(Short answer for anyone left still wondering if this show lives up to the hype: goodness, yes. On the most basic musical-theater level, you’ll have the earworms of songs like “My Shot,” “Helpless,” “Washington on Your Side,” and many others stuck in your head for days.)

The production, a filming of a June 2016 performance at New York’s Richard Rodgers Theatre, has been brought to the screen with intelligence and craft, eight cameras pulling us “into” the show without sacrificing the sense of spectacle. (There are a few choice Busby Berkeley-style shots from overhead, just for fun.) Taking place from 1776 to 1804, “Hamilton” is constantly in motion, with the large cast of characters and ensemble players whirling through Miranda’s songs and Andy Blankenbuehler’s choreography. Thomas Kail directs the filming as fluidly he did the original show but with judiciously edited close-ups that preserve the visual flow while heightening the dramatic conflicts. More than ever, Leslie Odom Jr.‘s Aaron Burr is revealed as the shadow star of “Hamilton,” rendered nearly Shakespearean by his lust for power and inability to stand for anything.

The title character’s story is pretty compelling, too, as readers of Ron Chernow’s 2004 biography know. Born illegitimate in the Caribbean, Hamilton bootstrapped himself into the American Revolution as one of its finest minds and most reckless personalities, and “Hamilton” places him in the context of a scrum of strivers: Odom’s Burr, aching to be in “The Room Where It Happens”; the Marquis de Lafayette (Act 1) and Thomas Jefferson (Act 2), both played by the puckish charmer Daveed Diggs; the godlike yet touchingly human George Washington (Christopher Jackson’s performance acquires a powerful graciousness in close-up); the blissfully tyrannical King George III (Jonathan Groff) with his show-stopping patter songs. Slightly off center-stage are the two Schuyler sisters, Eliza (Phillipa Soo), who married Hamilton and put up with his infidelities, and Angelica (Renee Elise Goldsberry), as politically astute as her brother-in-law and less rash. The dramatic themes and recurring musical motifs that define these characters are part of what makes the show so richly satisfying.

These are all powerhouse singers, actors, and dancers, and they capably negotiate Miranda’s lickety-split lyrics, as percussive as hip-hop and as multi-layered as Sondheim. People who dismiss “Hamilton” as “that rap musical” are always shocked by the actual breadth of the show’s sonic palette, which includes pop, R&B, and a full history of show-tunes. But there’s no denying that having our great white founders played by the descendants of slaves — and having them engage and debate each other in the cross-rhythms of the people they enslaved — is a masterstroke that brings everyone into the tent of the American dream, on stage if not outside the theater. (For anyone having trouble following the rapid-fire lyrics, closed captioning will be a boon of this televised version — but even subtitles might have trouble keeping up.)

At the center of “Hamilton” the musical and “Hamilton” the phenomenon is Miranda, who took the project from a ridiculous light bulb over his head as he was beach-reading the Chernow book to 11 Tonys and a Pulitzer Prize. He’s a compact, sad-eyed imp of a performer, and as Hamilton he seems slightly out of his element among his strapping co-stars, most of whom have stronger or more trained voices. I saw the show on Broadway with Javier Munoz, who was Miranda’s alternate and who replaced the star after he moved on; Munoz gave a galvanizing, muscular performance, and yet the essential Hamilton remains Lin-Manuel Miranda, and seeing this filmed version is a reminder why. Especially in the final scenes, after tragedies of his own and others’ making have brought Hamilton crashing to earth, the actor conveys a sorrow that’s beyond bone-deep — that conveys something about the frailties and follies of trying to be a great man or build a great country.