Soundboard Vibration Research Articles

A Three-Dimensional Method for Analysis of the Body Mode of Classical Guitars Using a Laser Displacement Sensor.

In classical guitar acoustic spectra, the lowest frequency body mode's amplitude often significantly surpasses that of the string overtones. However, the characteristics of the body mode have not been systematically utilized to quantitatively represent the timbre of classical guitars. In this study, we propose a quantitative method for describing the body mode, which can effectively differentiate the timbre of classical guitars. Our approach involves three key parameters presented in a three-dimensional space, as follows: the frequency and quality factors of the body mode, along with the amplitude ratio of the plucked string note to the body mode in the soundboard's vibration spectrum. This representation allows for the visualization, quantitative comparison, and classification of the body mode note and damping properties across classical guitars. The differences in body mode among guitars can be analyzed quantitatively using Euclidean distance.

Impact of Damping on Oscillation Patterns on the Plain Piano Soundboard

The influence of internal damping on the vibration of a piano soundboard is investigated using a Finite-Difference Time Domain (FDTD) physical model and experimental measurements. The damping constant of the model is varied according to a range similar to those found with measurements on a real grand piano at different production stages. With strong damping, a clear driving-point dependency of the forced string oscillation on the oscillation pattern of the soundboard is found. When decreasing the damping, this driving-point dependency is decreasing, nevertheless, it is still present. High damping, therefore, decreases soundboard vibration when strings drive the soundboard at the soundboard’s eigenfrequencies. However, such large damping increases soundboard vibrations when strings drive the soundboard at frequencies which are not eigenfrequencies. Therefore, strong damping smooths out the frequency response spectrum of an instrument. Extreme damping without any presence of distinct eigenmodes leads to a radiation of the strings sound spectrum without soundboard filtering. Low damping leads to a strong influence of the soundboard on the string’s radiated sound. Therefore, the amount of soundboard characteristics can be designed to alter internal damping process by choice of materials, including wood or varnish, and geometry. Additionally, damping reduces the presence of ’dead spots’, notes which are considerably lower in volume compared to other notes.

Prediction of lute acoustic quality based on soundboard vibration performance using multiple choice model

The vibrational performance of wood materials critical affects the acoustic quality of a lute. The purpose of this research was to apply a multiple choice model to predict the quality of musical instruments based on data on lute soundboard vibrational properties of Paulownia wood. In the lute production, lute material selection mainly depends on the subjective evaluation of technicians, which is not only inefficient, but inaccurate. In this study, nine lutes were fabricated. Using the multiple selection model, the lute tone quality was predicted by the soundboard wood vibration data. Compared with the actual value, the dependent value predicted by the count of observations with the maximum probability had 22 erroneous judgments. The model precision is 87.78%. The results confirmed that the prediction model can be used as a guideline for the selection of the soundboard wood in musical instrument plants.

Prediction of Yueqin acoustic quality based on soundboard vibration performance using support vector machine

As an important material of making instrument resonant component, paulownia has a significant influence on instrument acoustic quality. Using the method of support vector machine (SVM), an evaluation model for predicting the Yueqin acoustic quality was developed based on the wood vibration performance. Generally, the wood selection in the Yueqin manufacture mainly depends on observance weighting by hands, knocking and listening by an instrument technician. The defect in scientific theory impedes the improvement of Yueqin quality. In this study, nine Yueqin were fabricated. Based on the information of their raw materials and Yueqin acoustic quality evaluation, a prediction model was proposed. In the total 180 groups of data, 60 groups of data were randomly selected for the training, 30 groups of data were randomly selected from the unused data for the verification. The radial basis function is used to establish the Yueqin soundboard wood acoustic quality evaluation model and simulate the prediction. The results revealed that the prediction of Yueqin acoustic quality could be achieved based on the soundboard wood vibration performance using the MATLAB simulation. The classification accuracy was 90.00%, indicating that the predicted values were highly consistent with the experimental values. The models are able to be used to precisely predict the Yueqin acoustic quality based on the vibration performance of soundboards.

