Cowboy yodeler Slim Whitman sings “It’s a Small World.”

Leonard Nimoy belts out “Proud Mary.”

Bing Crosby croons “Hey Jude,” complete with his trademark “bum-ba bum bum.”

Sound about as appealing as fingernails on a blackboard? Then public radio’s Jim Nayder, creator of the weekly show “Annoying Music,” has chosen well.

The show is built on the assumption that listeners won’t rush to change the station when the Brady Bunch starts chirping “American Pie.” So many people have stayed tuned, in fact, that the show is going national, offering excruciating music to listeners coast to coast.

“Bad music, you switch the station. Annoying music is sort of like passing an accident - you know you don’t want to look, but you sort of have to,” Nayder says, explaining the popularity of a show that started out as an experiment for listeners of WBEZ-FM 17 months ago.

As Nayder recalls it, the station had a few spare minutes in its Saturday lineup. Someone asked Nayder, a 43-year-old independent producer known for his dry humor, if he could fill in.

Nayder happily obliged, playing a yodeling version of “It’s a Small World.”

“‘It’s a Small World’ is annoying on its own, but this particular version was like a train wreck,” Nayder says. “The phone started ringing as soon as it was over, people saying they loved the show and when would it next be on.”

It has been on ever since, a program of a mere three minutes or so featuring one song each week, such as Kate Smith belting the Beatles’ soothing ballad “Yesterday.”

Nayder picks the tunes, based on a loose set of rules. They can’t be intentionally funny or bad. Which is why Pat Boone’s recent heavy metal album didn’t qualify.

The show goes national on Aug. 20 on 90 public radio stations.

“I just feel sorry for the country,” says WBEZ general manager Torey Malatia.