I had a post prepared saying basically the same thing (Chazelle's algorithm work is awesome), but then I realized that bdr is, strictly speaking, correct: the number of combinations of notes you can play is a factorial of the number of notes, and factorials grow faster than exponential functions.
Of course, when you're writing an essay on the relationship of music and very simple math, I think it's forgivable to use "exponential" to mean "growing at or faster than an exponential rate". Using a more specific term like "factorial", "combinatorial", or "super-exponential" sounds pedantic and out-of-place.
I don't understand. If you have 300 notes, and 12 tones, the number of different melodies you can play is 12^300 (12 choices at each step). Why is it 300 factorial? You don't have 300 distinct entities to permute.
It was in the context of drawing the diagonals on the polygon, so I thought of quadratic growth. I guess everyone interpreted it differently, and the author is justified in using 'exponential' in an informal way.
