Physical modelling techniques for the dynamical characterization and sound synthesis of historical bells

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Capable of maintaining characteristics practically intact over the centuries, bells are musical instruments able to provide important and unique data for the study of musicology and archaeology essential to understand past manufacturing and tuning techniques. In this research we present a multidisciplinary approach based on both direct and reverse engineering processes for the dynamical characterization and sound synthesis of historical bells which proven particularly useful to extract and preserve important information for Cultural Heritage. It allows the assessment of the bell’s 3D morphology, sound properties and casting and tuning techniques over time. The accuracy and usefulness of the developed techniques are illustrated for three historical bells, including the oldest recognized bell in Portugal, dated 1287, and two eighteenth century bells from the Mafra National Palace carillons (Portugal). The proposed approach combines non-invasive up-to-date imaging technology with modelling and computational techniques from vibration analysis, and can be summarized in the following steps: (1) For the diagnosis of existing bells, a precise assessment of the bell geometry is achieved through 3D scanning technologies, used for the field measurement and reconstruction of a 3D geometry model of each bell; (2) To access the modal properties of the bells, for any given (at the design stage) or measured geometry, a finite element model is built to compute the significant frequencies of the bell partials, and the corresponding modal masses and modeshapes. In the case of existing bells, comparison of the computed modes with those obtained from vibrational data, through experimental modal identification, enables the validation (or otherwise correction) of the finite element model; (3) Using the computed or experimentally identified modes, time-domain dynamical responses can be synthesized for any conceivable bell, providing realistic sounds for any given clapper and impact location. Although this study primarily aimed to better understand the morphology and sounds of historical bells to inform their conservation/preservation, this technique can be also applied to modern instruments, either existing or at design stages. To a larger extent, it presents strong potential for applications in the bell industry, namely for restoration and re-tuning, as well as in virtual museology.
Original languageEnglish
Article number157
Pages (from-to)1-17
Number of pages17
JournalHeritage Science
Issue number1
Publication statusPublished - Dec 2021


  • 3D scanning
  • Bells
  • Cultural heritage
  • Dynamical characterization
  • Music acoustics
  • Physical based modeling
  • Reverse engineering
  • Sound synthesis


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