I like that you mocked up your end-goal. That helps frame your discussion well. Your various little applets show your thinking and progression through your idea nicely. As for the work itself, this is hella ambitious, so I’d have been a little stunned if you met your mockup (and indeed, the fact that you haven’t is placated by the fact that I saw your mockup first, and I’m mentally associating it with your current state.) What you have come up with is quite complete, in terms of all of the functional components that prove you understand what the hell is going on and how to get to your mock-up, eventually. So cool project! 🙂 I like how you flattened the 3D visualization to 2D by using cones (a smart move, and one that still looked well.)
That said, if you want to understand FFT better to take this stuff further, read up on convolution first. FFT didn’t really *click* for me until I understood convolution as the base case for time-to-frequency transformations.
Oh, and for Gilbert Strang’s Linear Algebra class (18.06), check out OCW. http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/VideoLectures/
-SB

For FFT and convolutions, you might consider checking out the lecture notes/slides from our Computational Photography class: http://graphics.cs.cmu.edu/courses/15-463/2010_spring/463.html It deals mostly with 2D imaging but a lot of it is analogous to sound as well.

A good first immersion in sound and 3D — but you have a long way to go 🙂

Very courageous! I really want to do something similiar (creating 3D organic lifeforms that respond to music). I think something that would’ve helped you out is to first implement it in 2D and then move on…but I’m not sure how much of your algorithm would have to change due to it being 3D. I know Processing has this nifty class called PVector that can take either 2 or 3 coordinates (so it would be easy to apply the vectors to a 3D space). Good start and awesome idea!
-Amanda