Is music a language?

This is not a question which can be answered with a yes/no answer. Music is like a natural language in some respects and very much unlike one in others. Here are some suggested similarities and dissimilarities.

Music is like (a) language in that:

• It can be described through a system of rules that operate on a limited vocabulary
• It combines small building blocks into large components that are like words, phrases, sentences and text
• It is recursively expressive
• It has dual articulation in that smaller segments like scales are organized independently of large segments like movements
• It has phraseology and idioms
• It can cross-reference between compositions (texts)
• It can communicate emotion both segmentally (sequences of notes) and suprasegmentally (expression, emphasis, etc.)
• It has styles, genres and dialects
• It can be acquired and learned
• It is culturally conditioned

Music is NOT like (a) language in that:

• It cannot be used to directly communicate propositional meaning
• It has radically smaller set of building blocks and rules for their combination than language
• It does not have internal instruments of disambiguation
• It can only be universally acquired in the most rudimentary sense (i.e. everybody can hum a tune but very few people can play an instrument)
• There is much a greater difference between receptive and productive competence
• There is much greater variability in individuals' ability to produce music beyond the most trivial
• Much more of the production process requires cooperation among individuals
• It is much more limited in its dialogic potential (i.e. is most often used for a one way communication between few producers and more recipients or joint co-production of producer/recipients)

I'm sure many more similarities and differences could be identified and the ones above could be refined but hope this will give you some idea of what's involved.

Regarding Zipf's law: It is not really surprising it would be observed here because it mostly concerns distribution of units in a human generated corpus. But it does not follow that music is a language.

UPDATE: I've added parentheses around the indefinite articles in (a) language to reflect the comments that music is (dis)analogous to human language in general rather than in particular. I think we could have some more analogical fun here arguing both sides, but it would not be particularly fruitful.