If you attach the same number of documents in the same order to each song, then each band member can change Settings > General Settings > Defaults > Document to show their document by default. For example, if the drummer's document is always the third one in the list, then drummer can change that setting to 3.
If you have different numbers of documents for each song, then the closest you can get is to assign each document only to the desired users, and then each user would see his or her documents by default, but would not be able to view the documents for the other users.