Taylor Swift spoke out last year about the economics behind Spotify. Now, she has taken aim at Apple over its decision not to pay musicians during a trial period for its new music service.

In a letter Sunday on her Tumblr page, called "To Apple, Love Taylor," Ms. Swift addressed a situation that has sent shock waves through the music industry: Apple, which has announced a subscription streaming service to compete with Spotify, Rhapsody and Deezer, says that no royalties will be paid during a three-month period in which customers can try it free.