Before the invention of a system for notating music in the ninth century, music was passed on from one person to the next only by aural transmission—that is, melodies were carried only in the memory, and learned by repeated hearing. A new monk, for example, would spend hours every day for several years learning by rote memory all of the chant melodies for the entire liturgical cycle, taught by the magister scholarum—the director of music. The first system of notating music was developed sometime during the Carolingian era after 800 for the purpose of transmitting information about.....