, in the studio and live, for that seminal label. Spanning the period between 1955 and 1961, it's the core of his recorded legacy. The set contains the disks of his that I return to most often, and it shows off a wide range of his art. For me, it's the most essential trove of Monk's recordings that exists. Most of the recordings in the set are available separately, as the albums on which they were originally released, but having them together in chronological order tells a musical story that is as much about Monk as it is about the musical times.

These fifteen disks find Monk in a wide range of musical settings—solo, trio, quartet, quintet, sextet, septet, and a big band—and locations, including the studio, New York’s Town Hall and the Five Spot, San Francisco’s Blackhawk, and concert halls in Paris and Milan. The list of Monk's sidemen in this set indicates the level of creativity on display; it includes John Coltrane, Coleman Hawkins, Sonny Rollins, Art Blakey, and Max Roach, and they’re all in stellar form, due not least to Monk’s own musical invigoration.

The boxed set was made under the aegis of Orrin Keepnews (who died in March, at the age of ninety-one), the producer and the co-founder of the Riverside label, who, as a critic in the late forties, was among the first to recognize Monk's genius. In 1955, he succeeded in poaching him from another record company, where his albums were unappreciated and his place on the roster was subordinate. Recordings were especially important to Monk at the time because, as a result of trumped-up drug charges, he had lost his cabaret card (in effect, a New York City performance license) and couldn't play in any venue that served alcohol—i.e., jazz clubs.

In the set’s copious booklet, Keepnews discusses his plan for establishing the modernist Monk—namely, by making explicit his ties to jazz tradition. He recorded the Monk trio playing compositions by Duke Ellington, in 1955, and followed that album early the next year with one of the trio performing standards from what wasn’t yet called the Great American Songbook. Those albums offer delightful shocks, such as the “Name That Tune” trouble that Monk so gleefully provokes with his radical rearrangements of familiar melodies. His revision of “Mood Indigo” seemingly puts more notes into the first phrase than Ellington’s whole composition contains. He reharmonizes Fats Waller’s “Honeysuckle Rose” nearly to the breaking point and plays exuberantly with “Tea for Two,” toying with its simple melody to tease out a comically obsessive syncopation.

In October, 1956, Keepnews had Monk throw down a wild gauntlet of compositional and organizational audacity, “Brilliant Corners,” featuring the saxophonists Sonny Rollins and Ernie Henry and the drummer Max Roach. In his notes, Keepnews details the trouble that the complex title tune caused the musicians, and the editing tricks that gave rise to the released performance. This recording has a grand, grave sense of moment: it is a coming out of the composer from behind the mask of eccentricity and idiosyncrasy and displaying, in several difficult and expansive works, his thoroughgoing and large-scale musical imagination, even within the relative intimacy of a quintet.

Monk was the master of the single note, perfectly selected, timed, and struck so that it would have a symphonic amplitude. The asymptote of his music is a punctuated silence, which is why he was especially sensitive to his drummers and dependent on them to organize the music's forward motion. In “The Complete Riverside Recordings,” Monk is joined by the best, including Roach, Blakey, Roy Haynes (who, at the age of ninety, is still working today), Kenny Clarke, Shadow Wilson, and Philly Joe Jones.

Monk made his drummers—and, for that matter, almost all of his musicians—rise to the occasion. For me, the most exhilarating of these occasions is the series of recordings issued on the album titled “Monk’s Music,” from June, 1957, featuring Coltrane, Hawkins, and, in particular, Blakey, who displays a scintillating synergy with the pianist. Blakey drives the band with an astonishingly contained heat that is tempered with lyricism—his accompanying accents are witty and melodic, and his solos are the most singable, witty ones that I've ever heard. The entire band is electrified. Coltrane wasn’t yet the meteoric inventor that he’d become after his six-month stint with Monk at the Five Spot, but his sound is searching, his tense rhythms and broken phrases pregnant with far-reaching ideas. Hawkins, who more or less single-handedly turned the tenor sax into a jazz soloist's heavy weaponry in the nineteen-twenties, is roaring, robust, and good-humored. The bassist Wilbur Ware, with his uniquely percussive tone, does some remarkable duets with Blakey, and the trumpeter Ray Copeland, who didn’t record often, displays a tone that veers between brazenly bright and intimately grainy for his concise, poised solos. I consider it Monk's single greatest studio recording.

Monk is more than a bandleader and a soloist. His work as a composer is central to his career, to his legacy, and to this set, which features five versions of "’Round Midnight," six of "Epistrophy," five of "Crepuscule with Nellie," four of "Rhythm-a-Ning," and multiples of "Jackie-ing," "Blue Monk," "In Walked Bud," "Well, You Needn't," "Straight, No Chaser," "Evidence," and other works in Monk's compositional canon. He could, and did, play anything brilliantly (the standards include such obscurities as “There’s Danger in Your Eyes, Cherie”), but in his compositions, he posed some very difficult problems of melody, rhythm, and harmony, which he himself worked out for most of his life and which other musicians to this day find fruitful and unresolved.

Last Thursday, the eighty-one-year-old saxophonist Wayne Shorter and his compositions were featured with the Jazz at Lincoln Center Orchestra, led by Wynton Marsalis. I was there, and the results were revealing. Shorter’s role in the jazz of the nineteen-sixties was similar to that of Monk in the jazz of the fifties. As a member, first, of Blakey's Jazz Messengers and then of Miles Davis's bands, from 1964 through 1970, Shorter was also these groups’ chief composer and, as such, was the leading jazz composer of the day. His solos, with their analytical yet spontaneous musical imagination—with their rhythmic jolts and their surprising, disjunctive succession of phrases—have an inner logic that’s entirely Shorter's own. Thursday’s concert, like Shorter's recordings, proved that his improvisations and his compositions are of a piece; as with Monk, Shorter’s compositions implant his DNA in the musical times in a reproducible way, whereas his inimitable solos are entirely his own.

Monk’s musical DNA had already taken root by the time he started recording for Riverside, and that connection gives rise to one of the most startling performances in the boxed set. In 1955, at the Newport Jazz Festival, Davis staked his claim for stardom with his performance of Monk’s “’Round Midnight” (Monk was a part of the pickup group with which Davis performed it). That composition became the centerpiece of Davis’s first album for Columbia, “’Round About Midnight,” which was released in March, 1957. Monk went into the studio with Keepnews the following month to record a solo album. His performances are brash, intellectually aggressive, and self-deconstructive, nowhere more so than in his recording of “’Round Midnight,” a mighty twenty-one-minute quest for the heart of the composition; the performance has a combative air, as Monk pounced on his own tune to reclaim it with harmonic daring and a leonine attack.