I don’t think there ever was a musical “common practice,” except maybe on a biological level. To assume that there was once a common way is to grant one approach a creative preeminence or even hegemony. In my opinion, the world of music is too wide for that.
If anything, we are closer to a common language now than we ever have been. Musicians from around the world are more aware than ever of the many ways of practice. Musicians are able to see, from the base of their own traditions, the areas of commonality they have with other approaches.
In the words of Toru Takemitsu, we’re all “confronting silence.” I think that, with respect for our differences, there is a growing awareness that all music comes from the same place.