Model-predicted geometry variations to compensate material variability in the design of classical guitars.

Musical instrument making is often considered a mysterious form of art, its secrets still escaping scientific quantification. There is not yet a formula to make a good instrument, so historical examples are regarded as the pinnacle of the craft. This is the case of Stradivari's violins or Torres guitars that serve as both models and examples to follow. Geometric copies of these instruments are still the preferred way of building new ones, yet reliably making acoustic copies of them remains elusive. One reason for this is that the variability of the wood used for instruments makes for a significant source of uncertainty-no two pieces of wood are the same. In this article, using state-of-the-art methodologies, we show a method for matching the vibrational response of two guitar top plates made with slightly different materials. To validate our method, we build two guitar soundboards: one serving as a reference and the second acting as a copy to which we apply model-predicted geometry variations. The results are twofold. Firstly, we can experimentally validate the predictive capabilities of our numerical model regarding geometry changes. Secondly, we can significantly reduce the deviation between the two plates by these precisely predicted geometry variations. Although applied to guitars here, the methodology can be extended to other instruments, e.g. violins, in a similar fashion. The implications of such a methodology for the craft could be far-reaching by turning instrument-making more into a science than artistic craftsmanship and paving the way to accurately copy historical instruments of a high value.

A neural network-based method for spruce tonewood characterization.

The acoustical properties of wood are primarily a function of its elastic properties. Numerical and analytical methods for wood material characterization are available, although they are either computationally demanding or not always valid. Therefore, an affordable and practical method with sufficient accuracy is missing. In this article, we present a neural network-based method to estimate the elastic properties of spruce thin plates. The method works by encoding information of both the eigenfrequencies and eigenmodes of the system and using a neural network to find the best possible material parameters that reproduce the frequency response function. Our results show that data-driven techniques can speed up classic finite element model updating by several orders of magnitude and work as a proof of concept for a general neural network-based tool for the workshop.

On the Virtualization of Audio Transducers.

In audio transduction applications, virtualization can be defined as the task of digitally altering the acoustic behavior of an audio sensor or actuator with the aim of mimicking that of a target transducer. Recently, a digital signal preprocessing method for the virtualization of loudspeakers based on inverse equivalent circuit modeling has been proposed. The method applies Leuciuc's inversion theorem to obtain the inverse circuital model of the physical actuator, which is then exploited to impose a target behavior through the so called Direct-Inverse-Direct Chain. The inverse model is designed by properly augmenting the direct model with a theoretical two-port circuit element called nullor. Drawing on this promising results, in this manuscript, we aim at describing the virtualization task in a broader sense, including both actuator and sensor virtualizations. We provide ready-to-use schemes and block diagrams which apply to all the possible combinations of input and output variables. We then analyze and formalize different versions of the Direct-Inverse-Direct Chain describing how the method changes when applied to sensors and actuators. Finally, we provide examples of applications considering the virtualization of a capacitive microphone and a nonlinear compression driver.

The impact of alkaline treatments on elasticity in spruce tonewood.

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.

A comparative analysis of the directional sound radiation of historical violins.

The directivity pattern of a musical instrument describes the sound energy radiation as a function of frequency and direction of emission. Violins exhibit a rather complex directivity pattern, which is known to show rapid variations across frequencies, and whose behavior cannot be easily predicted except in the lowest frequency range. The acoustic behavior of the violin is a fascinating research topic that has prompted numerous published works, but a thorough, comprehensive, and comparative analysis of violin directivity patterns is long overdue. In this article, we propose a set of metrics for characterizing the radiative behavior of musical instruments and, in particular, for comparing their directivity patterns. We apply such metrics for a comparative analysis of the directivity patterns of some of the most prestigious historical violins ever made, including grand masters such as Antonio Stradivari, Giuseppe Guarneri "del Gesú" and members of the Amati family. The instruments are preserved in the Violin Museum of Cremona, Italy, where our lab is located. The analysis methodology introduced in this work allowed us to quantitatively evaluate the similarity of directivity patterns of such extraordinary instruments and draw some interesting conclusions.

Deep Prior Approach for Room Impulse Response Reconstruction.

In this paper, we propose a data-driven approach for the reconstruction of unknown room impulse responses (RIRs) based on the deep prior paradigm. We formulate RIR reconstruction as an inverse problem. More specifically, a convolutional neural network (CNN) is employed prior, in order to obtain a regularized solution to the RIR reconstruction problem for uniform linear arrays. This approach allows us to avoid assumptions on sound wave propagation, acoustic environment, or measuring setting made in state-of-the-art RIR reconstruction algorithms. Moreover, differently from classical deep learning solutions in the literature, the deep prior approach employs a per-element training. Therefore, the proposed method does not require training data sets, and it can be applied to RIRs independently from available data or environments. Results on simulated data demonstrate that the proposed technique is able to provide accurate results in a wide range of scenarios, including variable direction of arrival of the source, room T60, and SNR at the sensors. The devised technique is also applied to real measurements, resulting in accurate RIR reconstruction and robustness to noise compared to state-of-the-art solutions.

A Physics-Informed Neural Network Approach for Nearfield Acoustic Holography.

