Sound Scattering by Gothic Piers and Columns of the Cathédrale Notre-Dame de Paris

Abstract

Although the acoustics of Gothic cathedrals are of interest to researchers, the acoustic impact of their many columns is often neglected. The construction of the Cathédrale Notre-Dame de Paris spanned several centuries, including a wide variety of architectonic elements. This study investigates the sound scattering of a selection of seven designs that are relevant to this building as well as to the architectural style itself. These were measured on scale models (1:8.5 to 1:12), using a subtraction method, for receivers at about 3 m at full scale and a far-field source. They were also numerically simulated using a finite-difference time-domain method in two-dimensional space with an incident plane wave. The method integrates a finite volume framework to employ an unstructured mesh conforming to the complex geometries of interest. The two methods are in strong agreement for the considered configurations. Relative levels to the direct sound of backscattered reflections between −10 dB and 2 dB and between −15 dB and −6 dB in the transverse directions were estimated for the dimensions considered, relative to reported reflection audibility thresholds. Cross-sections with smaller scale geometrical elements on their perimeter can produce diffuse reflections similar to those of surface diffusers.

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“…That said, for a large portion of source/receiver positions and for the high-mounted conditions, the majority of low-order reflections arrive later than 50 ms and would reduce C 50 . In Notre-Dame and other similar cathedrals, most early reflections in the nave come from the columns and piers [16]. Naturally this preliminary analysis is overly simplified as it does not include specular reflections or contributions from the floor and columns.…”