In late Medieval and early Renaissance dance music, a transition was sometimes made in 6/8 time between two groups of 3 beats to 3 groups of 2 beats. In other words from a group of (2/8 + 2/8 + 2/8) to (3/8 + 3/8) in each measure.

This effect had a specific name associated with it. Can anyone tell me what the name was for that very popular change in meter during that age in music?

Thanks!