Last year, Tom Stoppard spent nine hours depicting the fertile minds that would plant the seeds for the Communist Revolution in “The Coast of Utopia.” Now, with “Rock ‘n’ Roll,” Mr. Stoppard has jumped forward almost exactly 100 years to taste the poisoned fruit that stemmed from this revolution. Substituting Dylan and Jagger for Bakunin and Turgenev, he completes this latest task in a third of the time and with nearly triple the impact.

Mr. Stoppard begins his dense but enormously satisfying tale in 1968, just as the Prague Spring (a reform movement aimed at creating “socialism with a human face”) came to an abrupt halt with the arrival of Soviet tanks, and proceeds through the steadily increasing repressions of the 1970s. The events of 1968 prompt Jan (Rufus Sewell), a rock music-loving Czech, to abandon his doctoral studies at Cambridge for an embattled life as “a critic of the future,” to use the author’s wonderful phrase.

He had spent his Cambridge years under the tutelage of the irascible, brilliant Max Morrow (Brian Cox), who was born in October 1917 — the same month as the Bolshevik revolution, he reminds anyone who will listen — and is proud never to have wavered in his support of the motherland. “I’d be a Communist with Russian tanks parked in King’s Parade, you mummy’s boy,” he sneers at Jan in the very first scene; in fact, Max clings proudly to his designation as a “tankie,” one of the few (and ever fewer) British Communists who clung to their affiliations after the Kremlin crushed the Hungarian revolt in 1956.

Also under Max’s roof: his wife Eleanor (Sinéad Cusack), a classics professor battling cancer, and their daughter Esme (Alice Eve), a hippie with a thing for her dad’s tousle-haired star pupil. The two men reconnect only twice more over the next 22 years. When “Rock ‘n’ Roll” resumes in the late 1980s, Eleanor has died, the grown-up Esme (Ms. Cusack again) has a teenage daughter of her own (Ms. Eve), and while a semi-infirm Max still appears to win every argument he has about the Party, history threatens to consign his lifelong ideals to the scrap heap.

The philosophic battles between Jan, who loves England unequivocally, and his fire-breathing mentor run the risk of becoming an unmitigated intensity fest; director Trevor Nunn pitches Mr. Sewell and especially Mr. Cox at temple-throbbing levels early on and only gradually turns down the volume. (Max is still breaking dinner plates at the age of 70, even if he needs a cane to do it.) And while Mr. Cox cuts a memorably irascible figure as the unreconstructed leftie, it is Mr. Sewell’s chastening journey toward political and personal serenity — christened by an awkward, beatific dance to the chugging chords of the Rolling Stones — that I will not soon forget.

As with “The Real Thing,” another emotionally gripping Stoppard play with a deep-rooted affection for popular music, the female characters gradually creep into the foreground only to command attention with sudden force. The astonishingly good Ms. Cusack delivers one of the single most powerful sequences in all of Stoppard, a ferocious demand that Max not reduce Eleanor and her cancer-ridden body to one of his dialectic constructs. “I am not my body,” she insists between sobs. “My body is nothing without me, that’s the truth of it. Look at it, what’s left of it. It does classics. It does half-arsed feminism, it does love, desire, jealousy, and fear — Christ, does it do fear! — so who’s the me who’s still in one piece?”

Mr. Stoppard, a rock buff who left Czechoslovakia as a young boy, contents himself with a few cheap laughs and not much else, with a subplot involving Alice’s boorish father (Quentin Maré), a clueless journalist who seeks out Jan for a perestroika-era story. And while Eleanor’s heart-rending parsings of the Greek poet Sappho illuminate the play’s larger themes on love’s “uncontrollable, uncageable” qualities with a quiet authority, the same cannot be said of Mr. Stoppard’s overreliance on Syd Barrett, the deposed mad genius of Pink Floyd, as a metaphor for rock’s simultaneously liberating and destabilizing powers. (“Shine On You Crazy Diamond” was reportedly written about him.) Barrett, who moved back into his mother’s Cambridge home after leaving the band, always shunned the spotlight; the thought of being forced to symbolize the blighted promises of youth, to say nothing of a brief incarnation as the priapic god Pan, would drive anyone into anonymity.

The other band to receive intense dramaturgical attention is the lesser-known Plastic People of the Universe. Here the symbolism sits more comfortably within Mr. Stoppard’s sprawling tale: The Plastics, as they were known, really did symbolize the promise of engaging with the West in alarming new ways — and were persecuted heavily as a result. “Rock ‘n’ Roll” includes Several snippets of their music passages that show the group’s mimicry of Western bands but also slight its more outré tendencies; the Plastics had more in common with Frank Zappa than with the Stones, but if these selections help contextualize their anarchic appeal for a Western audience, so be it.

Throughout, Messrs. Nunn and Stoppard show a refreshing refusal to be yoked to the month-to-month specificity that plagues so many period productions; people who loved Pink Floyd in their 30s, they realize, are likely to still enjoy Pink Floyd in their 50s. They don’t buy entirely new wardrobes and replace their entire record collections with each new year, as so many plays and films would have you believe. On my way to “Rock ‘n’ Roll,” my digital music player shuffled its way through a song by the Pixies from 1990, one by Peter Bjorn and John from last year, and one by the Beatles from 1967. Kids I admired in college loved the Pixies, a coworker burned me a Peter Bjorn and John CD after taking a rare night off from watching his infant son to see them perform, and I was fascinated and slightly unnerved by my parents’ “Magical Mystery Tour” album cover as a youngster.

I would never claim that these songs carved a permanent space in my worldview the way the Velvet Underground and the Plastics did for Jan, or the way that Syd Barrett encapsulated a perhaps inevitable descent into obsolescence and confusion for Esme. They’re just tunes with beats and harmonies, with all the comfort and chaos that implies. It’s only rock ‘n’ roll, but I happen to like it quite a bit. Same with “Rock ‘n’ Roll.”

Open run (242 W. 45th St., between Broadway and Eighth Avenue, 212-239-6200).