In a convergence, two or more distinct paths of dimensional attributes within the same hierarchy functionally determine the same dimensional attribute.

For instance,

Month®Quarter, Quarter®Semester, Semester®Year
®4-MonthsPeriod, 4-MonthsPeriod ®Year

and, for each month (e.g., July 2014), the corresponding year (2014) is the same whatever of the two roll-up paths are followed. Also note that 4-MonthsPeriod has a many-to-many relationship with both Quarter and Semester.