Seikilos epitaph
The Seikilos epitaph is the oldest surviving complete musical composition, including musical notation, from anywhere in the world. The epitaph has been variously dated, but seems to be either from the 1st or the 2nd century AD. The song, the melody of which is recorded, alongside its lyrics, in the ancient Greek musical notation, was found engraved on a tombstone (a stele) from the Hellenistic town Tralles near present-day Aydın, Turkey, not far from Ephesus. It is a Hellenistic Ionic song in either the Phrygian octave species or Iastian tonos. While older music with notation exists (for example the Hurrian songs), all of it is in fragments; the Seikilos epitaph is unique in that it is a complete, though short, composition.
History of lute-family instruments
Western scholarship has traditionally credited the Greeks, including Pythagoras (c.  570 – c.  495 BC), with discovery of this math. However, as modern scholars have looked at cuneiform texts, it is clear that the Greeks were not the first. Recorded thinking in Mesopotamia about the mathematical ratios of strings predates the Greek thinking by at least 1500 years. Furthermore, a form of written music came out of that era, called the Hurrian songs, currently the oldest known written music, and is based on modes of music, created through string ratios. The Persian and Arab thinkers from the Umayyad and Abbssid periods (7th to 13th centuries A.D.), however, did not access this ancient mathematical thinking, but began working with the math again after they accessed Greek thinking.