Physical modelling of a harp from Central Africa.

Central Africa harps are string instruments, often anthropomorphic, serving an essential cultural role. Compared to pedal harps, their body is small in size with a soundboard mainly made of animal skin and a neck made of a wood beam. In this paper, a physical model is developed as a tool for assessing the specificities of these musical instruments, from a vibro-acoustic perspective. The modeling strategy is based on the modal Udwadia-Kalaba formalism which is a multibody substructuring technique. Input modal parameters of the body and the strings are experimentally identified and the main steps of the estimation procedures are detailed. The reliability of the physical model is investigated via the comparison between simulated and experimental data for several plucking configurations. Different hypotheses are assessed such as the string/neck coupling which proves to strongly influence the dynamic response of the body when there is a coincidence between string and neck modal frequencies. The inclusion of geometrical nonlinearities proves to be of major importance, even for a weak plucking, as it allows qualitative representation of double frequency terms in the simulations. Overall, physical simulations of the soundboard motion are in good agreement with measurements indicating characteristic features of the instrument are captured.

Vibrotactile Thresholds on the Wrist for Vibrations Normal to the Skin.

In order to facilitate the development of wrist-worn vibrotactile devices, detailed knowledge about how vibrations are perceived by the users is needed. In particular, perceptual thresholds in amplitude are really important. Thresholds have been measured in the literature for other areas of the body, but given the variability reported between areas (shape of the threshold curve, position of maximum sensitivity), thresholds on the wrist can not be inferred from previous measurements and must be measured. The amplitude thresholds for vibrations normal to the skin surface were evaluated on 28 participants, with a three interval forced choice method. They were measured for 7 frequencies that are classical in the literature about vibrotactile perception (25, 40, 80, 160, 250, 320, and 640 Hz). The classical U-shape of the amplitude-threshold curve is observed, with a maximum sensitivity at around 160 Hz, which differs from other body areas, but confirms recent results obtained for vibrations parallel to the skin surface of the same body area. The sensitivity thresholds of vibrotactile signals appear to be in the micrometer range.

Whistling in the clavichord.

Sympathetic string vibration plays an essential role in the clavichord's sound quality and tonal identity. Sympathetic vibration comes from the undamped string segments between the bridge and tuning pins. Under some conditions, a specific note, a whistling tone, stands out of the reverberation halo due to sympathetic vibration. It is hypothesized that this whistling tone comes from resonance between played and sympathetic segments of strings that are coupled through the bridge. Vibratory measurements for three pairs of excited and sympathetic strings are conducted on a copy of a historical instrument built by Hubert in 1784. The influences of bridge mobility and tuning on sympathetic string frequency and damping are studied. The results show a significant increase in vibratory amplitude, frequency veering, and damping increase in the string segments when tuning approaches frequency coincidence. Numerical simulations of a reduced clavichord model corresponding to the experiments are conducted using the modal Udwadia-Kalaba formulation. Simulation gives a more accurate picture of the veering phenomenon. Simulation and experimental results are in good agreement, showing that whistling in the clavichord comes from string resonance. It is favored by frequency coincidence between excited and sympathetic string segments and by higher bridge mobility.

Toward a physical model of the clavichord.

String excitation by the tangent in the clavichord is a unique mechanism. The tangent, keeping in contact with the string after the initial strike, continuously controls the string tension. Four main flexible subsystems are considered in the clavichord: the tangent/key subsystem, the string subsystem, the bridge-soundboard subsystem, and the string damper subsystem. A modal description of the dynamics of these subsystems is proposed. Parameters of the subsystems are estimated on a copy of a historical instrument by Hubert (1784). The different subsystems and their couplings are modeled using a modal Udwadia-Kalaba formulation. The string-tangent interaction is modeled via the intermittent contact dynamics, using the Kirchoff-Carrier string model. Realistic string, soundboard, and tangent motions are obtained using a time-domain synthesis scheme that computes the dynamics of the uncoupled subsystems and the constraints resulting from coupling between them. Simulated motions of the model in response to a driving force on the key are analyzed. The results are consistent with experimental measurements and published data on the dynamics of the clavichord. The model is able to reproduce the main acoustic features of the instrument: force on the key for intonation control, key velocity for dynamic nuances control, and constant spectral slope for varying dynamic nuances.

Influence of the player on the dynamics of the electric guitar.

