In reply to:

In my experience, really captivating beauty arises from symmetry (including periodicity) which is just slightly broken.

Similarly, to me the most beautiful tunes combine harmony and dissonance. For example, at times the note in the melody is in harmony with the underlying bass or chords, and at other times is off a little, like a D note played over a C major chord. (Not sure if I explained that properly...oh well.)