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By the end of their respective halves of a double bill celebrating the 25th anniversary of the tap dance company M.A.D.D. Rhythms, its co-founders, Bril Barrett and Martin “Tre” Dumas III, were visibly emotional. Each has described this latest production as a dream show, drawing from intensely personal histories to produce, for one night only in Bronzeville, some of the finest tap dancing I’ve seen. Period.

I left the Harold Washington Cultural Center after Saturday’s performance, however, frustrated by the experience. The single show is a highlight of the weekend’s Chicago Tap Summit, a series of workshops, classes and public events also taking place at the Cultural Center, which has looked to ramp up partnerships and get more use out of its theater.

It was clear from the beginning that the dancing was ready, but this show was not. It started 20 minutes late due to technical difficulties, which would be fine, but the problems didn’t stop there.

The evening opened with Barrett’s vintage-tinted “Oscar Plays Gershwin,” a faithful tap telling of Oscar Peterson Trio’s celebrated 1959 album covering George Gershwin’s songbook.

Barrett has jazz in his bones and has frequently soloed to Peterson’s version of “Summertime.” He’s never done the whole record until now, though. In creating “Oscar Plays Gershwin,” Barrett recruited M.A.D.D. Rhythms company members to sketch vignettes to each track. Instead of “Summertime,” Barrett kept “A Foggy Day” for himself, appearing with special guest Ayrie Easley King III, aka “Mr. Taps,” the man who introduced Barrett to tap dance as a street performer in the 1980s.

Forty years later, Mr. Taps remains among Chicago’s most celebrated performers, though he no longer frequents subterranean venues. King passed to Barrett two essential, if seemingly dichotomous traits for any good tap dancer: improvisation and showmanship.

Both came in handy when “Foggy Day” didn’t play, forcing Barrett and King to get creative and riff off one another for the better portion of 5 or 10 minutes. At first, it was the wrong song, then no song at all, leaving Barrett to literally beg the sound operator from the stage to play the right track and still not getting it.

I thought for a while that this might be a bit — and a brilliant one at that — I mean, there’s almost no one who can unexpectedly vamp better than Bril Barrett and Mr. Taps. It wasn’t until a cast member came from backstage to nudge the sound guy that no, oh no — this is not supposed to be happening.

That wasn’t the only issue. Poorly mixed microphones left some dancers (and a few singers in Dumas’ piece) over-amplified and others practically inaudible. The crew frequently let a computer go to sleep, sending a waking up “bloop” over the speakers before playing the next track.

Whether they, too, were asleep or simply in over their heads, I don’t know, and it’s worth saying that this was a warm and supportive audience that seemed to just go with it.

In light of that, am I being too nitpicky? Not really, no. A tap dancer’s feet are his instrument. These are some of the city’s very best instrumentalists, performing exceptionally brilliant, deeply personal repertoire that deserved more respect than it got.

Dumas’ half, called “My Personal Stash,” isn’t the first time he’s choreographed or performed since returning to the company he helped launch after a long break. But it’s certainly the most real estate he’s had since coming back into the M.A.D.D. Rhythms’ fold, presenting an expanded version of a piece first developed with students in Vancouver, Canada, supported by an Illinois Arts Council grant.

“My Personal Stash” unfolds a bit like if Dumas were sorting through his curio box. Childhood photos scroll on an upstage projection screen as recordings of his voice reflect on how his life has intersected with music from the short-lived Chicago funk/soul band Rasputin Stash. Dumas’ father, session musician Martin Dumas Jr., was the band’s frontman.

Rasputin Stash released just two albums, three years apart, in the 1970s. Demos and recorded, unreleased music garnered two more records well after Dumas, Jr.’s death in 1991, when Tre was just 21. In “My Personal Stash’s” musings, Dumas frequently ponders why the band didn’t get that big hit, that single. The dancers’ costumes are newly created band shirts like the ones sold for $80 at stadium concerts these days. With “My Personal Stash,” it’s like Dumas is finally giving the band its due.

Dumas’ impeccable treatment of his dad’s catalog is careful to let the music rise to the top, even as choreographic intricacies pull it apart and put it back together again. Every song but one is played from a recording, imploring us to hear these tracks as they were intended, by the original band members with just one instrument added: feet.

The exception is “Mr. Cool.” In the original, it’s Barry Butler whose swanky, soulful voice soars atop organ, brass and a funky rhythm section. Butler and Dumas Jr. were brothers, we learn in the piece. Here, it’s Justin Butler, Barry Butler’s son, singing as “Mr. Cool,” plus four back-up singers and keys, with cousin Tre’s feet sitting in with that aforementioned rhythm section.

Saturday’s double bill was subtitled “Two icons, one stage.” Each has said he was tempted to make these dances to show they’ve “still got it.” But a quarter century since recruiting a few youngsters into their brand-new tap academy, Dumas and Barrett don’t have anything to prove. To my eyes, these are icons, titans of tap who have nurtured an extraordinary art form and passed it to two generations dancing side-by-side this weekend. The occasion featured two second-generation mainstays who’ve been there from the start: spitfires Donnetta Jackson and Star Dixon. It brought storied alumni back to the M.A.D.D. Rhythms stage not seen there in many years: Ian Berg, Nico Rubio and Megan Davis, for example, and boy howdy, are they good. Then there’s the slightly younger crop — Andrew Carr, Sterling Harris, Davon Suttles, Caleb Jackson and others — legends in the making who are asserting their own voices and, increasingly, are primed for leadership in Chicago’s crowded tap scene.

If you were there on Saturday, then you already know. You see, the acronym M.A.D.D., short for Making a Difference Dancing, has so clearly done that. Now, if we could just get the sound guy to play “Foggy Day.”

Lauren Warnecke is a freelance critic.