Art is an entirely useless thing. And it should be so. Sure, music and art are a form of language that can be used to convey ideas, concepts and emotions, it is not as quantifiable as say written words with laws of grammar and technical drawings.
The listener is free to be moved or not moved and interpret art at his own will according to his intelligence or internal biases. One could just as easily ask is it subjective or objective that there are good listeners of music.
Therefore, I would say that music and art is entirely subjective.
Those who think it is objective are projecting their own or someone elses point of view upon it and measuring it according to their own criteria. That is a delusion in itself. For if art could be measured it would cease to be useless and you could reliably communicate with it.
Yet the world NEEDs to have plenty of useless art in it to keep our imaginations stirring in strange and unpredictable ways. Without our imagination, all our knowledge is completely useless and we cannot advance as a species.
Art is a form of communication, so I would argue that it is not useless.
In Hegel's Philosophy of History, he argues that the course of human history is in fact objective in that there is a teleological endpoint. Our individual subjective experiences are insignificant because they are miniscule in the context of the entirety of human history and evolution, and will not affect the endpoint. In his philosophy, art is essential because it is often the vehicle through which we can detect future changes to society - in other words, it is a leading indicator, not a lagging indicator.
The postmodernist movement sharply critiqued that kind of objective viewpoint - but it is still very much present in society today. All major religions have objective viewpoints.
In other words - if the majority of the world's population can hold an objective viewpoint with respect to religion, why could there not be an objective 'good' in the form of music? Plato argued that soldiers should only be allowed to listen to music in Dorian or Phrygian. He believed the harmonic and tonal characteristics would make them stronger.
Complex music has been proven to disrupt brain patterns the first time they are encountered largely because the brain has a certain expectation based on learned knowledge, and when that expectation is not met, the brain must use a lot more power to understand and make sense of the new complexities. Upon repeated listens (and then other similar complex music), the brain no longer struggles because it has adjusted its expectations.
Music also has (or can have) an enormous effect on mood - you wouldn't play metal in a prison if you wanted to calm prisoners down. You wouldn't play dance music at a funeral because it disrupts deep thought and reflection. Loud and very chaotic music has been used in torture. Would this hold true at any point in history? I'm not sure - there is a ton of social conditioning that goes into what we do every day, so it's possible that it would not hold up. But, there might also be something in the way the brain is wired and interprets melody and tonal characteristics that remains constant, regardless of the level of brain development, historical placement, ethnicity, culture, etc.
So on some of these points, it might be possible to argue that there is an objectivity to music, and that in fact, you could label some music 'good' and some music 'bad', but I think you would need to add a specific purpose.