In the 1970s and 1980s, the pianist Cedar Walton called his band Eastern Rebellion, and though he no longer uses that name, there is still a hint of Eastern rebellion in his playing. Mr. Walton, who is beginning a rare twoweek engagement at Dizzy’s Club Coca-Cola, will often start a tune or a solo with a minor chord phrased in a way that suggests Asian music (a similar piano sound to what Horace Silver achieved in “The Tokyo Blues”).

Mr. Walton uses the Asian effect brilliantly in the title track on his excellent new album, “One Flight Down” (High Note Records), and interspersed it carefully throughout his opening set on Wednesday night. It’s especially effective when he follows the Asian touch with the Latin tinge, using the combination of piano and percussion to lead the listener to Havana from Shanghai in a matter of a few bars, or, perhaps, to one of those Cuban-Chinese restaurants that used to line Eighth Avenue 20 years ago, a few blocks from where Jazz at Lincoln Center is now.

The pianist now simply calls his group the Cedar Walton Quartet or the Cedar Walton Quintet, depending on who’s playing with him.Most of the new album is performed by Mr. Walton’s trio, with longstanding partner-in-time David Williams on bass and Joe Farnsworth on drums. For Dizzy’s, he has added alto and tenor saxophonist Vincent Herring to make the group a quartet, and this week the addition of SteveTurre on trombone makes a quintet.

Mr. Walton began on Wednesday with the two most basic structures of jazz,”Raymond’s Blues,”in the familiar 12-bar blues format, and “The Vision,” in standard AABA song form. Yet both were far from conventional: The blues had Mr. Walton alternating passages of the melody with Mr. Herring on tenor, while the second structure saw him move from minor to major and back again in the different sections. “Raymond’s Blues” also incorporated a three-note phrase reminiscent of the vamp to John Coltrane’s “Giant Steps,” which was altogether fitting, since Mr. Walton played on Coltrane’s first recording of the song, taped in April, 1959 (a month before the famous version with Tommy Flanagan).

The third tune was “Seven Minds,”by the late bassist Sam Jones, who recorded it several times with Mr. Walton. It is the only number from the Wednesday set included on the new album, and in both cases, it serves as a feature for Mr. Williams. He launched into it with a long rubato vamp of the kind you almost never hear a bassist play, while Mr. Walton’s accompaniment and his own solo was full of more Eastern Rebellion figures. Four tunes in and it was time to introduce Mr. Turre, who joined the band on “Hindsight,” a mostly minor piece with a distinctive vamp, essayed by the unusual front line of trombone and alto.

Mr. Walton’s settings of standards are almost as distinctive as his original compositions, and he and Mr. Turre came up with a new setting of the perennial “My Funny Valentine” that was like no other treatment I’ve ever heard. They changed everything about the song but the melody and the customary ballad tempo; it was still Rodgers and Hart’s song, but recast in a darker, more mysterious context, and wound up with a dramatic trombone cadenza. They followed this with a different kind of pop song, Stevie Wonder’s “Another Star.” Here, as Mr. Herring’s tenor blended with Mr. Turre’s trombone on a funky groove over the three-piece rhythm section, the overall sound conjured the early years of the Jazz Crusaders.

For years it was standard practice for bebop bands to end sets with a brief run-through of the tune that Miles Davis recorded as “The Theme.” Mr. Walton followed suit, but completely recast it in his own image, adding sections and phrasing the melody in a completely original way — not to mention throwing in a few of his characteristic, left-field quotes. “The Theme” had echoes of both “Let’s Fall in Love” and “Tip Toe Through the Tulips.”

One thing Mr. Walton did not do was mention that he had a new album, much less instruct everyone to run out and buy it.(Other bandleaders: take note!) Apart from the bass feature, he didn’t play any music from “One Flight Down,” though he can be expected to on other sets. The new album pivots around two exceptional new compositions by Mr. Walton, both of which feature Mr. Herring on tenor: “Rubber Man” a catchy, Latin-informed line (which could be a countermelody to Milt Jackson’s “Bags Groove”) and the bluesy title song.

The rest of the album is devoted to the music of other composers, all of which (except Jule Styne’s “Time After Time”) are by well-known jazz composer-instrumentalists. The focal point of the album is a 15-minute segment labeled as the “Billy Strayhorn Medley,” but that’s not an accurate description. A medley usually includes short snippets of a lot of tunes, whereas here we get full-length, fully realized revamps of three Strayhorn classics. Mr. Walton treats us to an audaciously fast and rhythmic treatment of “Lush Life,” a tune that is almost always played without tempo, throwing in a surprising number of funky vamps and countermelodies. He does the same for “Day Dream,”marking the first time I’ve ever felt the urge to dance to Strayhorn’s normally introspective soliloquy. One of the composer’s bright bouncers, “Raincheck,” here becomes even faster and more boppish, phrased the way one would expect to hear Bud Powell play it, incorporating an exchange of licks with Mr. Farnsworth’s drums.

The rest of the album includes a tune each by Wayne Shorter (“Hammer Head”) and Freddie Hubbard (“Little Sunflower”), both of whom first worked with Mr. Walton in the 1961–64 edition of Art Blakey’s Jazz Messengers.

Between the show at Dizzy’s and the new album, I’m left with only one question: Why hasn’t Cedar Walton, who turned 72 a few months ago after 50 years of being one of the best pianist and composers around, yet been named a jazz master by the National Endowment of the Arts?

wfriedwald@nysun.com