Séminaire n°42


Recent studies on assessing the tuning properties of historical carillons and on the identification of the original modes of bells subjected to constraining boundary conditions


Intervenant : José Antunes, Instituto Superior Técnico, Université de Lisbonne, Portugal

Contact : jantunes (at) ctn.ist.utl.pt

Date : 14/10/13

Abstract :
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 garantee the historical significance of these outstanding musical instruments, a detailed diagnosis of their current 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 modal testing experiments on the historical bells of the Mafra carillons.

For each carillon bell which plays a separate note of the instrument, tuning charts displaying the frequency relationships between its most important partials were obtained, as well as the modeshapes, decay times and beating frequencies between modal-doublets for every single musical partial of the bell. Furthermore, since carillon bells also must be tuned very accuratly one relative to the others, the important topic of estimating the reference pitch and musical temperament of the musical instrument was addressed by developing optimization techniques. After presenting the modal identification procedure and optimal strategies devised for this work, the feasability and interests of this instrumental approach are illustrated for the two Mafra carillons.

In the second part of this seminar we present some ongoing work motivated by the need to diagnose the tuning of large bells which, for security reasons, had to be provisionally supported using scaffolds at several locations of their rim. Since the presence of these additional supporting fixtures significantly changes the modes of the free structure, a direct estimation of the original bell vibrational properties from measurements is not feasible. However, the dynamical problem can be formulated in terms of structural modification techniques, from which the original modal frequencies of the bells, as well as the local mass and stiffness constraints, can in principle be recovered.

We present our identification strategy, developed for a 1D conceptual system and then considering a continuous 3D axisymmetric shell, accounting for dissipation phenomena. We start by briefly presenting the relevant dynamical formulations and then illustrate the technique on a simulated realistic axisymmetric shell. Our identification results highlight the robustness of the proposed technique. Interestingly for many pratical situations, the method is not prone to disturbing effects from modal identification nor truncation errors since it operates directly on the constrained transfer function measured at the constrained locations. Identification results based on simulated vibration data proved quite encouraging, and we are preparing experiments for testing the approach.