Less well known and less used liturgically is the ancient Song of Hannah as recorded in 1 Samuel 2:1-10. The Magnificat and Hannah's song are properly mentioned together, because the former is literarily and thematically dependent on the latter. Both Hannah and Mary are mothers rejoicing at the birth of an unexpected child. Hannah praises God that he has seen fit to end the curse of her barrenness, while Mary glorifies the Lord because he has chosen her to bear the promised Messiah. Each knew to her sorrow that she would have to give up her son one day.
John Mark Reynolds alludes to an ancient tradition which identifies Mary's parents as Joachim and Anna. Though the tradition has no explicit scriptural basis, it could conceivably represent a continuing memory of genuine persons who lived in the first century before Christ. However, I myself wonder whether there might not be another explanation for at least Anna's name. The Greek name Anna (Άννα) is, of course, a transliteration of the Hebrew Hannah (חנה). If Hannah's song is the "mother" of Mary's song, might this explain the identification of Mary's biological mother as Hannah? I will defer to the biblical scholars here, but it seems plausible to this admitted amateur.
Last summer I wrote a metrical versification of Hannah's song to be sung to the Genevan tune for Psalm 98. The music can be found here. Back in 1987 I versified Mary's Magnificat and composed an original melody, SOUTH BEND, named for where I was living at the time. The music can be found here and a descant for the 4th verse here.
"My soul magnifies the Lord, and my spirit rejoices in God my Saviour."