You may be interested in the work of Suzanne Haik-Vantoura, whose work deciphering the te-amim of the Masoretic Texts is noteworthy (no pun intended).
Beginning with the premise that the marks are primarily musical and secondarily exegetical, she developed a key that when consistently applied produces beautiful liturgical music.
She believes the school in Tiberius preserved the "true tradition." In otherwords, she believes the Masoretic texts contain the original melodies of David and other psalmists.
I can't go that far with her, however, there's no doubt in my mind she has decoded an ancient notation. You can sample some of the melodies of the Psalms here:
http://www.cgmusic.com/library/musicofthebible.htm