If you load the sound into Audacity and view the spectrum (i.e. the FFT), you can get a moderately clear view of what's happening. For the first 14 seconds, pitches wander around randomly. Then they start sliding up in several jumps (interesting not a smooth progression), and end up at the final pitches (both lower and higher than the beginning) at around 19 seconds. You could probably extract the pitch tracks from the FFT if you want to re-create this sound. (I'd like to write up a detailed blog post on this, but don't have time, so I'll just leave a comment.)
A few other notes from the spectrum: the final chord is D major, with little F#. Between 14 and 19 seconds, the pitches take 5 jumps to their destination, at about .9 seconds per jump. (This is the part that sounds like rising tones before the final chord.) The jumps aren't synchronized, or else there would be a 67bpm rhythm to this part. The jumps aren't smooth, but an exponential decay, where they move rapidly at first, and then slow down. In the first part, the frequencies wander between about 130 and 260 Hz, with a noticeable peek at exactly 200 Hz. (And of course the harmonics.)
This will make more sense if you see the spectrum; I've put a picture of the spectrum at:
https://picasaweb.google.com/lh/photo/qbuyIVSC2Bsvgxg5HlSD4-...
Time is the X axis, and frequency is the Y axis. The lines that move in parallel are harmonic frequencies.
