Simply put, continuity is what give sense to a sequence of sounds. So what do you do when the sequence of sounds is repeatedly interrupted either by leaps or by rests, that is, by silences?
It took me a while to realize that all leaps, like fractions, can be reduced to smaller intervals, especially if, in the course of the leap, two or more voices cross. As for rests, more often than not they indicate an interrupted duration, as the same note often occurs both before and following the rest. It is fascinating how hard it is for musicians to spot this, especially when the rest is longer than a measure.