Notation writes only what a tradition decides matters
Musical notation is any visual system for capturing sound, and each tradition writes down only what its players need. Classical musicians read staves and noteheads, Nashville session players use a number system, guitarists favour tablature—and the oldest known example is a Babylonian tablet from about 1400 BCE.
That tablet, from Nippur in what is now Iraq, gives fragmentary performance instructions showing music built on thirds in a diatonic scale. Another from about 1250 BCE names the strings of a lyre whose tuning other tablets describe. Its reading is still argued over, yet these clay pieces hold the earliest notated melodies found anywhere, used for both temple and court music.
Greek notation ran from at least the sixth century BCE to about the fourth century CE, writing pitches as letters above the syllables and marking rhythm only as long or short. Just a few complete works survive, including the Seikilos epitaph and hymns by Mesomedes of Crete, plus some 40 fragments; the system seems to have faded as the Western Roman Empire declined. Byzantine chant took another route, with neumes from the tenth century that mark steps relative to a modal key rather than fixed pitches. Modern Greek singers call these brushstroke-like signs gántzoi, hooks, and must work out the intervals from context.
Today's Western staff descends from medieval church efforts to make plainsong chants sound the same from region to region. It grew through the Renaissance and Baroque and kept adapting in the Classical and Romantic eras as instruments improved. Twentieth-century composers added graphic scores, and since the 1980s scorewriter software has done much of the engraving.
Marks have been cut into stone, pressed into clay and inked on papyrus, parchment and paper, then printed by press from around 1400 and by computer printer from around 1980. Because ancient systems were never very complete, our grasp of their music stays limited.
Source: Musical notation