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This is a work in progress...
How aimless? How's this:
17 39 08 30 52 21 43 12 34 03 25
47 16 38 07 29 51 20 42 11 33 02
24 46 15 37 06 28 50 19 41 10 32
Those are the keys in which it wanders, spending only a measure in each. In 53 tone equal temperament, those are all 22 steps, or a perfect fourth apart. You can see we get close to the start, when it hits 16, then 38, which is like the first two chords 17 & 39. After a short while the repetitive chord changes just leave one with a feeling of never ending change. Not a pleasant feeling in my mind.