The lives of Lee de Forest, Edwin Howard Armstrong and David Sarnoff were as improbable as any radio melodrama. De Forest, a shameless self-promoter of dubious ethicality, invented the vacuum tube that made radio practical-without ever quite understanding how it worked. The discoveries of Armstrong, a brilliant if naive idealist, formed the basis for virtually all radio reception today. Sarnoff, an impoverished Russian immigrant who rose to the presidency of RCA, hit upon the notion of mass broacasting. Ultimately, their lives collided in endless court battles for the rights to patents. “Empire of the Air” begins as a study of genius and ends as a dark tale of egomania, avarice, deceit and tragedy.

If there’s a hero here, at least to Burns, it’s Edwin Armstrong. After unveiling his revolutionary inventions, including FM radio, he spent half a lifetime defending his work against the bogus claims of others. An avid scaler of lofty heights, Armstrong once posed atop the RCA globe 400 feet above 42nd Street, just to irritate Sarnoff. (He did.) At last, embittered and depressed, he donned his hat, overcoat and gloves, opened his bedroom window and dropped 13 stories to his death. “Armstrong’s name should be as well known as Edison’s,” says Burns. “The reason it isn’t is the reason we’ve done this film.”

Almost as obviously, Burns casts Sarnoff as his heavy. After founding RCA, Sarnoff became so obsessed with promoting his own legend that he instructed underlings to refer to him as “the General. " He summed up his managerial style in seven words: “I don’t get ulcers. I give them.” In one memorable scene, a lavish party in honor of RCA’s ruler, an uncharacteristically nervous Frank Sinatra warbles “The Gentleman Is a Champ” as Sarnoff and his wife glide alone in the dance-floor spotlight.

Mostly, though, this is television for the ears. Burns’s soundtrack deftly mixes excerpts from vintage radio comedies, commercials, news broadcasts, concerts, political harangues, soaps-the electronic background noise of an era it helped transform. The show’s talking heads talk wonderfully, especially Red Barber and Garrison Keillor. One jarring note: the documentary’s last sound is that of a telegraph tapping out “Baseball next” in Morse code, a coy plug for Burns’s upcoming PBS study of the national pastime. Any more of that sort of thing and they’ll start calling this TV genius “the Little General.”