Tempo also plays a big role. The soundtrack to Across the Universe includes slowed-down versions of “I want to hold your hand” and “Blackbird” which become almost unrecognizable thanks to a change of tempo (and instrumentation).
Rhythmic variations can dramatically change the perception of a piece. I used to play a choral piece by Poulenc (“O Magnum Mysterium”) with a swung jazz rhythm and it takes a very different character when you do that (see also countless jazz reinterpretations of Beatles and other pop songs).
One other piece of fun trivia: The rhythm of Hall of the Mountain King is exactly the same as the rhythm of Mary had a Little Lamb.
The number of pitch intervals is theoretically infinite, but as a practical matter if a pitch is close to another it's likely to be mistaken for it. If we suppose that the threshold for a note to be different enough in pitch to be distinguished as a different note in a certain context is, say, five cents, then that gives us about 240 unique notes per octave. That's a bit of an oversimplification, but anyways the point is there's more than 12 notes, and music is like a vast continent with a thriving metropolis in one small corner but the vast majority of the land has never had more than a cursory exploration, if that.
Here's a list of pitch intervals that were deemed interesting enough to be included in wikipedia:
It seems the message is: there’s a lot of room for creativity.
Any increase in the rhythm resolution will only further balloon that figure.
Agreeing with the message exponentially more.