With 18.5 million listeners and 35,000 new sign-ups each day, popular music Web site Pandora.com has the potential to remake the radio landscape, according to Pandora founder Tim Westergren who spoke at the Harvard Law School yesterday afternoon.

Fans of the site range from your run- of-the-mill indie-loving college students to their Johnny Mathis-loving grandmas.

Using a complex algorithm created by the Music Genome Project, a company Westergren helped found earlier, Pandora takes a listener’s favorite song or artist and recommends similar music based on a series of factors present in that song or artist’s catalogue.

“[Pandora] replicates your best friend, but with almost perfect knowledge of an enormous catalogue of music,” Westergren said at the talk, which was sponsored by the Berkman Center for Internet and Society.

A team of musicians measure and score each song using nearly 400 factors, which frame them in what Westergren calls the “musical double helix.” Once a user inputs a given song or artist, a mathematical algorithm creates a playlist that orders songs based on their similarity.

Pandora launched in Nov. 2005 and has since spread even though the Web site has never advertised.

Pandora grew out of Westergren’s years of work as a musician and film composer, during which he also served as a male nanny (or “manny,” as he called it). After years of trying to promote his music, Westergren drew on his experiences attempting to discover film directors’ tastes and preferences to found the Music Genome Project eight years ago.

Part of what makes Pandora so appealing, Westergren said, is that it exposes listeners to a large quantity of music that they would never have otherwise encountered, while simultaneously connecting thousands of great artists to a new fanbase. Seventy percent of the 60,000 artists on Pandora are not even signed to a major label, he added.

Pandora recently became available on the iPhone, which allows listeners to access it on the road. By offering mobile service, Westergren said, Pandora’s vision for connecting listeners to new artists and artists to new listeners can be more widely available and accessible.

“We want to completely fix radio,” he said.