Does bad music exist?

Does bad music exist? This questions needs to be clarified. It is certainly true that a given piece of music (or even whole genres of music) might not be interesting to you. But that doesn't make the music bad. It just means that the music lacks appeal to you, and this is NOT what I mean by "bad music". Bad music is music that is actually wrong in that it has incorrect notes, chords, rhythms, etc. It is true that individual styles of music have their own rules, and violating these rules leads to music that is regarded as bad by purists of the style. But breaking the rules can also lead to innovation, even creating a new style of music. So the bad music may not be bad after all. Some say that the innovators can get away with breaking the rules because they know they are breaking the rules. However, ultimately this makes no sense because it makes no difference to the final product whether or not a broken rule was deliberate.

The point is that regardless of what any given piece of music sounds like, there will always be someone who likes it. And if someone likes a given piece of music, then it deserves to exist even if no one else likes it. If this is the case, then maybe bad music doesn't exist. What to you think?