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If you're interested, this blog did a recent post that covers the first question with regard to major chords http://metinmediamath.wordpress.com/2014/03/16/overtones-what-they-are-and-how-to-compute-them/ As for the second question, I would hazard a guess that the circle of fifths could shed some light. However, these things are subjective, I happen to quite like the progression I -> III!
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