The acoustics of pianos

The manufacturing of pianos remains largely empirical, with numerous trial-and-error procedures and fine adjustments at each step of the building process. The “skeleton” of the instrument obeys fundamental principles of vibrations, acoustics, and material science. An abundance of literature is available on its different constitutive parts. However, scientific studies based on a global model of the instrument that connects all of these constitutive parts together are more recent. Such modeling sheds useful light on the essential coupling properties between elements and, in particular, on the string-soundboard coupling at the bridge, and on the radiation of the soundboard. Fine analysis of piano tones also shows that in most cases, a nonlinear model of the strings is necessary to account for perceptually significant features such as precursors in the time-domain and the so-called “phantom partials” in the spectrum. This nonlinearity is based on the coupling between transverse and longitudinal waves in the string. In this lecture, a time-domain model of a complete piano is presented that couples together nonlinear strings, soundboard vibrations, and radiation in air. It highlights the transmission of both transverse and longitudinal string forces to the soundboard, and the influence of rib design and bridge on soundboard mobility and radiation patterns. Comparisons between the results of the model and measurements made on real pianos will be discussed.

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.

Influence of ribs on the radiation of a piano soundboard.

The presence of ribs attached to the soundboard of a piano influences the transfer of energy from strings to soundboard through the bridge. Measurements and simulations show that the input admittance at the bridge depends on the distance between string end and ribs. A second effect of ribs is related to the periodicity of rib spacing. Simulations of soundboard driving‐point mobility were conducted for three different spacing rules: periodic, almost periodic with small random fluctuations, and random distribution of spacing within a given interval. The results show that aperiodicity reduces the emergence of strong peaks in the mobility spectrum. Finally, measurements and simulations were made on the radiated sound in an anechoic chamber. The primary effect of ribs here is due to the additional stiffness, compared to a flat plate, which reduces the critical frequency and thus increases the frequency range where the radiated sound power is significant. In addition, the presence of ribs influences the directivity of the sound field: strong differences exist in a plane parallel to ribs compared to ribs perpendicular to them. These results also serve as references for comparison with time‐domain simulations of the complete piano including strings, soundboard vibrations, and radiation.

Modeling of piano sounds using FEM simulation of soundboard vibration

Pattern-matching methods for polyphonic transcription of piano sounds require a set of patterns that can be obtained by modeling the piano-sound spectra. The modeling should take into account not only the string stiffness but also the effect of the soundboard impedance on the string vibration. Studies on that effect corresponding to a wide range of impedance values have previously been carried out by the authors. However, actual impedance values for real pianos must be used in the model. Although the impedance value of a few grand-pianos have been measured by the authors, these results are not significative enough to create a model. Thus, a FEM simulation of soundboard vibration is proposed to obtain nearly-actual impedance values. The simulation considers several cases of vibrating plates from the simplest rectangular one and increasing the similarity to real piano soundboards. The quality of the simulation is verified comparing the obtained results with either recognized theoretical results for the simplest cases or measured values for the more complex ones. The complexity of the simulated soundboard is limited to the case that produces only slight variations in the modeled spectrum. [This work has been supported by Spanish National Project TEC2006-13067-C03-01/TCM.]

Piano soundboards: Experimental and modeling studies

The piano has attracted the attention of many researchers, and most of that work has focused on piano hammers and string vibrations. The vibrational and radiative properties of the soundboard have drawn much less attention, but are essential for an understanding of the sound produced by the instrument. We review experimental studies of the soundboard’s vibrational modes and their radiative efficiency. We also describe modeling studies of soundboard vibrations and radiation, which aid in understanding the measurements. Prospects for future work and for applications to other instruments are suggested. [Work supported by NSF grant PHY-9988562.]

Piano bridge and soundboard motion

The bridge of a piano is the place where two important components, the strings and the soundboard, meet and interact. The motion of the bridge is important for understanding soundboard vibrations and sound production. This motion is also central to the interaction between strings, and to coupling of the different modes of a single string. Recent experimental and theoretical studies of bridge and soundboard motion are described. While the dominant motion is, as one would expect, perpendicular to the plane of the soundboard, the experiments show that motion parallel to this plane is also quite significant. Quantitative results for the in-plane motion are presented, and its role in sound production is discussed. We also consider the implications for modeling of soundboard and string motion. [Work supported by the National Science Foundation through Grant PHY-9722031.]

Characteristics of piano sound (Acoustical research on the piano, Part 4).