The sound of the electric guitar is strongly dependent on the string vibration. Where a mode of the structure coincides with a mode of the fretted string, coupling between the string and structure occurs at that "deadspot." The coupling significantly lowers decay time, leading to the name [Paté, Le Carrou, and Fabre (2014). J. Acoust. Soc. Am. 135(5), 3045-3055]. But how the guitarist affects the dynamic behavior of the structure by grasping the neck, holding the instrument with the strap, or laying the instrument on his/her thigh remains to be investigated. This is the aim of the paper. Two methods are proposed to identify the modal parameters of the electric guitar structure, either by a classical modal analysis in simulated playing configuration, or by an operational modal analysis in real playing configuration. For this latter method, modal parameters are identified from dynamic measurements performed when each string is plucked. Both methods are compared and allow one to quantify the modal frequency modification and the added modal damping, which depend on the player's body-part in contact with the structure and on the modal shape considered. Consequences of these modal parameters on the modeled sound show that the player can increase the decay time close to a deadspot.

Nonsmooth contact dynamics for the numerical simulation of collisions in musical string instruments.

Collisions in musical string instruments play a fundamental role in explaining the sound production in various instruments such as sitars, tanpuras, and electric basses. Contacts occurring during the vibration provide a nonlinear effect which shapes a specific tone due to energy transfers and enriches the hearing experience. As such, they must be carefully simulated for the purpose of physically based sound synthesis. Most of the numerical methods presented in the literature rely on a compliant modeling of the contact force between the string and the obstacle. In this contribution, numerical methods from nonsmooth contact dynamics are used to integrate the problem in time. A Moreau-Jean time-stepping scheme is combined with an exact scheme for phases with no contact, thus controlling the numerical dispersion. Results for a two-point bridge mimicking a tanpura and an electric bass are presented, showing the ability of the method to deal efficiently with such problems while invoking, as compared to a compliant approach, less modelling parameters, and a reduced computational burden.

Acoustic dissipation in wooden pipes of different species used in wind instrument making: An experimental study.

In this study, the acoustic dissipation is investigated experimentally in wooden pipes of different species commonly used in woodwind instrument making: maple (Acer pseudoplatanus), pear wood (Pyrus communis L.), boxwood (Buxus sempervirens), and African Blackwood (Dalbergia melanoxylon). The pipes are parallel to the grain, except one which forms an angle of 60° with the fiber direction. An experimental method, involving input impedance measurements with several lengths of air column, is introduced to estimate the characteristic impedance and the attenuation factor in the pipes. Their comparison reveals significant differences of acoustic dissipation among the species considered. The attenuation factors are ranked in the following order from largest to smallest: maple, boxwood, pear wood, and African Blackwood. This order is the same before and after polishing the bore, which is an essential step in the making process of wind instrument. For maple, changing the pipe direction of 60° considerably increases the attenuation factor, compared to those of the other pipes, parallel to the grain. Further, polishing tends to reduce the acoustic dissipation in the wooden pipes, especially for the most porous species. As a result, the influence of polishing in the making procedure depends on the selected wood species.

Auditory display of seismic data: On the use of experts' categorizations and verbal descriptions as heuristics for geoscience.

Auditory display can complement visual representations in order to better interpret scientific data. A previous article showed that the free categorization of "audified seismic signals" operated by listeners can be explained by various geophysical parameters. The present article confirms this result and shows that cognitive representations of listeners can be used as heuristics for the characterization of seismic signals. Free sorting tests are conducted with audified seismic signals, with the earthquake/seismometer relative location, playback audification speed, and earthquake magnitude as controlled variables. The analysis is built on partitions (categories) and verbal comments (categorization criteria). Participants from different backgrounds (acousticians or geoscientists) are contrasted in order to investigate the role of the participants' expertise. Sounds resulting from different earthquake/station distances or azimuths, crustal structure and topography along the path of the seismic wave, earthquake magnitude, are found to (a) be sorted into different categories, (b) elicit different verbal descriptions mainly focused on the perceived number of events, frequency content, and background noise level. Building on these perceptual results, acoustic descriptors are computed and geophysical interpretations are proposed in order to match the verbal descriptions. Another result is the robustness of the categories with respect to the audification speed factor.

Influence of plectrum shape and jack velocity on the sound of the harpsichord: An experimental study.

A controversial discussion in the musical community regards the ability of the harpsichord to produce sound level or timbre changes. The jack velocity (controlled in real time within a musical context) and the plectrum shape (modified by the musician or maker prior to the performance) appear to be the two control parameters at the disposal of the harpsichord makers and players for shaping the sound. This article initiates the acoustical study of the control parameters of the harpsichord, presenting a framework for the investigation of these two parameters with means of experimental mechanics measurement. A robotic finger is used for producing repeatable plucks with various jack velocities and plectrum shapes. The plectrum bending, vibrating string's initial conditions, and radiated sound are recorded and analysed. First, results are obtained from measurements carried out on one string, for four plectrum shapes and four jack velocities. The plectrum shape has been found to have an influence on its bending behavior when interacting with the string; on the string's initial conditions (position and velocity); and on the resulting sound (sound level, spectral centroid, and decay time). The jack velocity does not have an influence on any of the measured quantities.

