At the time there was no way of recording music so it didn't protect reproduction of the music in a form you could listen to. But as the court case "Bach vs. Longman" established in 1777 that statute did cover sheet music which was how Bach made money.
http://www.newstatesman.com/music/2008/12/public-century-com... gives a better overview of how the problems of music today are the same problems as back then. This includes a deal of piracy and stealing of works, and also mentions the other problems copyright introduces, such as the dilution of quality. Dickens and Haydn could have created greater works if they weren't focused on public patronage for money.
In other words, the Statute of Anne protected publishers of books. Not musicians.