The 1950s were probably even more of a great Jazz Age than the era that F. Scott Fitzgerald famously titled “the Jazz Age.” It was the decade when a handful of pure jazz instrumentalists were headliners, could fill clubs, and even appeared on TV variety shows. As jazz moved into concert halls, four superstars of the piano brought a largely unprecedented combination of mass-market success and academic respect to the music: In order of appearance, they were George Shearing, Dave Brubeck, Erroll Garner, and Oscar Peterson, who is appearing between Tuesday and Sunday at Birdland in celebration of his 81st birthday.

The course Mr. Peterson has charted through more than 60 years of performing and recording has differed from those of his colleagues in a couple of important ways: First, Messrs. Shearing and Brubeck and Garner all each had at least one major hit record or album, while Mr. Peterson is recognized more for his entire body of work. Second, where his three contemporaries all have a signature style that even a layperson can identify a mile away, it takes a more serious fan or a fellow pianist to pick out Mr. Peterson in a blindfold test.

The drawback to having a trademark sound or a hit song, especially with a popular following, is that you run the risk of becoming tethered to it. By contrast, Mr. Peterson has always taken full advantage of the full range of possibilities open to him. On his 1950 recording, “Salute to Garner,” one of his first made in America after settling here from his native Canada, he recaptured Garner’s patented ebullience, bouncing rhythm, and cascading notes. On the 1964 “Goodbye J.D.” (on “We Get Requests”), Mr. Peterson played the opening head in a wacko time signature, very much inspired by Mr. Brubeck. On another original work, “The Music Box Suite,” documented only once, in a 1958 concert in Vancouver (not released until 45 years later), Mr. Peterson displayed his knowledge of baroque fugal styles in a way that referenced Mr. Shearing.

Mr. Peterson sometimes seems to have as much chops as his three contemporaries put together — in addition to being as physically imposing as the other three combined. Tom Lord’s “Jazz Discography,” the standard work on the subject, lists an incredible 417 recording sessions by Mr. Peterson, more than half of which are as a leader. One reason his output was so large was that he continued to record as a sideman and accompanist long after he had established himself as a soloist.

In a recent phone interview, the contemporary pianist Bill Charlap described Mr. Peterson as “one of the most profoundly important pianists in the history of the music. He straddles the entire history of jazz piano. Everything everyone says is true!”

Mr. Peterson, who was born in Montreal in 1925, earned his professional stripes with local big band leader Johnny Holmes, and first recorded in that city in 1945. Working with what would later become the standard piano trio (with bass and drums), he recorded 32 sides for Canadian RCA before 1949.That same year he was invited by impresario Norman Granz to participate as a special guest at a Jazz at the Philharmonic concert at Carnegie Hall. In Granz, Mr. Peterson found a manager and producer whose appetite was as capacious as the pianist’s talent was prodigious. From 1950 forward, Granz recorded Peterson continually, both in his own trios and duos, and as sideman.

Around that time, Mr. Peterson began garnering comparisons to the legendary pianist Art Tatum, who died in 1956. Mr. Peterson once said that when he first heard Tatum play, he was so overcome that he couldn’t touch the piano for a week.Though he has sometimes even described himself as Tatum’s heir, he is no imi-Tatum; it’s rare to hear Mr. Peterson re-create a Tatum-esque set of runs and arpeggios. As Mr. Charlap put it, “He assumed the mantle of Tatum, but Oscar doesn’t play Art’s stuff — it’s Oscar’s stuff.”

Mr. Charlap has also pointed out that “Oscar also has that churchy, bluesy feeling that he didn’t learn from Tatum.” For that matter, he’s also more directly connected to the lyric and more emotional — Tatum couldn’t break your heart the way Mr. Peterson does on “Tenderly.” Part of the difference was also attitudinal, as the clarinetist Buddy DeFranco says in the current issue of “All About Jazz”: “I loved Tatum’s playing,” he said, “but working with him could be difficult. It was his ball game. When I played with Oscar he had more sensitivity and he played for you.”

Mr. Peterson’s other major influence was Nat King Cole, whose importance to the legacy of jazz piano is still generally under-appreciated. In fact, the influence of the King Cole Trio was so pervasive in the 1940s that even Tatum worked for most of that decade with a Cole-inspired backing of guitar and bass. That was still the format when Mr. Peterson assembled his first widely successful trio in 1952; he even hired guitarist Irving Ashby, who had only recently left the King Cole Trio, to fill the same roll in the new Oscar Peterson Trio.

Given wide exposure by Granz on recordings and JATP tours, the original OP3 quickly became one of the great jazz groups in a great jazz era, thanks largely to the telepathic playing of Mr. Peterson, his equally formidable bassist Ray Brown, and the brilliant guitarist Barney Kessell. When, in 1958, Kessell left the group, Mr. Peterson decided to change the format rather than replace him. The following year, Mr. Peterson introduced his second great trio, with Brown remaining on bass and the superlative drummer Ed Thigpen creating a whole new roll in Mr. Peterson’s musical universe.

The switching of drums for guitar did not make the OP3 swing more — that would have been impossible — but, oddly, it gave the trio more of a relaxed feeling. The earlier group sometimes seemed to be pushing as hard as it could to compensate for the absence of percussion.With Mr. Thigpen on board, they seem more inclined to lay back and let it go.

Two years into the group’s existence, the Peterson-Brown-Thigpen trio made its definitive statement, when Verve recorded the threesome at the London House in Chicago.Although the company released some of the material at the time over four LPs (including Mr. Peterson’s marvelous, bittersweet re-conception of “Put On A Happy Face”), the entire works were finally released as the essential four-CD box, “The London House Sessions,” 10 years ago.

As Mr. Charlap said, one of the trademarks of great jazz “is that you can hear everything in it, the past, the present, and the future.” Mr. Peterson has worked mostly with the piano-bassdrum combination, even since the Brown-Thigpen unit broke up in 1965. He was slowed down somewhat by a stroke in 1993, but even today at 81, he plays more piano than any three other great pianists put together.