If any musician were to warrant a jukebox musical right now, it would be the one with the moxie to release an album called “Black President” and the chops to back it up.

That record came out almost 30 years ago, and it’s one of many scorching titles by Nigeria’s Fela Anikulapo Kuti, he of the 27 wives and the 200 arrests and the martyred mother. Kuti’s Afrobeat sound may have drawn liberally from other musical giants, among them the Chairman of the Board and the Godfather of Soul. But as the boisterous and somewhat ramshackle new musical “Fela!” makes clear, these self-anointed icons could have learned (and, in the latter case, actually did learn) a thing or two about how to make hips shake, fists raise, pulses quicken, and minds soar from this mercurial, priapic master. Director/choreographer/co-writer Bill T. Jones, a modern-dance legend who has dipped his toe into commercial theater (his “Spring Awakening” choreography won a Tony last year), struggles to craft this overstuffed life into a digestible package.

The notional verisimilitude of Mr. Jones’s concept — we are ostensibly watching Kuti’s last performance before leaving Nigeria, a country he had repeatedly denounced as a kleptocracy — is outweighed by the absence of crucial outside voices that might have put his alternately charmed and snakebitten life into context. But while the book by Mr. Jones and Jim Lewis has its share of lumps, the telling goes down remarkably smoothly, thanks to the Brooklyn-based Afrobeat ensemble Antibalas and, in a star-making performance, the hypnotic Sahr Ngaujah.

They see to it that Kuti’s almost impossibly charismatic sound withstands the various bruises and dings it receives along the way, leaving in their wake a high-energy voltage that is far more entertaining than it deserves to be.

The high point comes early, as this sound is dissected by a process Kuti describes as “breaking it down — the how and why of Afrobeat.” The sentiment itself is unremarkable, even trite. But it achieves an unlikely apotheosis as Antibalas spotlights the individual layers that would first augment and then transform the Highlife genre (itself a hybrid) that thronged African dance halls in the 1950s and ’60s.

The bone-deep rhythms of Kuti’s native Yoruba culture, the plush swing of Nelson Riddle-era Sinatra, the Cuban-inflected bebop of Chano Pozo, the agitated, skittering unison guitars of James Brown’s band: Kuti dutifully catalogs and then promptly morphs these elements into an ornery, libidinous new sound, all his own. This microscopic focus on process isn’t new to Mr. Jones — he created a memorable performance at Lincoln Center in 2000 around his creation of a dance solo, technical step by technical step, mental association by mental association.

But this irresistible piece of assemblage represents something new and quite welcome: musicology you can dance to. (Or, rather, musicology you will dance to: In addition to the occasional bout of call-and-response, Mr. Jones has the audience stand mid-show and have a go at a dozen or so hip gyrations.)

This is the most blatant but hardly the only sequence to spotlight Mr. Ngaujah, a virtual doppelgänger of Kuti and easily the most compelling reason to see “Fela!” A slight man with a penchant for spliffs roughly the size of his powder-blue bikini briefs (which is all the real-life Kuti wore during some concerts), Mr. Ngaujah melds the baroque showmanship of James Brown, the bantamweight preening of Prince, and especially the feline insolence of Miles Davis into a galvanizing package.

For someone so interested in structure, however, Mr. Jones — whose near-constant choreography deftly melds traditional African dance with a sweatier, angrier ferocity — shows a curious lack of discipline in imparting any reliable cohesion on the show itself. For all of its enormous visual oomph (including eye-catching animations by Peter Negrini that surround the audience) and polyrhythmic complexity, “Fela!” is a bit of a mess.

An early monologue gives crucial background about Kuti’s mother, a pioneering African feminist who died when 1,000 policemen stormed the family compound in 1977. (She was thrown from a second-story window.) After this initial flurry of context, however, Funmilayo Ransome-Kuti exists solely as a beatific figure (played forthrightly by Abena Koomson) singing atop a platform with animated beams of heavenly light emanating from behind her. Legitimate questions might well be raised about how a mother-son dynamic plays out in a man who had 27 wives and condemned condoms as “un-African.” But Mr. Jones never remotely raises these questions, and the musical suffers from his hagiographic treatment. The overlong second act is filled with similarly questionable choices, including a perfunctory sequence given over to Kuti’s wives — a mere nine in this telling — and a protracted invocation of the Yoruba gods that slides into dream-ballet kitsch. It’s almost as if Kuti’s 1975 album “Everything Scatter” was interpreted less as a lament for a corruption-ravaged homeland and more as a dramaturgical suggestion. At the time, this pell-mell lack of discipline was excused and even indulged. With the benefit of a few decades of hindsight, however, it’s harder to forgive.

So many albums, so many arrests, so much tumult: Messrs. Jones and Lewis often seem to be scrambling to keep up with their tempestuous subject. And as Kuti demonstrates in one of the show’s few glimpses of his temper, a brief but telling scene in which he hisses the correct backing rhythm to his momentarily perplexed band, he didn’t like to be slowed down. Antibalas and its equally dynamic front man see to it that “Fela!” surges and pulses over the dramaturgical speed bumps that Messrs. Jones and Lewis leave in their way.

Until September 21 (450 W. 37th St., between Ninth and Tenth avenues, 212-560-8912).