It's 8 o'clock on a Sunday night and Fats Waller's 1939 hit "You Meet the Nicest People in Your Dreams" is bounding out of your speakers. In 2006, that can really only mean one thing: "The Big Broadcast," WFUV-FM's weekly, four-hour celebration of 1920s and '30s jazz and pop, is on the air.

On the other end of the signal, old-time meets high tech as the show's vivacious host, Rich Conaty, holds forth from the gleaming studio's ultra-modern console, taking requests via e-mail and spinning rare 78s from CDs he's burned at home. The program has been kicking and crooning across the New York airwaves for close to 35 years, and tonight's installment is highlighted by birthday tributes to lyricist Gus Kahn and Chicago cornetist Mugsy Spanier. Conaty plays an ethereal waltz, then a bouncy dance band track featuring suave vocalist Scrappy Lambert. But then it's time to heat things up.

"Get a load of this— 'Cloey' by Henry 'Red' Allen's Orchestra, from 1936," he announces. As Allen's steamy trumpet and shuffling rhythms send listeners to the stratosphere, Conaty grins wide and bops his head in time.

While a few other left-of-the-dial shows do feature Depression-era sounds, you'll have a hard time finding one that does it as regularly—or with such deep love for and knowledge of the music. It's easy to understand why "The Big Broadcast" is one of New York radio's longest-running, fanatically followed programs.

Those who believe pre-World War II American popular music is strictly the stuff of goofy, old cartoon soundtracks and "Little Rascals" episodes are way off. After all, early jazz was outlaw fare, the syncopated clatter of the bathtub gin-wrecked Daisy Buchanans and wannabe mobsters who rocked the Charleston in smoke-filled speakeasies. It's the bold realm of musical revolutionaries like Louis Armstrong, Jelly Roll Morton, and Bix Beiderbecke. Of peppy, proto-garage bands like Ben Bernie's orchestra and the Mound City Blue Blowers; of sweet crooners like Rudy Vallee, Russ Colombo, and a hip upstart named Bing Crosby. And it's the sophisticated, dream-like domain of the Gershwins, Cole Porter, Irving Berlin, and other legends of the Great American Songbook. Truly a magic time, one to match any segment of the subsequent rock 'n' roll decades.

Listening to "The Big Broadcast" (named for the 1932 film starring Crosby and others), it's hard not to be swept up by Conaty's boundless enthusiasm. An affable kid in a 52-year-old's body, he grew up in Queens, where the Jazz Age bug bit him early and hard.

"I was 13 or 14, and I was fishing around on the radio and found this show on the Hofstra University station out of Long Island that played these old records by the Mills Brothers, Paul Whiteman's Rhythm Boys [with the youthful Crosby]," he recalls. "Hearing that is what got me interested in both the music and in radio." By the time he was 16, Conaty had his own show on the very same station.

So in 1971, while his fellow high school students were banging their heads to Led Zeppelin, Conaty was tapping his toes to Ukulele Ike. Didn't the other kids give him a hard time? "No, they dug it," he says. "They liked me because I was different, and I was on the radio. That was kind of a big deal to them." On one occasion, for show-and-tell, he was even asked to bring in some of his vintage records to play for the class.

When it came time to pick a college, however, he chose Fordham, not Hofstra, "more on the strength of its radio station's signal than any academic consideration," he says. And though the show did run briefly on another station, it's Fordham's WFUV that has been home to "The Big Broadcast" for the majority of the years since its January 1972 debut.