The effects of player grip on the dynamic behaviour of a tennis racket.

The aim of this article is to characterise the extent to which the dynamic behaviour of a tennis racket is dependent on its mechanical characteristics and the modulation of the player's grip force. This problem is addressed through steps involving both experiment and modelling. The first step was a free boundary condition modal analysis on five commercial rackets. Operational modal analyses were carried out under "slight", "medium" and "strong" grip force conditions. Modal frequencies and damping factors were then obtained using a high-resolution method. Results indicated that the dynamic behaviour of a racket is not only determined by its mechanical characteristics, but is also highly dependent on the player's grip force. Depending on the grip force intensity, the first two bending modes and the first torsional mode frequencies respectively decreased and increased while damping factors increased. The second step considered the design of a phenomenological hand-gripped racket model. This model is fruitful in that it easily predicts the potential variations in a racket's dynamic behaviour according to the player's grip force. These results provide a new perspective on the player/racket interaction optimisation by revealing how grip force can drive racket dynamic behaviour, and hence underlining the necessity of taking the player into account in the racket design process.

Predicting the decay time of solid body electric guitar tones.

Although it can be transformed by various electronic devices, the sound of the solid body electric guitar originates from, and is strongly linked with, the string vibration. The coupling of the string with the guitar alters its vibration and can lead to decay time inhomogeneities. This paper implements and justifies a framework for the study of decay times of electric guitar tones. Two damping mechanisms are theoretically and experimentally identified: the string intrinsic damping and the damping due to mechanical coupling with the neck of the guitar. The electromagnetic pickup is shown to not provide any additional damping to the string. The pickup is also shown to be far more sensitive to the out-of-plane polarization of the string. Finally, an accurate prediction of the decay time of electric guitar tones is made possible, whose only requirements are the knowledge of the isolated string dampings and the out-of-plane conductance at the neck of the guitar. This prediction can be of great help for instrument makers and manufacturers.

A model of harp plucking.

In this paper, a model of the harp plucking is developed. It is split into two successive time phases, the sticking and the slipping phases, and uses a mechanical description of the human finger's behavior. The parameters of the model are identified through measurements of the finger/string displacements during the interaction. The validity of the model is verified using a configurable and repeatable robotic finger, enhanced with a silicone layer. A parametric study is performed to investigate the influence of the model's parameters on the free oscillations of the string. As a result, a direct implementation of the model produces an accurate simulation of a string response to a given finger motion, as compared to experimental data. The set of parameters that govern the plucking action is divided into two groups: Parameters controlled by the harpist and parameters intrinsic to the plucking. The former group and to a lesser extent the latter highly influence the initial conditions of the string vibrations. The simulations of the string's free oscillations highlight the large impact the model parameters have on the sound produced and therefore allows the understanding of how different players on the same instrument can produce a specific/personal sound quality.

Experimentally based description of harp plucking.

This paper describes an experimental study of string plucking for the classical harp. Its goal is to characterize the playing parameters that play the most important roles in expressivity, and in the way harp players recognize each other, even on isolated notes--what we call the "acoustical signature" of each player. We have designed a specific experimental setup using a high-speed camera that tracks some markers on the fingers and on the string. This provides accurate three-dimensional positioning of the finger and of the string throughout the plucking action, in different musical contexts. From measurements of ten harp players, combined with measurements of the soundboard vibrations, we extract a set of parameters that finely control the initial conditions of the string's free oscillations. Results indicate that these initial conditions are typically a complex mix of displacement and velocity, with additional rotation. Although remarkably reproducible by a single player--and the more so for professional players--we observe that some of these control parameters vary significantly from one player to another.

Some characteristics of the concert harp's acoustic radiation.

The way a musical instrument radiates plays an important part in determining the instrument's sound quality. For the concert harp, the soundboard has to radiate the string's vibration over a range of 7 octaves. Despite the effort of instrument makers, this radiation is not uniform throughout this range. In a recent paper, Waltham and Kotlicki [J. Acoust. Soc. Am. 124, 1774-1780 (2008)] proposed an interesting approach for the study of the string-to-string variance based on the relationship between the string attachment position and the operating deflection shapes of the soundboard. Although the soundboard vibrational characteristics determine a large part of the instrument's radiation, it is also important to study directly its radiation to conclude on the origins of the string-to-string variation in the sound production. This is done by computing the equivalent acoustical sources on the soundboard from the far field sound radiation measured around the harp, using the acoustic imaging technique inverse frequency response function. Results show that the radiated sound depends on the correlation between these sources, and the played string's frequency and location. These equivalent sources thus determine the magnitude and directivity of each string's partial in the far field, which have consequences on the spectral balance of the perceived sound for each string.