Time varying media recently emerged as promising candidates to fulfill the dream of controlling the wave frequency without nonlinear effects. However, frequency conversion remains limited by the dynamics of the variations of the propagation properties. Here we propose a new concept of space-time cascade to achieve arbitrary large frequency shifts by iterated elementary transformation steps. These steps use an intermediate medium in which wave packets enter and exit through noncommutative space and time interfaces. This concept avoids high frequency or subwavelength demanding metamaterials. Upward and downward frequency conversions are performed. The transmitted energy yield is given by the frequency ratio, regardless of impedence mismatch. We implement this concept with water waves controlled by electrostriction and achieve frequency conversion over 4 octaves.