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? Proofs?
Tizku Lemitzvos
Yosey
I have always assumed that they had specific tunes for the Shir Shel Yom. I also heard about a certain song that was purported to have been sung by the Levi'im in the Beis-Hamikdash, which bears this out.
And as for the term 'Omrim' is concerned, maybe it is used with regard to the Shir Shel Yom, because the Ikar was the words, which the tunes merely embellished and rendered more meaningful. If I'm not mistaken, the same term 'Omrim' is used with regard to the Mal'achim.
On the other hand, Tehilim does have Trop, which suggests that this is how it was sung. Though it is highly likely that the Trop of Tehilim is not the same as that of Chumash (just as the Trop of Navi is different than that of Megilas Esther, and that of Megilas Esther than that of the other Megilos). Perhaps it was more tuneful, in which case the two possibilities will merge into one.
Kol Tuv,
R. Eliezer Chrysler