In this manuscript, we describe a novel methodology for nearfield acoustic holography (NAH). The proposed technique is based on convolutional neural networks, with autoencoder architecture, to reconstruct the pressure and velocity fields on the surface of the vibrating structure using the sampled pressure soundfield on the holographic plane as input. The loss function used for training the network is based on a combination of two components. The first component is the error in the reconstructed velocity. The second component is the error between the sound pressure on the holographic plane and its estimate obtained from forward propagating the pressure and velocity fields on the structure through the Kirchhoff-Helmholtz integral; thus, bringing some knowledge about the physics of the process under study into the estimation algorithm. Due to the explicit presence of the Kirchhoff-Helmholtz integral in the loss function, we name the proposed technique the Kirchhoff-Helmholtz-based convolutional neural network, KHCNN. KHCNN has been tested on two large datasets of rectangular plates and violin shells. Results show that it attains very good accuracy, with a gain in the NMSE of the estimated velocity field that can top 10 dB, with respect to state-of-the-art techniques. The same trend is observed if the normalized cross correlation is used as a metric.

Modal analysis of free archtop guitar top plates.

We analyze the modal response of the top plates of archtop guitars using free boundary conditions. Starting from the three-dimensional scan of a real archtop guitar, we build a mesh of its top plate using a non-invasive process. Once the mesh of the plate is built, we compute its vibrational response by finite element method simulations and perform many different analyses. The outer surface of the mesh matches the scan, while we retain the freedom to control the shape of the inner surface. This way we can change some of its aspects (e.g., thickness distribution) depending on what we intend to study. We investigate the similarities of its mode shapes with those of similar instruments (e.g., violin and classical guitar), analyze the carving process of the plate's inner surface and study the influence of resonant holes on its final vibratory response.

A data-driven approach to violin making.

Of all the characteristics of a violin, those that concern its shape are probably the most important ones, as the violin maker has complete control over them. Contemporary violin making, however, is still based more on tradition than understanding, and a definitive scientific study of the specific relations that exist between shape and vibrational properties is yet to come and sorely missed. In this article, using standard statistical learning tools, we show that the modal frequencies of violin tops can, in fact, be predicted from geometric parameters, and that artificial intelligence can be successfully applied to traditional violin making. We also study how modal frequencies vary with the thicknesses of the plate (a process often referred to as plate tuning) and discuss the complexity of this dependency. Finally, we propose a predictive tool for plate tuning, which takes into account material and geometric parameters.

Eigenfrequency optimisation of free violin plates.

We discuss how the modal response of violin plates changes as their shape varies. Starting with an accurate 3D scan of the top plate of a historic violin, we develop a parametric model that controls a smooth shaping of the interior of the plate, while guaranteeing that the boundary is the same as the original violin. This allows us to generate a family of violin tops whose shape can be smoothly controlled through various parameters that are meaningful to a violin maker: from the thickness in different areas of the top to the location, angle, and dimensions of the bass bar. We show that the interplay between the different parameters affects the eigenmodes of the plate frequencies in a nonlinear fashion. We also show that, depending on the parameters, the ratio between the fifth and the second eigenfrequencies can be set to match that used by celebrated violin makers of the Cremonese school. As the parameterisation that we define can be readily understood by violin makers, we believe that our findings can have a relevant impact on the violin making community, as they show how to steer geometric modifications of the violin to balance the eigenfrequencies of the free plates.

A Minimal Metric for the Characterization of Acoustic Noise Emitted by Underwater Vehicles.

Underwater robots emit sound during operations which can deteriorate the quality of acoustic data recorded by on-board sensors or disturb marine fauna during in vivo observations. Notwithstanding this, there have only been a few attempts at characterizing the acoustic emissions of underwater robots in the literature, and the datasheets of commercially available devices do not report information on this topic. This work has a twofold goal. First, we identified a setup consisting of a camera directly mounted on the robot structure to acquire the acoustic data and two indicators (i.e., spectral roll-off point and noise introduced to the environment) to provide a simple and intuitive characterization of the acoustic emissions of underwater robots carrying out specific maneuvers in specific environments. Second, we performed the proposed analysis on three underwater robots belonging to the classes of remotely operated vehicles and underwater legged robots. Our results showed how the legged device produced a clearly different signature compared to remotely operated vehicles which can be an advantage in operations that require low acoustic disturbance. Finally, we argue that the proposed indicators, obtained through a standardized procedure, may be a useful addition to datasheets of existing underwater robots.

3D Beam Tracing Based on Visibility Lookup for Interactive Acoustic Modeling.

We present a method for accelerating the computation of specular reflections in complex 3D enclosures, based on acoustic beam tracing. Our method constructs the beam tree on the fly through an iterative lookup process of a precomputed data structure that collects the information on the exact mutual visibility among all reflectors in the environment (region-to-region visibility). This information is encoded in the form of visibility regions that are conveniently represented in the space of acoustic rays using the Plücker coordinates. During the beam tracing phase, the visibility of the environment from the source position (the beam tree) is evaluated by traversing the precomputed visibility data structure and testing the presence of beams inside the visibility regions. The Plücker parameterization simplifies this procedure and reduces its computational burden, as it turns out to be an iterative intersection of linear subspaces. Similarly, during the path determination phase, acoustic paths are found by testing their presence within the nodes of the beam tree data structure. The simulations show that, with an average computation time per beam in the order of a dozen of microseconds, the proposed method can compute a large number of beams at rates suitable for interactive applications with moving sources and receivers.