Delay Lengths

• FDN delay-line lengths are generally chosen to be mutually prime, which maximizes the psuedo-random behavior of the system.

• A rough guide to the average delay-line length is the “mean free path” of the desired reverberant environment, which is defined as the average distance a ray of sound travels before it encounters a reflecting obstacle.

• The mean free path can be approximated as $\bar{d} = 4 V / S$, where $V$ is the total volume and $S$ is the total surface area enclosing the space.

• The desired modal density can guide the determination of the total sum of the delay line lengths $M$. Schroeder suggests a modal density of 0.15 modes per Hz for a 1 second $t_{60}$. This can be generalized to $M \geq 0.15 t_{60} f_s$.