Kennedy Center Artistic Adviser and jazz pianist Jason Moran plays a sold-out show at the Kennedy Center’s Jazz Club in the District. (Marlon Correa/The Washington Post)

Jason Moran is a specialist in the field of jazz abstraction. The pianist and leader of the trio Bandwagon has a rich knowledge of the music’s history and context — part of the reason, no doubt, that he serves as the Kennedy Center’s artistic adviser for jazz. But Moran rarely reads it straight: He prefers to dissect, fragment, distill and subvert it.

That includes the music of pianist and composer Thomas “Fats” Waller, whose music is under ongoing investigation by Moran, who performs a live “Dance Party” of Waller’s tunes and is planning to record some of them with Bandwagon later this year.

On Saturday night, Moran offered samples of that project — and others — for a packed house at the Kennedy Center’s KC Jazz Club. Pulling from any number of angles, and punctuating the experiments with oddly edited audio clips, Moran nevertheless left one constant in place: a soulful, often danceable core.

In one inspired moment, the band presented Waller’s “Jitterbug Waltz” without the waltz. Instead, the stride piano rode on what sounded like a Motown rhythm line, bassist Tarus Mateenplaying a flowing series of riffs (a la Motown bassist James Jamerson) and drummer Nasheet Waits poking and prodding his way to funky soul. But Moran didn’t abandon the gleeful dance rhythms of Waller’s music; certainly he stretched them into free territory, but even here he made frequent allusions to the “thump” of confident swing.

This was also true of his opener, “Honeysuckle Rose,” Waller’s most famous composition. The swaggering, hip-shaking lope was in place, but the trio set it at a severely skewed angle that involved Waits playing New Orleans “big four” beats and a crashing breakdown in the middle section. Moran took an extended break of smooth, 21st-century post-bop as well, but he brought it back around to the happy gait of 1920s Harlem anyway.

It wasn’t just Waller’s music that received these treatments. One soundscape was built on the cadences of Waller’s quote — “I think swing will be here forever and a day without a letter.” Moran made similar intrigues of work by Billie Holiday, using her 1945 rendition of “Big Stuff” to segue into his own trio arrangement. And he infused the meditative “Blessing the Boats” — sung by his wife, opera singer Alicia Hall Moran — with deep gospel.

Nevertheless, the night’s finest moment again involved Waller. Bandwagon closed the set with the standard “Sheik of Araby,” as based on Waller’s 1939 performance. As they started, Moran called up his 5-year-old twins to join the trio onstage. One flawlessly joined the groove on tambourine, while the other danced feverishly next to his dad’s piano bench. It brought the house down.

One caveat, however: the acoustics of KC Jazz Club did not mesh well with Waits’s thunderous drumming style. The drums drowned out the bass entirely and frequently impinged on the piano, obscuring what was surely magic.