Analysis and optimisation of the tuning of the twelfths for a clarinet resonator

Even if the tuning between the first and second register of a clarinet has been optimized by instrument makers, the lowest twelfths remain slightly too large (inharmonicity). In this article, we study the problem from two different points of view. First, we systematically review various physical reasons why this inharmonicity may take place, and the effect of different bore perturbations inserted in cylindrical instruments. Applications to a real clarinet resonator and comparisons with impedance measurements are then presented. A commonly accepted idea is that the register hole is the dominant cause for this inharmonicity: it is natural to expect that opening this hole will raise the resonance frequencies of the instrument, except for the note for which the hole is at the pressure node. We show that the real situation is actually more complicated because other effects, such as open holes or bore taper and bell, introduce resonance shifts that are comparable but with opposite sign, so that a relatively good overall compensation takes place. The origin of the observed inharmonicity in playing frequencies is therefore different. In a second part, we use an elementary model of the clarinet in order to isolate the effect of the register hole: a perfect cylindrical tube without closed holes. Optimization techniques are then used to calculate an optimum location for the register hole; the result turns out to be close to the location chosen by clarinet makers. Finally, attempts are made numerically to improve the situation by introducing small perturbations in the higher part of the cylindrical resonator, but no satisfactory improvement is obtained.Comment: 28 June 2004 (submitted to Applied Acoustics

Simulation of Single Reed Instruments Oscillations Based on Modal Decomposition of Bore and Reed Dynamics

This paper investigates the sound production in a system made of a bore coupled with a reed valve. Extending previous work (Debut, 2004), the input impedance of the bore is projected on the modes of the air column. The acoustic pressure is therefore calculated as the sum of modal components. The airrrflow blown into the bore is modulated by reed motion, assuming the reed to be a single degree of freedom oscillator. Calculation of self-sustained oscillations controlled by time-varying mouth pressure and player's embouchure parameter is performed using ODE solvers. Results emphasize the par ticipation of the whole set of components in the mode locking process. Another impor tant feature is the mutual innnfluence of reed and bore resonance during growing blowing pressure transients, oscillation threshold being altered by the reed natural frequency and the reed damping. Steady-state oscillations are also investigated and compared with results given by harmonic balance method and by digital sound synthesis

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

SFRH/BD/91435/2012 PTDC/ART-PER/32568/2017 UIDB/00472/2020 UIDP/00472/2020Capable 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.publishersversionpublishe

a numerical and experimental investigation on the subtle dynamics of Tibetan bowls

UID/EAT/00472/2013Tibetan bowls have been traditionally used for ceremonial or meditation purposes, but also in contemporary music-making. They are handcrafted and produce different tones depending on their shape, size, mass and their alloy composition. Most important is the sound producing technique by impacting and/or rubbing, as well as the excitation location, the hardness and friction characteristics of the excitation stick. In a previous paper, we developed a physically-based method for nonlinear time-domain simulation of Tibetan bowls. Our computational approach, based on a compact modal formulation, produces realistic dynamical responses. In the present paper we focus on an interesting feature of Tibetan bowls: in order to produce self-excited responses, the stick must rub the bowl against the external side of the rim, e.g. adially\pressing outwards the bowl center. Indeed, experimenting with many bowls showed that they do not sing when rubbed internally. We start documenting this claim with experimental results from representative bowls, and then exploit our computational model in order to reproduce the observed behavior qualitatively. Our results are in good agreement with experiments, thereby demonstrating that internally excited bowls are dissipative and hence unable to sing.publishersversionpublishe

Stability of Resonant Opto-Mechanical Oscillators

We theoretically study the frequency stability of an opto-mechanical radio frequency oscillator based on resonant interaction of two optical and one mechanical modes of the same optical microcavity. A generalized expression for the phase noise of the oscillator is derived using Langevin formalism and compared to the phase noise of existing electronic oscillators.Comment: 6 pages, 1 figur

Optimization of baffle configurations to prevent aeroacoustic instabilities in heat exchangers - preliminary experiments

It is well known that gas heat exchangers are prone to aeroacoustic instabilities, which often lead to severe noise levels, structural vibrations and fatigue. These are unacceptable, as they threaten the component integrity and expose the plant workers to excessive noise levels. Such phenomenon is due to a cooperative interplay between the Karman vortices generated by the cross-flow and the heat exchanger acoustical modes (mainly those transverse to the tube banks). Energy exchanges are then such that, for certain operating velocities, self-excitation of one or more acoustical modes arises. Actually, this problem is solved by placing rigid baffles inside the container, which modify the acoustic modal fields and eventually inhibit the instability. However, an effective location of such baffles is more or less difficult depending on the system complexity and on the range of flow velocities of interest. For realistic industrial components - using a restricted number of acoustical baffles - their optimal location is a challenging problem, as trial and error experimentation is often a costly and frustrating procedure. In this paper we improve a recently proposed strategy for the optimal location of a given number of baffles, in order to inhibit instability of the acoustical modes in a given frequency range. Our approach is based on a stochastic global optimization technique. Some preliminary experiments are also performed and compared with the simulation results

Single-Longitudinal-Mode Brillouin/Erbium Fiber Laser with High Linewidth-Reduction Ratio

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Modelling And Experiments

UIDB/00472/2020 UIDP/00472/2020In some mallet percussion instruments, such as vibraphones and marimbas, tubular acoustic resonators areplaced beneath the tuned bars to enhance sound radiation. Although widely used in commercial instruments, thevibroacoustic interaction between the tuned bars and theirresonators has not been studied extensively, and previousmodelling attempts regularly neglect important aspects ofthe coupling dynamics. This work develops on a previousstudy, where a minimal model for the coupling between asingle bar mode and a single resonator mode was presented. Here, the same modelling principles are applied toa system composed of a 1-D beam and a 1-D cylindricalacoustic resonator, leading to a lumped-parameter modelincluding the coupling dynamics between several barmodes and several resonator acoustic modes. The dynamics of the lumped-parameter model are explored throughtime-domain simulations and eigenvalue analysis, revelinga number of interesting (and rarely mentioned) features, forexample: the role of the ratio of damping coefficients between a bar mode and a resonator mode, the placementof the resonator along the bar’s length as well as its proximity to the bar, etc. Additionally, experimental results arepresented to validate the model and demonstrate its capacity to emulate real instruments, both qualitative andquantitatively.publishersversionpublishe

Some simulations of the effect of varying excitation parameters on the transients of reed instruments

This paper considers the simulation of self-sustained oscillations in reed and brass instruments, based on a compact continuous-time formulation of the sound production mechanism. The control parameters such as the mouth pressure and the player's embouchure, but also the acoustic resonator and the reed may vary with respect to time, allowing the analysis of transient and non-stationary phenomena like changes of regime. A particular attention is first given to staccato notes, with comparison of the evolution of the instantaneous frequency in simulations to theoretical and experimental results. This shows the importance of using realistic control parameters on the onset of the oscillations. When the acoustic resonator is modelled using a modal expansion with non-stationary resonance frequencies and damping, it is also possible to simulate and study slurs and musical effects like the wah-wah, gaining some insight on the mechanisms involved