A Schroeder reverberator builds artificial reverb from parallel comb filters and series allpass filters, with mutually-prime delay times

Schroeder’s classic artificial reverberator is a network of recirculating delay units: several comb filters in parallel generate a dense set of decaying echoes, feeding into a chain of allpass filters in series that multiply the echo density without changing the overall spectrum. A crucial design rule is that the unit delay times must be mutually prime (share no common divisor). If two delay lengths share a common factor, their echoes periodically coincide and reinforce, producing audible regular ‘bumps’ or a fluttery, non-smooth decay; choosing relatively-prime lengths pushes the first coincidence far into the future, yielding a smooth, natural tail. Delay time correlates with apparent room size (≈50 ms combs for a concert hall, ≈10 ms for a small tiled room); the allpass loop times are kept short (<100 ms) since their job is density, not duration. Later Schroeder designs add a multitap delay line up front to simulate the early reflections of a specific hall.

Examples

Comb delays of 799 and 997 samples (relatively prime) at 40 kHz keep echoes from coinciding for ~20 seconds — a smooth decay. Divisible delays like 800 and 1000 samples produce audible bumps every 200 ms.

Assessment

You wire two comb filters into a reverberator with delay lengths of 600 and 900 samples and hear periodic ‘bumps’ in the tail. Explain the cause and how re-choosing the delay lengths fixes it.