Classifying MOS

Igs wrote:

"After years of consideration and trying (and failing) to find better alternatives, I've come to prefer the nL+ms approach."

It's a good approach, but to deal with the question of classifying MOS you need to be able to navigate the tree structure (related to the Stern-Brocot tree) which relates all the MOS with a given period. Given 5L2s, you know the period is an octave, since 2 and 5 are relatively prime. Then its parent is 2L3s, and its children are 7L5s and 5L7s. Now we can go on to grandchildren and great-grandchildren. The children of 7L5s, the 12-note meantone MOS, are 12L7s, the septimal meantone range, and 7L12s, the flattone range. The children of 5L7s are 12L5s and 5L12s. And so forth.