I thought the answer would rely on factorials (and it does), but after a little searching, combination seems to be the function I'm looking for...
C(1,12) + C(2,12) + C(3,12) + ... + C (12,12) = 4095
Does this fit?
That would include one- and two-tone combinations. How might I find the answer if only (three-and-greater)-tone scales are considered?
Also, this may be a question for programmers, how could I get a list of all those scales?