Spider Robinson explored this in his 1983 story, Melancholy Elephants:

http://www.spiderrobinson.com/melancholyelephants.html

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There are eighty-eight notes. One hundred and seventy-six, if your ear is good enough to pick out quarter tones. Add in rests and so forth, different time signatures. Pick a figure for maximum number of notes a melody can contain. I do not know the figure for the maximum possible number of melodies--too many variables--but I am sure it is quite high.

"I am certain that is not infinity.

"For one thing, a great many of those possible arrays of eighty-eight notes will not be perceived as music, as melody, by the human ear. Perhaps more than half. They will not be hummable, whistleable, listenable--some will be actively unpleasant to hear. Another large fraction will be so similar to each other as to be effectively identical: if you change three notes of the Moonlight Sonata, you have not created something new.

I do not know the figure for the maximum number of discretely appreciable melodies, and again I'm certain it is quite high, and again I am certain that it is not infinity

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Do read it It's scary and prescient.