Basically phonons in crystals can either be acoustic or optical according to my book. But then it stresses that a necessary condition for this to hold is that the crystal has more than atom per primitive basis. The optical modes are then when neighbouring atoms oscillate out of phase (i.e. no motion of the center of mass) and the acoustical mode is the exact opposite. But I don't understand why it is so crucial that the crystal has two or more atoms per primitive basis. Can't optical and acoustical modes happen between neighbouring atoms regardless of this?