Another philosophical attempt: There is nothing in this world that we can be 100% sure of. Bertrand Russell showed us so (even though he was not the first to think of that, but the one who developed and popularized this thought) and as far as I know, no one has proven him wrong.
Thus we can neither answer this question with a "yes" nor with a "no".
BUT, we can and must work with probabilities. And I think because of various highly plausible indications, that, no, there is most likely no objective measure of quality for music. Even if you take a non-musician and let him beat your bass, and 100 people agree that the results are awful, somewhere, someone might like it; possibly me.
Is this argument settled now? No, we approach it differently by altering our definition of the word "objective". If by "objective" we mean "that which a selected group of people or their vast majority agrees on", then the answer can be a yes. For example: If 90% of all musicians say Britney Spears sucks, then that is objective by this definition.
Of course, this definition bears problems, but it is pretty much the definition we use most often in everyday contexts.
Thus it is, as everything else, a matter of definition.