The dance and the music are both in three. The waltz is an old dance, and has both old world and new world styles that can be mixed at will. In old world, you turn slightly counter-clockwise with each group of three steps, kind of a mix of diagonal and turning motions. New world, you just move down the line of dance. An old world way to move down a line of dance is the Vienese Cross, a complex manuver in which one partner revolves 180 degrees around the other, and then the other revolves around the first... repeat. Stunningly beautiful when executed with grace, a waltz can flow like water.