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
Septimal major third 3:2 / 9:7 = 7:6 ). Similarly, the septimal major third is the interval between the third and the fifth of the septimal minor triad. In the early meantone era the interval made its appearance as the alternative major third in remote keys, under the name diminished fourth. Tunings of the meantone fifth in the neighborhood of Zarlino's -comma meantone will give four septimal thirds among the twelve major thirds of the tuning; this entails that three septimal major triads appear along with one chord containing a septimal major third with an ordinary minor third above it, making up a