Thinking is great, so lets do some more.
Bardsley, the paradox with alternating 1's and 2's is actually an (alternating) divergent row, meaning that whenthe variable tends to infinity,the row does not have an unique value( unlike 1/n or (n-1)/n).
A finite set of finite subsets being finite would be applicable if we were talking about combinations of defined, fretted notes but even then it would take a lot of people to work for all of their lives to work out all the combinations out (even if you leave out the impossible-to-fret ones).
when I bend to a 3rd, 5th, and in other occasions, I rarely bend dead-correct. I prefer trying to hit the in-between notes and make my guitar sound like a spoilt cat.
However, as I was told by a violin teacher once, although there are a lot of similarities between music and mathematics, there is one great difference : maths is exact (solve a problem as many times as you want and you should get the same result) and music is spiritual. Otherwise, we'd have a whole lot of math professors creating perfect songs. which contradicts human imperfection as opposed to nature's perfection.
Aaah I'm getting brain cramps from thinking too hard!

P.S. Linear Algebra, Mathematic Analysis, Numeric Algebra, Discrete and Concrete Math, Combinatorics, Set Theory, Regular Differential Equations and then some. And I'm still not completely crazy. At least my imaginary friend says so.