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Towards a model-based decision support tool for stringed musical instrument making

  • Institut Technologique Européen des Metiers de la Musique


This work proposes a methodology for the transfer of industrial and research domain methods toward arts and crafts domain. The virtual prototyping and mechanical characterization of materials are used for the stringed musical instruments making domain. The studies are addressed to the guitar and violin making. This domain is historically driven by empiricism and it is studied here using objective criteria. The main topic is the mechanical vibratory behaviour of musical instruments. Firstly, the mechanical behaviour of the material used (tonewood) is studied. A non-destructive methodology is proposed and applied on spruce and maple species. The reliability of the numerical models is studied by a process usually used in industry and research, the verification and validation process. The models developed are used as a support for the study of complex phenomena in musical acoustics. Finally, the utilization of numerical method for a practical application in instrument making (decision support under uncertainties, geometric and material optimization) is proposed. The methodology for a transfer to art and crafts domain is discussed.
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... From a mechanical point of view, wood exhibits a complex behaviour, since it is anisotropic, heterogeneous, elasto-visco-plastic, thermo-hygroscopic and discontinuous. Nevertheless, and considering vibrations at low strain levels, and tested frequency domain and dimensions, it is often considered as an orthotropic, continuous, homogeneous, elastic and hygroscopic material, as detailed and summarized in [22]. Criteria such as acoustic conversion efficiency (ACE) or radiation ratio are common features in musical acoustics and can be used fruitfully to compare different wood species and samples, as shown in [23][24][25]. ...
... The elastic constants values of E L ; E R and G LR depend on the relative humidity and, in a lesser degree, on the temperature. In order to implement this dependence, the values of the elastic properties are implemented as a function of RH and T, laws are taken from [22], given in the Eq. 3: E L RHT ¼ E Lq ð1 À 0:0015 Â ðRH À 50Þ À 0:0008 Â ðT À 21ÞÞ E R RHT ¼ E Rq ð1 À 0:005 Â ðRH À 50Þ À 0:0025 Â ðT À 21ÞÞ ...
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Nowadays, the virtual prototyping method is widely used for industrial applications and can lead to a powerful tool for musical instruments making and conservation. Nevertheless, physics-based models of musical instruments are barely developed for this purpose and the confrontation between model predictions and experiments have been the focus of very few researches. The objective of this paper is to highlight the predictive capability of physics-based models in vibratory domain, even in presence of variable by nature material and climatic conditions. To this end, a finite element model of the soundboard of a Spanish guitar is developed for model validation purposes. The simulated modal bases are compared with experimental ones from a previous study. Screening and stochastic analyses are performed to rank which are, among material and climatic parameters, the most influential ones on the dynamics of guitar soundboard. Moreover, uncertainties are taken into account to evaluate the dispersion of the response for a given design, and simulations are validated facing experimental data. It is shown that specific elastic parameters of the wood (in longitudinal and radial directions and longitudinal-radial plane) of the top plate are mainly influential with regard to the dynamics of the soundboard, and the relative humidity changes have a non negligible impact. Moreover, test-model correlations have shown that a nominal model with average material parameters is able to predict the vibratory behaviour of a real braced sound-board with an average error on the first eight eigenfrequencies lower than 4%. In addition, when uncertainties are taken into account, the model is able to predict every experimental data. Finally, dynamic features like CFDAC and Fuzzy-FRF are proposed in an innovative way in this application domain.
... The impact of pre-treatments and sizing on wood stiffness was assessed by measuring the change in the longitudinal and radial Young's moduli and in the density of the specimens. We focused on these material properties since they have been proved to be important for determining the vibroacoustic properties of complete instruments 23,[27][28][29] . Indeed, their correlation with the first modes of the instrument is found to be higher than others 30 . ...
