Szilard-Wigner distributions completely define physics and perceptions of concert halls

Abstract

At the second joint meeting of the Acoustical Society of Japan and the Acoustical Society of America in 1988 Yamasaki and Itoh presented time-frequency measurements of several concert halls employing Fourier transforms on autocorrelations, the same device Szilard and Wigner had developed for quantum theory in the 1920s. In 1995, it was proved that resonant scattering in the body of good halls generates power spectra resolved in time and frequency, correctly presenting musical information emanating from the orchestra. In poor halls specular reflections from hard flat surfaces generate echoes encoding architectural information about size, shape, features of the hall, necessarily detracting from desired musical information. Yamasaki and Itoh also demonstrated that “reverberation-time” tells essentially nothing about properties, physical or perceptual, of concert halls; impulse responses, from which Szilard-Wigner distributions are computed, tell much more. Careful study of these matters explains why after the era of Wallace Sabine, when “reverberation-time” became the sine qua non of concert hall theory, design of fine concert halls became impossible.