My shul's chazzan and I have a good relationship, B"H. I ask him nusach questions; he asks me (A Torah reader) Torah questions. So, I'm passing this on from him...
We both understand that the main purpose of the trope notation was for grammar and pronunciation. At some point in history, it was used for musical purposes.
Related questions - I'm assuming that the music was needed for public reading of Torah, Nevi'im and the 5 Megillot (i.e., not for individual reading. Although, there seem to be halachic references to requiring "music" if reading the 13 Middot individually. There may be a few other similar verses that have the same halacha.) Why does public reading need to be sung at all?
When did music become a part of the trope notation?
(Note: I am not referring to specific "modes" of the music used for trope such as the different music for Torah vs. Nevi'im, etc. or the different music used by various groups e.g. Ashkenazic vs. Yemenite. I am looking for a general answer as to when and why music was used by anyone.)