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It is commonly believed that violins sound differently when finished. However, if the role of varnishes on the vibrational properties of these musical instruments is well-established, how the first components of the complete wood finish impact on the final result is still unclear. According to tradition, the priming process consists of two distinct stages, called pre-treatment and sizing. The literature reports some recipes used by old Cremonese luthiers as primers, mainly based on alkaline aqueous solutions and protein-based glues. In this manuscript, we analyze the impact of these treatments on the mechanical properties of the material. The combination of two pre-treatments and three sizes is considered on nine different plates. We compare the vibrational properties before and after the application and assess the effects of the different primers, also supported by finite element modeling. The main outcome is that the combination of particular treatments on the violin surface before varnishing leads to changes not only to the wood appearance, but also to its vibrational properties. Indeed pre-treatments, often considered negligible in terms of vibrational changes, enhance the penetration of the size into the wood structure and strengthen the impact of the latter on the final rigidity of the material along the longitudinal and radial directions.
... As for the soundboard, studies focused on the vibratory proprieties of wood [60]. Wood is a material sensitive to hygrometry, which means that its vibratory proprieties can change depending on hygrometric conditions. ...
The objective of this PhD is to study the vibro-acoustic behaviour of the clavichord, from its ex- citation system to the sympathetic strings vibration. The Udwadia-Kalaba formulation is used to model the instrument as a coupled mechanical system, reduced to its main vibratory substructures: the key-tangent substructure, the string, the damper and the bridge-soundboard. The Kirchhoff- Carrier model is introduced to model the non-linear geometric deformation of the clavichord string responsible for the change in its fundamental frequency when it is excited by the tangent. Sim- ulation of this model give satisfactory results compared to the measurements and experimental results found in the literature. The main features of the excitation system are satisfactorily repro- duced, among which the pitch shift caused by the string uplift as well as the linearity between the vibratory level and the logarithm of the impact velocity. The "clavichord paradox", referring to the demanding gesture of the musician’s finger to balance between pitch shift and sound level, is studied experimentally with the help of a clavichord player and by means of a robotic finger on a specific clavichord, made from a model conceived by C.G. Hubert. Sympathetic string vibration in the clavichord create two different vibro-acoustic effects: the reverberation effect similar to that found in room acoustics, and string resonance occurring when frequency coincidence between two string partials take place. These two effects are studied experimentally and numerically.
... The strain field is computed with initial values of elastic constants of wood, as shown in the figure 3. It is interesting to observe that the strain field is consistent with the usual location of cracks and damages on real instruments, such as soundpost cracks of the soundboard and back cracks, f holes, top and bottom heel cracks of the soundboard and breaking of the neck and pegbox. [7]. The Hill criterion increases for decreasing values of the radial modulus of maple, which is the most influential parameter. ...
... table 2 [28]. The dependence of the material properties with respectto the relative humidity is taken from[1]. The guitar soundboard and bars are entirely made of spruce wood which is treated as an orthotropic material. ...
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It is generally alleged that the design choices of acoustic guitar bracing patterns lead to a specific sound of the instrument. However, in the presence of strong uncertainties due to variability of material properties and climatic conditions, the robustness of the soundboard dynamics has yet to be investigated. In this study, three types of bracing patterns are studied using physics-based models and stochastic analyses are performed to account for material and climatic uncertainties. It is shown that the choice of a brace design leads, at least in the low frequency domain, to a dynamic behaviour that is not stackable with another design, even in the presence of strong aleatory uncertainties. This assessment supports the conjecture that guitar brace design choices have a greater impact than material variability where guitar soundboard dynamics are concerned. More generally, these results illustrate the usefulness of detailed physics-based models in the understanding, design and making of guitars.
