The tallest trees in southern Africa are shrouded in mystery; a grove is said to exist in Zimbabwe where trees sprout to unimaginable heights, but no researcher has visited the site in decades and the claims remain unverified. There is far less mystery regarding the outstanding pianist and composer Randy Weston, who has towered over the jazz world for more than 50 years as the genre’s most imposingly tall and most Afro-Centric performer. The 6-foot-9-inch Mr. Weston, who turns 81 next month, is still at the top of his game, playing at a level so high it takes a fan of the stature of Kareem Abdul-Jabbar to get a bird’s-eye view of what he’s doing.

Mr. Weston is spending this week at Jazz Standard with two different ensembles — his African Rhythms Trio (with Alex Blake on bass and Neil Clarke on percussion) and his Quartet (which adds the tenor saxophonist Billy Harper to the lineup). Unlike that mysterious patch of forest in Zimbabwe, it’s no secret where Mr. Weston’s music comes from: He came of age musically at the height of the first bebop era, and very early on came under the spell of both Duke Ellington and Thelonious Monk. In the mid-1950s, he cut several fine albums of show tunes (his first LP was 1954’s “Cole Porter in a Modern Mood”) and wrote several tunes that became jazz standards — “Hi Fly” and “Little Niles.”

In 1960, Mr. Weston’s “Uhuru Africa,” a collaboration with the poet Langston Hughes, made him perhaps the first jazz man to fully explore the African roots of both music and culture, long before it became trendy among black Americans.

The basic complexion of Mr. Weston’s music is a distinctly African exterior, enriched by Mr. Clarke’s use of an elaborate Pan-African-American percussion set up in place of a traditional American trap drum kit. Yet apart from the “heads,” or opening choruses of melody, Mr. Weston’s own piano solos still essentially consist of bebop and the blues.

The African Rhythms Trio is one of the most percussive ensembles around: It often seems like a unit of three drummers, with a drummer on bass and a drummer on piano. In the tradition known to Westerners as African “talking drums,” Mr. Clarke is just as likely to play melody on his congas as Mr. Weston is to play percussion on the keyboard. Mr. Blake is frequently a one-man band, slapping his strings low down on the fret board as if they were part of the drum kit, moaning and chanting as he gets caught up in the spirit, and keeping time further by stamping his feet on the floor.

Mr. Weston began the opening set Wednesday with two of his own African-style works from 1998’s “Khepera”: “Boram Xam Xam,” a word from the Wolof peoples of Senegal, and “Anu Anu,” which alludes to the African origins of Egyptian religion. Mr. Weston spun riffs and melodies over the deep grooves laid down by Messrs. Blake and Clarke. Then came “Caravan,” the lead track from his excellent 1989 album “Portraits of Ellington,” played here in a very different treatment, beginning with an elaborate introduction that combined essentially Ellingtonian chromaticisms with an Art Tatum-esque sense of drama. After “Caravan,” the trio finished with an elemental 12-bar blues, obviously informed on some level by “Blue Monk.”

Mr. Weston let us all know exactly where he was coming from when he introduced “Caravan” as “the first piece of African music I ever heard … back when I was a tot — not a small tot, but a tot.” The lyrics may describe a journey across the desert, but the “Caravan” melody sprang forth not from the Nile or the River Niger, but from the pen of Puerto Rican trombonist Juan Tizol and the orchestra of the Washington D.C.-born Ellington. Mr. Weston has taken every measure to make his music authentically African. But for him to refer to “Caravan” as African music reveals that he realizes that the Mother Continent is a state of mind, an idea as much as a place, and an eternal inspiration for jazz musicians of all nations, genders, and skin tones.

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Taking a show tune or even a jazz standard (like “Caravan”) and placing it in a new context is an indispensable part of a jazz musician’s arsenal. Cabaret singers do the same thing in a different way when they take a song from a musical comedy and place it in the context of a one- or two-person nightclub set. With their new production, “Make Someone Happy,” the team of K.T. Sullivan and Mark Nadler elevate the concept of re-contextualization to a whole new level.

It’s a brilliant move for the Oak Room’s first couple. I’ve long thought the traditional songbook show, in which the songs of a single composer or team are interspersed with biographical factoids, was not something that they did as well as, say, Mary Cleere Haran or Eric Comstock.

What Mr. Nadler and Ms. Sullivan do better than almost anyone, however, is comedy; I would much rather hear them spout punch lines with their trademark impeccable comic timing than rattle off names and dates. In the new show, wisely subtitled “The Words of Betty Comden & Adolf Green” (who, like Ms. Sullivan and Mr. Nadler, were strictly a platonic partnership), they not only treat us to songs from a dozen shows, but hammer together dialogue from that many films into a gloriously ersatz new narrative — it’s kind of the cabaret equivalent of sampling.

They sing wonderfully, to the tune of Mr. Nadler’s increasingly sophisticated and contrapuntal medley arrangements (with their familiar Broadway style modulations). But what really makes the show so entertaining is the incongruous, almost Dadaist way the twosome radically juxtaposes the lines and plots of such classic musicals as “The Bandwagon” and “On the Town.” Never before had I realized that the line “I had Miss Hodges too” could have a double meaning, or that “Never Met a Man I Didn’t Like” — the Will Rogers maxim transformed into song — could be taken for a Blue Angel-like résumé of sexual conquests, a requiem for a “cooch dancer,” sung in Coney Island, “Playground of the Rich.”

It’s good to know, to quote that eminent sage Lena Lamont (in “Singin’ in the Rain”), that their “hard work ain’t been in vain fer nothin’!”

wfriedwald@nysun.com