Symphonic bells of ‘‘fantastic’’ proportion

2014

Dated 1287, the bell from the church of S. Pedro de Coruche is the oldest recognized bell in Portugal. Unfortunately, being fragmented and incomplete, its original sound cannot be heard anymore. This paper deals with the dynamical analysis of this 13 th century bell, as well as a reconstruction of the possible original bell response through physical modeling techniques. As a first step, based on the measured bell shape and material properties of bell bronze, numerical modal computations through the Finite Elements Method (FEM) where used to predict the relevant dynamic properties of the bell and to access the tuning frequencies of its partials, for an adequate number of modes. Then, using the modal parameters estimated through the FEM analysis, modal vibration synthesis techniques have been applied in order to simulate the dynamical bell responses to percussive excitations. Although the sound radiation is not addressed in the present analysis, realistic "sounds" can be produced based on the model vibratory responses. Several possible dynamical responses were computed, for different assumptions concerning the unknown bell clapper mass, shape and contact properties, as well as the strike location. From the musicological point of view, the bell of interest to the present study is located in a time period of transition between the use of two different bell shape profiles, which would lead to major musical consequences. In this context, the frequency ratios found for the first modes (partials) of this bell are of historical significance-as is, in the same vein, the greater or lesser musical attractiveness of the simulated response sounds.

Heritage Science

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 model...

The Journal of the Acoustical Society of America, 2013

In this paper, the analysis and synthesis results from a complete set of Chinese chime-bells (also known as Chinese two tone bells) are presented. Consisting of 65 bells with different sizes and tones, Marquis Yi of Zeng's set is an ancient musical instrument with fascinating acoustical features but scarcely appears in current music performances for being huge and inaccessible. To preserve this cultural legacy in digital form, sounds of a complete set of replicated Marquis Yi of Zeng's chime-bells were recorded and analyzed, and the pitch discrimination of fundamental frequencies between this replica and the original set has been evaluated. Sound synthesis models of chime-bells were constructed using multiple inharmonic digital waveguides, creating chime-bell like sounds. Quality of synthetic sounds was evaluated using both objective and subjective measures. Objectively, the similarity between synthetic and recorded sounds was compared in both the spectral and the temporal domains. The subjective measure was achieved through listening tests. Results show that sounds from different bells on the rack could be successfully generated from the proposed models, leading toward the realization of virtual chime-bell set in the future.

International Journal of Impact Engineering, 2015

In this paper we investigate dynamics of church bells, characterize their most common working regimes and investigate how to obtain them. To simulate the behavior of the yoke-bell-clapper system we use experimentally validated hybrid dynamical model developed basing on the detailed measurements of the biggest bell in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. We introduce two parameters that describes the yoke design and the propulsion mechanism and analyze their influence on the systems' dynamics. We develop two-parameter diagrams that allow to asses conditions that ensures proper and smooth operation of the bell. Similar charts can be calculated for any existing or non-existing bell and used when designing its mounting and propulsion. Moreover, we propose simple and universal launching procedure that allows to decrease the time that is needed to reach given attractor. Presented results are robust and indicate methods to increase the chance that the instrument will operate properly and reliably regardless of changes in working conditions.

Applied Sciences

Study of swinging clapper bells involves aspects encompassing sound and acoustic engineering, mechanical engineering, and structural engineering. From the musical point of view, clapper bells are directly played idiophone instruments, where the playing device, the clapper, although directly excited, is not explicitly controlled by the bell ringer. The achievement of a clear and optimal sound mainly depends on the acoustic characteristics of the bell and on the regularity of the clapper strokes, which is not only governed by the ringing style and the relevant parameters of clapper and bell but also by the real time corrections to the excitation introduced by trained bell ringers. In fact, despite centuries of experience allowed to optimize the bell performances, standardizing proportions and mounting arrangements, effective sound control requires some fine tuning of the forcing function. Another crucial topic, especially in view of assessing existing structures, regards the evaluatio...

International Journal of Impact Engineering, 2015

In this paper we present a hybrid model of church bell. The dynamical system of yoke-bell-clapper is nonlinear and discontinuous. We use the Lagrange equations of the second type to derive formulas that describe the system's motion. The energy between the bell and the clapper is transmitted via impacts, here modeled using a coecient of energy restitution. The values of the system's parameters have been determined basing on the measurements of the biggest bell The Heart of Lodz in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. Using the same bell we also validate the model by comparing the results of numerical simulations with experimental data.

The Journal of the Acoustical Society of America, 2008

1997

The Western bell has a 1000-year history of development as a musical instrument. The technical improvements in that time have been a mixture of seren– dipidity and science. An historical overview is given in this presentation, and some current problems and research mentioned. About the year 1000 cast bronze bells for use in belltowers began a development from the cylindrical shape borrowed from the East. From then to the present day seven important stages can be seen: ,(1)movement to a new (flared) shape which would give an identifiablemusical note -– by about year 1200; (2) appreciation of the design laws for bells in a musical scale (without resort to mechanical tuning)—by 1500; (3) understanding the vibrational complexities of the bells, leading to the possibility of harmonic tuning –– before 1700; (4) description (without understanding)of the modal content of the bell -by 1950; (5) revelation of the physical significance of the vibrational modes -by 1980; (6) building on the pas...

Journal of The Acoustical Society of America, 1983

The time-domain description of musical and other nonlinear oscillators complements the more commonly used frequency-domain description, and is advantageous for some purposes. It is especially advantageous when studying large-amplitude oscillations, for which nonlinearity may be severe. It gives direct insight into the physical reasons for the variation of waveform as playing conditions vary, and into certain phenomena which may seem counter-intuitive from the frequency-domain viewpoint, such as the musically undesirable flattening in the pitch of a bowed string when the bow is pressed too hard onto the string. It is easy to set up efficient time-domain simulations on a small computer, a fact that has been surprisingly little exploited in musical acoustics. The simplest relevant model is described here. It demonstrates some of the basic nonlinear behavior of the clarinet, violin, and flute families with very little programming effort.

JOURNAL OF PURE & APPLIED SCIENCES, 2024

The Fourier Series is considered one of the most important computational tools in mathematics and has widespread usage, specifically in music. The present paper aims at presenting Fourier Series in the context with sound analysis and synthesis. Since Fourier Series decomposes complicated waves into simple sinusoids, that improves our approach to harmonics and thereby the synthesis of sounds. The present discussion shows how this mathematical method offers to musicians and sound engineers new approaches as to how to generate and evaluate musical tones and sounds. Analyzing various examples, this paper will help to explain the relationship between mathematics and music, with a focus on the role of Fourier analysis in modern music production and its role in creating and designing the new exceptional sound.