I'm no theorist, but two things come to mind. The concept of "major/minor" is a fairly western one. It really doesn't exist in most world music--which happens to be monophonic (one melody, little or no harmony). The descending minor third and the major second in the sequence that you speak of is described by Kodaly as the "universal baby chant" and used as his basis for elementary classroom music education.
And I for one would love to abandon the tempered scale, The technicalities become so much more interesting.