The pasuk says למנצח על השמינית מזמור לדוד - To the conductor with melodies on the sheminith, a song of David.
Rashi explains that there is an instrument called "שמינית" that was played with this perek.
But why שמינית - 8???
7 is nature [7 days of the week etc.] while 8 is above nature. Milah is on the 8th day because it places us above nature. This שמינית instrument is about taking all of the seven of nature and elevating it to the supernatural.