| The general public's perception of the quality of graduate schools is irrelevant; but academics are very snooty about provenance, and they do the hiring. This is not to say that you can't be successful if you go to a school that is not recognized by academics in the field as a "top" program, but it will help. It is true, though, that if you have a strong speciality interest going in, it could be a good idea to include among your considerations the specific specialities of the professors in the program you are interested in.
Investing years in graduate school to wind up with few if any prospects is a dismal idea -- 5 years into the program it is downright depressing to think that you might not get a job, and that applies to students even at the "top" schools -- the rate of hiring is not so great and the openings are erratic.
I don't believe the same is true of undergraduate institutions for musicology; for example, there are plenty of graduate students now at Harvard (which lists its students and where they are from) who went to non-Ivy-level schools. |