Bad Brains remain one of rock's greatest conundrums. After 34 years of (still relatively underacknowledged) musical peaks and momentum-derailing implosions — working in rarefied air, crackling with creative energy, if also charged with inherent instability — the Washington, D.C., rock/reggae quartet has both a checkered past (and present) and a positive legacy. But after sets by Maryland's reggae-rockin' openers Lionize, and the Wu-Tang Clan's magisterial GZA, Thursday's notably mixed-race full house at the Trocadero witnessed something else the influential Brains remain: fascinating.

The backstory has always compelled: Four musically gifted African American teens form a Return To Forever-influenced jazz-rock fusion group called Mind Power, get turned on by English punk, embrace reggae's Rastafarian religio-ideology after catching Bob Marley in concert … and proceed to both pioneer and perfect the speedy, punk-rock subgenre of hardcore. And also deliver the sweetest original reggae yet from any American act (including "I & I Survive" and "I Luv I Jah," both dub-fully mesmerizing at the Troc). In their heyday, they were arguably the most exciting live band around. Singer Paul "H.R." Hudson's twitchy, kinetic presence — crooning in Rasta terms of Jah love or decrying "Babylon" (any corrupt power structures) in howls channeling latent Middle-Passage rage — placed him among rock's greatest front men ever.

But that was then. The enigmatic H.R. hardly moves now; instead, he smiles beatifically, takes liberties in phrasing, goes inaudibly sotto voce, and can seem, as nonetheless satisfied concertgoers remarked, "kind of crazy." But crazy like a loon — or a fox?

Thursday, Bad Brains sailed through 17 songs, mostly such chops-brandishing classics as "Attitude" and "Fearless Vampire Killers" — both on 1983's Rock For Light LP and their self-titled 1982 debut on the ROIR cassette label. Gary "Dr. Know" Miller blazed on melodic guitar, evoking, yes, Al DiMeola on the mini-solo in their autobiographical "Banned in D.C." (Bad Brains: A Band in DC, the well-received documentary screened at SXSW recently, awaits its theatrical release.) They ended with something new, presumably from their forthcoming album (first since 2007's Build A Nation, produced by longtime Brains devotee, Beastie Boy Adam Yauch). The saga continues.