The songs of Enheduanna (later 2300s or early 2200s BCE) comprise the oldest literature by an identified author written in cuneiform.
She was first appointed high-priestess during the reign of her father the Sumerian king, Sargon, who united Sumer and Akkad (southern and northern Mesopotamia) located in what is now Iraq.
Her portrait on a limestone disc was discovered during an excavation of Ur. Among her 45 extant songs she wrote three long hymns to the Goddess Inanna. Although Akkadian born Enheduanna wrote in Sumerian as she was placed in the Sumerian city of Ur by Sargon.
Inanna, known as the Venus star, was the Sumerian goddess of love and war and is identified with the Akkadian goddess Ishtar. As En-priestess, Enhdeduanna served the moon god Nanna, father of Inanna.

Excerpts from one of Enheduanna's hymns to Inanna and citations from the CD Booklet, "Sounds of Silence: Recent Discoveries in Ancient Near Eastern Music" by Anne D. Kilmer, Richard L. Crocker and Robert R. Brown are included below. According to a letter from Dr. Kilmer, "Enheduanna's religious poetry was certainly sung, and probably accompanied by a stringed instrument. Enheduanna seems to have composed the music and written the words."

"During the last sixteen years documents have come to light that have provided us with the most specific information yet available about the music of the ancient Near East. These documents include information on the structure of the scale and the tuning system as far back as 1800 B.C, and also an actual song dating from around 1400 B.C. Both the tuning documents and the song predate comparable documents by at least a thousand years, thus pushing back the limit of our specific knowledge of music from a little over 2000 years ago to a little over 3000 years ago.

CD, LP, and large, 23-page illustrated booklet titled: "Sounds of Silence: Recent Discoveries in Ancient Near Eastern Music." Anne D. Kilmer, Richard L. Crocker and Robert R. Brown, 1976, (send $24, check payable to Bit Enki Publications, Anne D. Kilmer, Dept. of Near Eastern Studies, Univ. of California, Berkeley 94720).

I thought this might be of interest for anyone looking into MiddleEastern Music. I have not bought it, I just came across it in a search.