Normally, a system (like a quartz) which is driven by an external frequency, oscillates at the same or a multiple of the driving frequency. This is because the

Normally, a system (like a quartz) which is driven by an external frequency, oscillates at the same or a multiple of the driving frequency. This is because the external conditions are symmetric under a time translation (i.e. a delay) by the period duration. This symmetry is normally preserved by the system. A time crystal, however, will oscillate with a fraction (or rational multiple) of the driving frequency. This breaks the original time translation symmetry.