Last weekend, Harlem came down to the Lower West Side. For the last few years, the Jazz Museum in Harlem has been such a key player on the New York music scene that it’s easy to forget that the actual, physical museum does not yet exist — or at least, its permanent home has not yet been constructed.

This past week, the Jazz Museum was involved in two outstanding concert events. On Thursday, the museum’s co-directors, Christian McBride and Loren Schoenberg, performed together in a big band under Mr. McBride’s leadership, as part of Jack Kleinsinger’s long-running Highlights in Jazz series at the Tribeca Performing Arts Center. Then, on Friday at the Rubin Museum of Art, the Jazz Museum’s regular performance series, Harlem in the Himalayas, presented the saxophonist and composer Chris Byars in a newly commissioned work.

Thursday’s concert was titled “Basses Loaded,” and the menu offered Mr. McBride’s orchestra as the main course, followed by a brief set by the Jay Leonhart Trio as dessert. When Mr. McBride emerged in the mid-1990s, the outstanding bassist was regarded as a hard-bopping young lion in the mold of the Marsalis brothers. More recently, he’s exhibited an appetite for ’70s-style jazz-funk fusion. He is one of very few bassists to lead his own big band (some others being Charles Mingus, Dave Holland, and Charlie Haden) and with it, Mr. McBride shows still another side of his artistic DNA — one that goes beyond pure music.

The 16-piece group, whose musical style is clearly rooted in the Count Basie “New Testament” band of the 1950s, announced itself with a fast major blues reminiscent of Neal Hefti or Quincy Jones. Mr. McBride has inherited more than a swinging sensibility from the Eisenhower era: His entire presentation was essentially a jazz variety show that could have been hosted by the Dorsey Brothers. After only two instrumentals by the band, he brought out a dazzling young tap dancer, Maurice Chestnut, who executed a brilliant, semi-improvised set of routines to “Broadway” and “Manteca.”

The other guests were both singers, of a sort, starting with Mr. McBride’s regular vocalist (and wife), Melissa Walker, who sang “A Taste of Honey.” It was a suitable song for her, in a “Bluesette” 3/4, but the tempo was just a little too fast for her to do more than merely keep up with the lyrics; “The More I See You” started slowly with the verse, and I was looking forward to a mellow ballad feature for her impressive voice, but instead the arrangement shifted to fox-trot tempo. Next, Mr. Schoenberg led the band in an impromptu blues while Mr. McBride told us he was preparing for the arrival of the next guest.

This turned out to be Mr. McBride himself, returning to the stage in a Rat Pack tuxedo and fedora, brandishing a prop cigarette, and introducing himself as “Black Frank.” No one was sure if he was doing a Sinatra homage or parody, but either way he included a lot of Sinatra vocal mannerisms as he sang two classic Johnny Mandel arrangements for the Chairman, “A Foggy Day” and “You and the Night and the Music.” The set concluded with another superfast, flag-waving blues, “In a Hurry,” in which nearly everyone onstage soloed, and it built to a battle between Mr. McBride and the band’s other bassist, Ben Williams.

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Now entering its third year of Friday recitals, Harlem in the Himalayas began with Mr. Schoenberg’s introduction of Chris Byars, after which the lights went out and a series of slides was projected on a screen behind the band. The new work was titled “Jazz Pictures at an Exhibition of Himalayan Art,” but the first sound we heard was an impromptu recording of a random bunch of men singing in a Russian or Balkan dialect.

The quartet then played a boppish arrangement of that melody, before we journeyed, musically, ever further east. Next stop was a jazz treatment of an Arabian folk theme, after which the group, joined by Mr. Byars’s father, James, on oboe, played a longer, Middle-East-inspired (and recently unearthed) work by the late jazz composer Gigi Gryce entitled “Al-Ghashiyah.”

The rest of the show consisted of five pieces inspired by Tibetan artwork, none of which employed minor seconds or any of the traditional devices used by jazz composers to depict an Asian mood, except that each began with a tinkling bell. One piece did have the drummer, Stefan Schatz, playing a tabla, although, since the lights were out, it was hard to see exactly what he was doing.

This music, too, was highly bass-based: In addition to Mr. Byars on four different reeds, Mr. Schatz on drums, and John Mosca on trombone, the bassist Ari Roland spent a lot of time playing arco; apparently, the use of the bow gives the instrument more of a harmonic presence, necessary to compensate for the lack of a piano.

Mr. Byars is in the pantheon of the contemporary breed of composer-bandleaders. His music is highly original and thoroughly eclectic yet solidly within the jazz mainstream: One piece used fast-moving sustained notes in a manner reminiscent of “Cherokee” (a different kind of Indian art), another suggested a swing-era dance number (in the vein of “It Don’t Mean a Thing”), and another was based on the standard 12-bar blues form. At its best, Mr. Byars’s music is at once challenging and accessible. When Mr. Byars’s father joins the group, the saxophone-oboe-trombone frontline is like nothing heard in jazz before.

Mr. Byars himself is impressive on all of his horns, particularly the dry, meaty timbre of his soprano sax, which, thankfully, recalled the late Steve Lacy more than it did the Celtic, New Agey way that the soprano is generally played these days.

Interestingly, because the lights were off, I tended to notice it less whenever he was switching horns. That was on the plus side for the lack of lighting; on the reverse, this being the end of a long day, once, and only once, I dozed off and dreamed that I was W.C. Fields, shooting sheep in the high Himalayas.

wfriedwald@nysun.com