The influence of wood choices on the sound produced by string instruments is a recurrent issue in musical acoustics. Moreover, the intrinsic variability of wood’s mechanical properties requires considerable attention to any analysis attempt. This paper presents a numerical investigation of the wood mechanical properties variability influence on the sound synthesis of a simplified string instrument consisting of a single string coupled to a square soundboard. The adopted synthesis model is based on a hybrid modal approach that combines analytical expressions to describe the string vibration and numerical data obtained from a finite element analysis of the instrument soundboard. For the sound synthesis multiple sets of random wood mechanical properties are assumed. Samples are generated using Monte Carlo simulations and the synthesized sounds statistical moments are performed. Results show the influence of parametric uncertainty in the instrument sounds.KeywordsString musical instrumentsSound synthesisWood variability
Quel est l’état mécanique d’un objet conservé dans les collections patrimoniales ? Cet état mécanique est-il compatible avec la valeur d’usage que les musées d’instruments de musique ont pour mission de conserver ? Afin de garantir des modalités déontologiques de conservation des instruments de musique à cordes, une plateforme numérique d’aide à la décision du maintien en état de jeu pour les instruments à cordes est en cours de conception. Prenant en compte l’état matériel de la structure et les différents efforts qui s’appliquent sur l’instrument de musique, l’approche mécanique développée, qui exploite les outils les plus récents de cette discipline, permet d’évaluer les paramètres qui influencent le plus le comportement dynamique de l’instrument, et avec quel niveau de méconnaissance des paramètres d’entrée le pronostic de remise en état de jeu demeure valable. Les modèles mécaniques présentés apportent des réponses quantifiées en termes de risque d’endommagement de l’œuvre maintenue en état de jeu et mettent en évidence que les états de contrainte induits par les gestes de fabrication initiaux doivent être pris en compte et peuvent conditionner la potentialité musicale des instruments.
This article aims at providing a synthetic view of the equilibrium moisture content (EMC) dependence of wood vibrational properties (i.e. dynamic mechanical properties in the audio-frequency range), including specific dynamic modulus of elasticity ( E′ / γ ) and damping coefficient expressing internal friction (tan δ ). A series of multi-trajectories experiments was designed to complete an analytical review. Literature indicates that: (1) in longitudinal (L) direction, the EMC dependence of E′ / γ shows a very consistent shape (rather linear) between studies, while its shape is non-linear for tan δ and varies significantly between studies; (2) EMC dependence of tan δ is rather well documented in the L direction, in adsorption, for softwoods, but data covering EMC dependence in both L and other anisotropic directions, and sorption hysteresis, are still scarce. Experiments were conducted on a softwood (spruce) and a hardwood (maple), in L and radial (R) directions, in full adsorption from oven-dry state, full desorption from water-saturated state, and relative humidity (RH) loops without extreme conditioning. Measurements were made at conditions considered “at equilibrium” and some were monitored through time. Results indicated that tan δ was much more (×3) sensitive to EMC differences than E′ / γ . R properties, especially tan δ R , were much more (×2–3) sensitive than L properties – resulting in strong increase of anisotropy with increasing EMC. In L direction, differences due to EMC remained moderate compared to the natural variability of wood for E′ / γ , while for tan δ the EMC-induced changes were at least equal to natural variability in high-grade spruce. Vibrational properties did exhibit a hysteresis as a function of RH, but very little hysteresis as a function of EMC. The tan δ -EMC relation strongly depended on the actual time of stabilisation after reaching EMC. A related paper will address the transient, out of equilibrium effects of changing moisture conditions on the vibrational properties of wood.
For centuries, wood, and more specifically spruce, has been the material of choice for violin top plates. Lately, carbon fiber instruments have entered the market. Some studies show that composite materials have potential advantages for making instruments [Damodaran, Lessard, and Babu, Acoust. Aust. 43, 117–122 (2015)]. However, no studies exist that evaluate violins made of different composite materials as judged by listeners. For this study, six prototype violins, differing only by the material of the top plate, were manufactured in a controlled laboratory setting. The six prototype violins were judged by experienced listeners in two double-blind experiments. In contrast to popular opinion that violins made from carbon have or lack a specific sound quality, the study provides insights in the diverse sounds and timbres violins from fiber-reinforced polymers can create. It allows an investigation of the links between the perception and the variations in material properties of the soundboards. Additionally, as neither players nor listeners are acquainted with these instruments, these results provide an interesting view on what type of qualities of violin-like sounds are preferred by listeners.
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