Mr. Conaty was 62 and had worked in radio for 43 years. The center of his life, his great achievement, was “The Big Broadcast,” his show of jazz and pop from the 1920s and 30s. He started it at WFUV, Fordham University’s station, which he joined as a freshman in 1973, and gave his last live broadcast in September. Except for a few years at WQEW in the 1990s, he stayed at WFUV, playing songs from his vast personal library of 78s, taking not a lot of money, giving lots of listeners a happy education in Sophie Tucker, Cab Calloway, Bing Crosby, Rudy Vallee, Cliff Edwards (Ukulele Ike) and Isham Jones.

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His slot was Sunday nights, 8 to midnight. I could think of no better company for a long drive home from a late shift or a weekend out of town. Mr. Conaty, a man of steady habits, would open with a song or two, then play the same snippet of an ebullient Fats Waller tune. “I’ve looked the universe over, from wacky Nagasaki to Dover, and now that we have met how sweet it seems! I love you more the more I know you, which only goes to show you: You meet the nicest people in your dreams.”

“Thank you, Fats,” Mr. Conaty would say.

Mr. Conaty stayed in his musical lane: those two decades, no others. His devotion was strict but without affectation; you’d never picture him in spats. He was just a New York guy who loved this music to death, the gems of a genre that is largely forgotten or trapped in period cliché. “He was trying to point out the timelessness of it, the universality of it,” said his friend Marshall Crenshaw, the singer and songwriter, who has a WFUV show of his own. “Rich had this spark about him,” Mr. Crenshaw told me. “You could tell that somebody was home upstairs. He wasn’t locked into some obsession with the past.”

Like his colleagues, Mr. Conaty wore his expertise lightly. His voice always wore a smile, though he had an odd tendency toward self-deprecation, which often made me think: Here is a sad soul. For all the years I listened in, I didn’t know much about him. He’d had a wife, whom he warmly called “Manhattan Mary.” She died in 2009. He would speak of visiting his mother, in Florida, but had no siblings or other close relatives. I later learned he lived in the Hudson Valley, two hours up the Taconic Parkway from the Bronx. For a while he drove a bus for an organization for adults with developmental disabilities.

Mr. Conaty was an efficient D.J.: He gave you song titles and artists’ names, and dates of birth and death, but mostly he gave you music. Hearing his birthday tributes to dead musicians made you aware of the cruel limits of the human life span but also of the uncanny ability of good songs to live outside of time. Before he got sick, Mr. Conaty had been anticipating his 50th radio anniversary, and mused about hanging it up then. Cancer robbed him of his plans, and saddened listeners like me who lost a chance to say, back to him, the one word that was his “Big Broadcast” signoff: Aloha.