PRD Diffuser

A diffuser using primitive root sequences, offering asymmetric scattering and wider bandwidth than QRD designs.

A Primitive Root Diffuser (PRD) is based on number theory sequences using primitive roots modulo a prime. Like QRDs, PRDs scatter sound across multiple angles, but with distinct characteristics that make them preferable in certain applications.

The sequence is calculated as: s_k = g^k mod P, where g is a primitive root of prime P. This creates a different pattern of well depths than the quadratic residue sequence.

Key advantages of PRD over QRD: • Wider effective bandwidth: maintains better scattering properties away from design frequency • Asymmetric scattering: naturally directs more energy in one direction, useful when you want to favor a specific listening position • Alternative aesthetic pattern

PRDs are particularly valuable when broader frequency coverage is needed or when directional scattering is desired. They're commonly used in professional recording studios and performance venues.

Formula

s_k = g^k mod P

s_k = Sequence Value (integer)
g = Primitive Root (integer)
k = Position (0, 1, 2...)
P = Prime Number (prime)

Practical Example

PRD using prime P=7 with primitive root g=3

Sequence: 3^0=1, 3^1=3, 3^2=2, 3^3=6, 3^4=4, 3^5=5 (all mod 7)

Well depths follow: 1, 3, 2, 6, 4, 5 pattern, creating asymmetric scattering.

Standards: ISO 17497-2

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