Pretty cool. Now, either all the sheets are played consecutively (melody) or simultaneously (harmony). (Plus, as before, they can be played individually too.) And all thanks to the injection of the Score object, which I separated out into a separate module that now contains all the business objects in the application.
Thanks Troy for laughing at my melody-only approach, which inspired me to work on the harmony support, which is pretty easy thanks to JFugue API!