From bell sound to architectural function: Quantitative vibroacoustic metrology applied to the Norman bell tower of Salerno Cathedral (Italy)

Abstract

This study formulates and assesses a measurement–model workflow for physical metrology applied to architectural heritage, using the Norman bell tower of Salerno Cathedral as a case study. Dominant spectral components of the 13th-century bell were identified through individually calibrated acoustic measurements, while a finite-element model provided the reference modal frequencies of the belfry-cell air volume. The two datasets were compared using perceptual frequency proximity based on the Equivalent Rectangular Bandwidth and restricted harmonic relations expressed in cents. Then, a Monte Carlo null model was used to determine whether the observed correspondence exceeded random spectral alignment. Sensitivity analyses addressed the effects of radiating aperture conditions and temperature-dependent variations in the speed of sound. Although the open-boundary model introduced mode-dependent frequency shifts, leakage, and modal reorganization, these effects did not materially alter the final interpretation. The study contributes an inspectable and transferable metrological chain linking measured quantities, model-derived outputs, influence factors, and statistical decision criteria for investigating sonic functions across the material and intangible dimensions of architectural heritage.