Shiras Haleviim

Also from Yosey G on daf 35a:

The gemmorah says when Wine was poured on the Mizbayach that is when the Shiras Leviim was sung.

A friend asked me: Did the leviim have a special tune(S) for the Shirah or did they use the TROP? His son's Rebbe said they used Trop. He said the Pe-As Hashulchon writes that the Vilna Gaon studied Music so as better to understand the Shiras Haleviim, and if all they used was Trop, why did he have to learn music? (If they used Trop, the term used all over "Shir she-hoyu OMRIM" the song they SAID, would seem to make sense!)

Any insights? Proof?