An acoustical diffusion manifold transducer system comprising: an acoustic loudspeaker driver; a manifold (101, 201) having: a manifold inlet to which the acoustic loudspeaker driver is coupled, a surface defining a manifold outlet (104, 307), and a plurality of acoustical pathways (302, 303, 304, 305) that each have an inlet end and an outlet end, the manifold being configured such that the inlet ends of the acoustical pathways are in communication with the manifold inlet, and the outlet ends of the acoustical pathways are arranged at the manifold outlet sequentially in an N x 1 array, where: N is the number of acoustical pathways, is an odd prime number, and is greater than or equal to 5, wherein the length of each acoustical pathway is determined by an individual element solution to a Quadratic Residue Sequence that is multiplied by a pre-determined unit length, plus a pre-determined constant; and wherein the individual element solutions to the Quadratic Residue Sequence are governed by the relationship: S n = n 2 rem N, for 0 < = n < = N − 1, in which n is the sequence element number, and S n is the individual element solution to the Quadratic Residue Sequence, characterized in that: the outlet ends of the acoustical pathways having the longest lengths are located inwardly of the outermost outlet ends in the N x 1 array at the manifold outlet, and in that the outlet end of the acoustical pathway having the shortest length is located centrally within the N x 1 array at the manifold outlet. an acoustic loudspeaker driver; a manifold (101, 201) having: a manifold inlet to which the acoustic loudspeaker driver is coupled, a surface defining a manifold outlet (104, 307), and a plurality of acoustical pathways (302, 303, 304, 305) that each have an inlet end and an outlet end, the manifold being configured such that the inlet ends of the acoustical pathways are in communication with the manifold inlet, and the outlet ends of the acoustical pathways are arranged at the manifold outlet sequentially in an N x 1 array, where: N is the number of acoustical pathways, is an odd prime number, and is greater than or equal to 5, wherein the length of each acoustical pathway is determined by an individual element solution to a Quadratic Residue Sequence that is multiplied by a pre-determined unit length, plus a pre-determined constant; and wherein the individual element solutions to the Quadratic Residue Sequence are governed by the relationship: S n = n 2 rem N, for 0 < = n < = N − 1, in which n is the sequence element number, and S n is the individual element solution to the Quadratic Residue Sequence, a manifold inlet to which the acoustic loudspeaker driver is coupled, a surface defining a manifold outlet (104, 307), and a plurality of acoustical pathways (302, 303, 304, 305) that each have an inlet end and an outlet end, the manifold being configured such that the inlet ends of the acoustical pathways are in communication with the manifold inlet, and the outlet ends of the acoustical pathways are arranged at the manifold outlet sequentially in an N x 1 array, where: N is the number of acoustical pathways, is an odd prime number, and is greater than or equal to 5, wherein the length of each acoustical pathway is determined by an individual element solution to a Quadratic Residue Sequence that is multiplied by a pre-determined unit length, plus a pre-determined constant; and wherein the individual element solutions to the Quadratic Residue Sequence are governed by the relationship: S n = n 2 rem N, for 0 < = n < = N − 1, in which n is the sequence element number, and S n is the individual element solution to the Quadratic Residue Sequence, characterized in that: the outlet ends of the acoustical pathways having the longest lengths are located inwardly of the outermost outlet ends in the N x 1 array at the manifold outlet, and in that the outlet end of the acoustical pathway having the shortest length is located centrally within the N x 1 array at the manifold outlet. the outlet ends of the acoustical pathways having the longest lengths are located inwardly of the outermost outlet ends in the N x 1 array at the manifold outlet, and in that the outlet end of the acoustical pathway having the shortest length is located centrally within the N x 1 array at the manifold outlet.