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75th comments on Harry Potter and the Methods of Rationality discussion thread, part 15, chapter 84 - Less Wrong
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I'm not sure how much music you know, and I'm not sure how much music Mathematica knows, so if this is all Greek or too hard, disregard it all:
Try different diatonic modes and different scales altogether. Switch from Major to Phrygian in the middle of a phrase. Switch to different sets of keys depending on whether consecutive tones are ascending or descending. Use a lot of Locrian mode, it is generally wrong-sounding. Try mapping diatonic scale degrees to octatonic ones somehow, and switch between the two octatonic scales at random. See if you can produce a portamento between two notes, and use it a lot when two notes are separated by only a semitone.
Additionally, switch tunings at random. This would be extremely difficult, but I'd imagine the disorientation caused would be related to how difficult it is. Switch from 12-ET to Pythagorean to Arabic to some obscure Baroque tuning, and base them all on different pitch centres.
When what you're listening to is purely melodic (like humming) I think such differences would either be unnoticeable or indistinguishable from just humming out of tune, to all but the most expert listeners.
A whole Pythagorean comma -- i.e., all the out-of-tune-ness you can get from Pythagorean tuning, crammed into a single interval -- is only about a quarter of a semitone. A quarter-comma meantone "wolf fifth" is actually even worse than this, but it's still only about 1/3 of a semitone.
If you have a computer with Python on it, you could grab the code from my discussion elsewhere in the thread with thescoundrel and experiment; I think you'll find that the sort of tuning-switching you describe would be altogether too subtle to be very effective as psychological warfare. [EDITED to add: in particular, I found that to my ears a quarter-tone error is quite often obtrusively unpleasant but a quarter-semitone is generally no worse than "a bit out of tune".]
Hmm. You're probably right. I've experimented with different tunings but I didn't play anything purely melodic. The effect is probably a lot more apparent when you're dealing with intervals rather than just pitches.
That said, changing the central pitch that the temperament is based around makes the differences bigger again; but that's not too useful as a tool for actually creating this melody. I think it'd be noticeable for the arabic tuning system too; that's extremely different to Western temperaments.