Are there a finite number of possible songs, or could humanity continue writing new songs forever (without repeats)?

For simplicity, let’s not consider the lyrics of a song i.e. “greensleeves” and “what child is this” are the same song.

Defining what constitutes a “song” is tricky, so please include your definition of “song” with your answer. With this question, I’m interested in songs that people would enjoy listening to (e.g. no danger music).