Objective estimation of the tuning features of historical carillons

The carillons of the Mafra National Palace are undergoing a restoration project. Together, the pair of carillons represent the largest surviving 18th century carillons in Europe. To guarantee the historical significance of these outstanding musical instruments, a detailed diagnosis of their current physical tuning state was achieved and results were analyzed with respect to historical, acoustical and musical concerns. In a first stage, we developed a suitable polyreference modal identification technique to infer the tuning status of bells from their modal parameters and we then systematically performed in-field modal testing experiments on a selection of historical bells of the Mafra carillons. For each carillon bell, tuning charts displaying the internal frequency relationships between its most important partials were obtained, as well as the mode shapes, decay times and beating frequencies between modal-doublets for every single musical partial of the bell. In a second part, since carillon bells also must be tuned very accurately one relative to the others in order to play in tune, the important topic of estimating the reference pitch and musical temperament of carillons was addressed by devising optimization techniques, here tentatively based on the actual modal frequencies of the bells. After presenting the modal identification procedure and optimal strategies developed for this work, the feasibility and interests of this instrumental approach are finally illustrated for the two carillons of Mafra.