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Another idea would be to use something like Fraps or some other screen capture or screen casting utility to capture the playback of a visualizer in a music player of your choice. The exact combinations of software to use would likely depend on your choices in music player though. I know Fraps will only work with ones that are DirectX based.
A free alternative for After Effects is Jashaka. It runs on every plattform and has some decent features. While it wont have the comfort of after effects for creating such an effect its certainly possible. If you just don't want to spend all that much but still willing to pay a small price you can go for Apple Motion which costs 50$ and is a fairly powerful ...
According to the this article, iTunes has a music visualizer. You would still need to get screen recording software (unless you want to point a camera at your monitor!). I'm sure that someone has asked about free screen recording software on this forum somewhere.
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