Musical notation existed in a more limited form around the time of the Roman Empire. The Greeks had a system, systema teleion, that had symbols for different tones for both vocalists and instrumentalists. They were experts at using math and geometry to craft and tune their instruments, allowing them to create a fairly complex system of recognizing tones and recording them, and the Romans are believed to have used it (there's not solid evidence either way, as no compositions have survived). Clay tablets from Mesopotamia also exist that appear to show musical notation and a scale, though it's difficult to read.

The big problem with musical notation from ancient times is that it's incomplete compared to modern day. There's often no specific rhythm noted, which means it can only serve as a basic guide for playing the song. It's believed that performing was thus based heavily on learning by ear and practice. Modern musical notation comes from Guido of Arezzo in the early 11th century, who developed an early form of staff notation as a way of quickly teaching the Gregorian chants used in church.