If Jazz at Lincoln Center had included Memphis in its Jazz Coast to Coast series (which resumes this week with Pittsburgh and next week with Los Angeles), the first man Wynton Marsalis would have called is George Coleman.

Mr. Coleman, who is appearing with his quartet at Birdland this week, was born two months after Elvis Presley, the most famous of all Memphis citizens. The tenor saxophonist is one of the most celebrated modern jazzmen from Memphis, having participated in the 1959 “Young Men From Memphis: Down Home Reunion” and the 1968 “A Few Miles From Memphis” with pianist Harold Mabern. Mr. Coleman made his recording debut for Blue Note in 1958, playing on two classic albums – Lee Morgan’s “City Lights” and Jimmy Smith’s “House Party” – on the same day. He is best known for his work in two of jazz’s all-time super groups, the 1958-60 Max Roach Quartet (with Tennessee trumpeter Booker Little) and Miles Davis’s 1963-64 quintet.

One of the few remaining big-toned, hard-bop tenors of the old school, Mr. Coleman hails form the same stylistic family as Junior Cook, Tina Brooks, and, in his early days, Joe Henderson. He plays with a competitive edge, a holdover from the days when jam sessions were like Southern duels, where the idea was to play as fast as possible and to do more imaginative things with the same basic material, chord changes, and melody lines. His current quartet includes Anthony Wonsey, piano; Dwayne Burno, bass; and Joe Farnsworth, drums, all of whom play regularly at the uptown club Smoke.

Mr. Coleman has never been known as a composer, but he doesn’t have to be. During his opening set at Birdland on Tuesday, he played five familiar tunes, three standards, and two jazz classics, and he put his personal stamp on all of them. He opened with Hank Mobley’s “This I Dig of You” and closed with Freddie Hubbard’s famous fast waltz, “Up Jumped Spring,” and in both cases played with the distinction between three-four time and four-four.

Mobley’s fetching melody – a fitting choice since Mr. Coleman essentially succeeded Mobley in the bands of both Davis and Mr. Roach – is written in four, but it opens with a distinctive pattern of an eighth note,a dotted half,and a rest. Mr. Coleman and his band used this to give the song an appealingly lopsided, three-ish kind of a feel. They played Mr. Hubbard’s tune simply and sweetly, giving it the feeling of a children’s folk song, like Miles Davis did with “Put Your Little Foot Right Out.”

Mr. Coleman reinterpreted the three standards – Rodgers and Hart’s “Easy To Remember,”Antonio Carlos Jobim’s “Wave,” and George Gershwin’s “Strike Up the Band” – with even more originality. The first two began as a ballad and a bossa, respectively, but the band gradually refashioned all three into hard-hitting, up-tempo, be-bop barn burners.

“Easy To Remember” started slowly and tenderly, equal parts Bing Crosby (in “Mississippi”) and John Coltrane (on “Ballads”), but got faster and tougher as Mr. Coleman’s solo proceeded. Likewise, “Wave” got further and further away from its bossa beginnings as it progressed – Mr. Coleman was bent on taking both tunes to a place where only the fastest can follow. But Mr. Wonsey took them back to their starting points when he began his solo, starting slowly and building to a fullfingered climax that recalled the most famous Memphis pianist, the late Phineas Newborn.

The show reached its climax with “Strike Up the Band.” This song has a long history as a bebop flag-waver, almost as much as “I Got Rhythm.” The Gershwin tune has, as Ira Gershwin’s lyrics put it, a “martial swing”that anticipates such militant bop numbers as Benny Golson’s “Blues March. “Mr.Coleman started by rendering the bridge as an a capella coda, then raced through a chorus of the melody at a barely recognizable clip. Then he surprised us by doing his second chorus in stop-time, which is generally how jazzmen play the blues, not Gershwin. He was pulling out all the stops for this number, double and then quadruple timing over the already fast melody, circular-breathing so he could play longer and longer phrases without pausing for air, as if he were trying to win over any holdouts in the crowd who didn’t already realize they were in the presence of a master.

Mr. Coleman, who is also playing Iridium in two weeks as part of the Four Generations of Miles band, didn’t say one word on the bandstand the entire 80-minute set. He just let the music speak for itself.

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As noted, this weekend’s installment of the Jazz Coast to Coast series is “Pittsburgh: From the Heart of Steeltown.” Doubtless this will be themed to composer-pianists, since that city produced a disproportionate share of them in the pre-war era: Erroll Garner, Billy Strayhorn, Earl “Fatha” Hines, Mary Lou Williams. Last month’s Detroitthemed concert was surprisingly good.

The other major concert worth catching this weekend is trumpetercomposer Dave Douglas at Zankel Hall on Saturday. Mr. Douglas’s latest outstanding ensemble, Keystone, plays just about the most palatable blend of electric music and jazz ever attempted.

The George Coleman Quartet will perform again February 17 & 18 at Birdland (315 W. 44th Street, between Eighth and Ninth Avenues, 212-581-3080).