A similar question has already been asked. Have a look at:

http://www.askphilosophers.org/question/729

It seems to me that 'music' and 'noise' are being used in two different senses here. First, an 'objective' sense, as types of things whose properties can be enumerated. Second, as values: 'I like this', 'this is important', 'this is what music should be' and so forth. Here as in so many cases, distinguishing these senses and keeping them separate is very difficult, perhaps impossible.

It may be possible to give a fully objective description of some types of noise (e.g. 'white noise') but otherwise the term is applied in a value-laden fashion: what is noise to one person is joyfully raucous to another; even to the same person at a different time. Moreover, music is not a thing, it is a cultural production and a cultural reception, and any definition will have to rely upon cultural norms and histories. So, a piece of contemporary music that appears as noise at first may 'resolve' itself into something meaningful for me simply because I become aware of the cultural traditions within which it rests.

The problem you identify is a real one, but it is not a problem of definitions or establishing a divide. Rather, the issue is understanding the processes of cultural production and both cultural and individual reception.