What is the most statistically significant group of scales in the 12TET tuning system, based strictly on objective structural criteria alone? To find out, I sorted/analyzed all of the 4,5,6,7, and 8-tone scales listed in Larry Solomon's online pitch class set table ( http://music.theory.home.att.net/pcsets.htm ) by the structural criteria of scale span (the distance in semitones between the extreme end pitch classes in the scale, when that scale is in its most compact rotational ordering [prime form in pitch class set theory]), symmetry/asymmetry, and cardinality (how many pitch classes in the scale). The largest body of scales resulting were the 19 asymmetrical 7-tone scales which spanned a 9-semitone distance.
I will be posting MIDI files giving a systematic sounding out of each of these scales (including all 42 possible successive pitch class pair orderings). Then I will proceed down the heirarchy of other scales from the largest statistical groupings downward.