> At this point, the part about the major third appearing in the harmonic series lacks explicatory power. I really don't think it does. Fifths (and their inve

> At this point, the part about the major third appearing in the harmonic series lacks explicatory power. I really don't think it does. Fifths (and their inverted form fourths) are the most consonant interval (ignoring octaves as the trivial case). Most cultures develop musical processes that involve fifths very early on in their history. Where do you go from fifths if you want to add another voice? If you have three notes and you want the most consonant result - you put a note that forms a third between the root and the fifth. Given a few basic assumptions ("prefer simpler integer ratios") there's no better way to play 3 non-octave notes together.