In its first two weeks, the Rock & Roll Hall of Fame app for iPhone and iPad has done something remarkable in an industry where most news about music buying is about how people don’t do it anymore: It convinced people to pay for music.

The $2 app includes information about 600 “songs that shaped rock ‘n’ roll,” and the company behind it reports an aggregate sales conversion rate of 31 percent. That means that in this two week period, every ten app purchases has already resulted in approximately three song purchases — an impressive ratio that the developer behind the app, Sideways, exp...