This paper investigates the characteristics of piano sound using the waveforms of velocity of vibration of strings, the waveforms of driving force and velocity of vibration of the soundboard, and waveforms of sound pressure. The waveforms for the investigation were generated by using a analog simulator so that the separation of conditions is easy. A pulse generated by striking a string with a hammer propagates along the string and reflects against the soundboard. This drives the soundboard producing its vibration, and a part of vibration energy radiates from the soundboard producing piano sounds. The soundboard vibration contains both forced and free vibrations. The latter is influenced by the driving point admittance of the soundboard, and this plays an important role in determining the piano timbre. Still more the characteristics of piano sound are clarified using waveforms obtained by digital simulation and their spectra.

Acoustics of pianos

Some of the recently published papers (in the last 10 or 15 years) on the physics of piano are reviewed. They are categorized into (1) actions, (2) hammers, (3) hammer-string interactions, (4) string vibrations and (5) soundboard vibrations and sound radiations. The authors concentrated on the physical aspect of piano acoustics and those on the analysis/synthesis and evaluation of piano sound are not included. Some documents other than formal publications are included. Also a slightly greater emphasis is placed on studies reported in Japan, which may not be very familiar to most of Western researchers. This review indicates that a significant advancement in piano acoustics has been made during the last couple of decades.

Influence of hammer velocity in piano sound

Recent models of piano string excitation suggest that string motion is proportional to hammer velocity. Preliminary to measuring dynamics in piano performance, the relationship between radiated piano sound and hammer velocities was studied. A computer‐monitored piano allowed reproduction of a range of hammer velocities, and a microphone placed near a pianist's head location recorded radiated sound. The first eperiment indicated that peak amplitude of the waveform was directly proportional to the hammer velocity of individual notes for a wide range of frequencies and hammer velocities. A second experiment investigated the waveforms of notes struck simultaneously and compared these with the waveforms of the individual component notes. The peak amplitude of the dyads was directly proportional (with proportionality close to 1) to the sum of the individual peak amplitudes. A third experiment extended these findings to a wider range of dyadic pitch intervals. These findings suggest linear relationships between hammer velocity, amplitude of string motion, bridge motion, and amplitude of the soundboard vibration for single notes. The additivity of dyads indicates that the principle of superposition is obeyed with a small energy loss. [Work supported by MIT Media Lab, Ohio State University Small Research Grant, and a Wellesley College Brachman Hoffman Fellowship.]

Fundamental theory and computer simulation of the decay characteristics of piano sound.

It is shown by theory and computer simulation that the decay characteristics of piano sound are dependent upon the degree of coupling between the strings. String and soundboard vibration are calculated using an equivalent circuit. Each string is comprised of resonance circuits that correspond to partials, and the behavior of individual partials is described independently of each other by these circuits. When the most simplified version of only one partial is considered, the equivalent circuit is expressed by the two resonant circuits coupled with the soundboard impedance. The degree of coupling between the two strings is dependent on the ratio of two constants: the degree of mistuning and the ratio of soundboard impedance to string impedance. If the former is smaller than the latter, the two strings are closely coupled with each other and a double decay characteristic results. If the relation between the two constants is reversed, the coupling is loose and a beat type decay characteristic results. The decay characteristics are changed by the above two constants. The results show that the degree of tuning and the characteristics of the strings and the soundboard determine the decay characteristics of piano sound.

Fundamental theory and computer simulation concerning the decay characteristics of piano sound

It is shown by theory and computer simulation that the decay characteristics of piano sound are dependent upon the degree of coupling between the strings. String and soundboard vibration are calculated using an equivalent circuit. Each string is comprised of resonance circuits that correspond to partials, and the behaviors of individual partials are described independently of each other by these circuits. When the most simplified version of only one partial is considered, the equivalent circuit is expressed by the two resonant circuits coupled with the soundboard impedance. The degree of coupling between the two strings is dependent on the ratio of two constants: the degree of mistuning and the ratio of soundboard impedance to string impedance. If the former is smaller than the latter, the two strings are closely coupled with each other and a double decay characteristic results. If the relation between the two constants is reversed, the coupling is loose and a beat type of decay characteristic results. The decay characteristics are changed by the above two constants. The results show that the degree of tuning and the characteristics of the strings and the soundboard determine the decay characteristics of piano sound.