From Philharmonic Hall to number theory: The way to more diffusion

Abstract

In September 1962, in the presence of Mrs. Jacqueline Kennedy, Philharmonic Hall in New York was inaugurated—the first building of the new Lincoln Center for the Performing Arts. To address the soon-apparent acoustic problems, Lincoln Center turned to Bell Laboratories for help, and I was asked to join a ‘‘committee of experts,’’ chaired by Vern O. Knudsen of UCLA. My work on Philharmonic Hall, assisted by B.S. Atal, G.M. Sessler, and J.E. West, and later, after my move to Göttingen, by my students D. Gottlob, F.K. Siebrasse, and U. Eysholdt, indicated a need for energetic early lateral sound. It was clear that better lateral diffusion could improve the acoustic quality and the feeling of ‘‘envelopment’’ by the sound. Knowing some Galois field mathematics, I lucked upon the design of diffusors which scattered incident waves into broad lateral patterns—but only for a single musical octave. Then, in 1977, during a celebration of the 200th anniversary of Gauss’s birth, I heard a talk by André Weil on Gauss sums and quadratic residues and, in a flash, it became clear to me that diffusors based on quadratic residues were the answer to broadly scattering waves comprising many musical octaves.