One-third hypothesis the cohesiveness of the group that is one-third. According to the binomial coefficient a group of size r occurs in a population of size n in formula_1 ways. Because each group of size r can dissolve in "2" subgroups, the total number of ways all groups of size r can emerge and dissolve equals "3", in keeping with the summation: formula_2 Said otherwise, large groups close to two-thirds of the population will be more likely than any other groups to dissolve into splinter groups. A corollary of this consideration is that much smaller groups will be the ones most likely
Ladder of thirds Ladder of thirds A ladder of thirds (coined by van der Merwe 1989, adapted from Curt Sachs) is similar to the circle of fifths, though a ladder of thirds differs in being composed of thirds, major or minor, and may or may not circle back to its starting note and thus may or may not be an interval cycle. Triadic chords may be considered as part of a ladder of thirds. It is a modal frame found in Blues and British folk music. Though a pentatonic type, the melodies come "into being through piling up thirds below and/or above a