ABSTRACT. Schelleng's diagram famously shows the region within which it is possible to sustain steady Helmholtz motion in a bowed string. It is a two-dimensional subspace of the player's parameter space, and gives a graphical overview of an important aspect of "playability". Guettler's diagram considers a different two-dimensional subset, and shows a region within which it may be possible to execute a "perfect transient" in a bowed string. The idea of representing playability via scans of two-dimensional subspaces of control parameters can be extended to other instruments. For reed woodwind instruments, the two main parameters governing steady note behaviour are the blowing pressure and the reed gap, controlled by the player via their bite pressure. This plane can be populated using simulation models, revealing a wedge-shaped region reminiscent of the Schelleng diagram. Examples will be shown for the clarinet and soprano saxophone. For a brass instrument, the corresponding pair of major parameters are blowing pressure and lip resonance frequency. Again, this plane can be populated via simulations, revealing the conditions (from a given initial transient) leading to the various possible playable notes. Examples will be shown for the trombone and the cornetto. Many other examples of this strategy are possible: it is a powerful way to explore and communicate important aspects of playability.

ABSTRACT. Physical models of bowed-string instruments are able to predict many aspects of bow-string interaction. However, reproducing time-domain waveforms of string oscillations is still a difficult problem. Aiming to shed some light on the challenges involved in modelling the frictional interaction between bow and string, this study compares the performance of physical models based on different friction modelling paradigms. To that end, the string is modelled in the absence of any feedback at its end supports. Two types of previously proposed friction models are examined: a static one, where the friction force depends only on the relative velocity between the string and the bow, and a dynamic one, where the relative velocity and the friction force are related through a differential equation. These models are applied assuming single-point bowing, as well as a finite-width bow. Results, based on steady-state measurements carried out on a monochord, show slight differences between the various models. It remains to examine how these differences may amplify in case of full instrument simulations.

ABSTRACT. Two approaches, a neural network and numerical simulation, for analyzing the sound of violins are introduced herein. First, the sounds (open strings and music) of more than 20 violins are recorded. A set of acoustic features, such as the spectrum envelope and mel-frequency cepstrum coefficients, is used to train the neural network and identify the violin timbre. The possibility of quantifying the similarity of the violin timbre and identifying the violin maker is demonstrated. Subsequently, the violins are scanned using a micro-computed tomography scanner to retrieve geometric data, and numerical simulations of the vibration and sound radiation of the violin body are performed. The vibration of the top plate due to the sinusoidal oscillation of the bridge and the sound radiation from the f-hole and C-bouts are calculated using finite-element software COMSOL Multiphysics and ADVENTURESound.

ABSTRACT. In order to achieve a desired sound, every experienced guitarist is able to vary a number of gestural parameters related to the guitar plucking action. Among these parameters, the plucking position plays a fundamental role in the timbre determination of a guitar. This paper presents a numerical investigation of a time-domain method for plucking position estimation. The method is based on the time lag assessment between the first and the third pulses passing through at an arbitrary point close to the bridge, called measurement point. This time lag is extracted from the autocorrelation function for one period of the acceleration response signal obtained at the measurement point, which allows the estimation of the plucking position. The influence of the variation of several parameters on the plucking position estimation is studied. By means of a modal synthesis framework a set of pluck simulations is generated using different parameter variations. The proposed method is then applied to estimate the plucking position in each case. In general, the obtained results show good agreement between estimated and actual plucking positions. Several limitations of the method concerning the variation of some parameters were also identified.

ABSTRACT. The soundpost is commonly used by bowed string instrument makers as an important link between the plates. Research into the function of the soundpost is of necessity and significance. The goal of this paper is to gather the variations of both vibration modes and human perceptions in response to the changes in the soundpost positions. An adjustable soundpost and a performance-level violin were used in the experiment. The soundpost was shifted towards or away from the centerline (left or right), closer or further from the bridge (upward or downward) for 5 mm separately during the experiment. Physical measurements of vibration modes of the violin with the soundpost fitting in different positions were carried out by an input hammer and a laser vibrometer. Eight skilled violinists and violin or bow makers were invited to play and evaluate the violin. They were asked to compare the violin with soundpost in each of the adjusted position and with soundpost in the original position and rate them on continuous scales according to seven criteria. Perceptual results indicated no significant differences except the violin became significantly softer or more balanced with soundpost position moved upwards or right respectively, comparing with soundpost in the original position.

ABSTRACT. Models of bowed-string motion have been developed over many years, but accurate simulation of transients remains a challenge. Reliable simulation-based explorations of playability questions will only become possible when this challenge has been met. This paper will present recent developments in friction modelling, and incorporate these into an enhanced model of finite-width bowing. The friction modelling draws on earlier work with a temperature-based model, extended in response to detailed comparisons with measured waveforms. The results will be illustrated by comparisons of Guettler diagrams: measured with a rigid rod “bow” and a conventional bow; simulated using point-bow models with a variety of friction models; and simulated with the same friction models with a finite-width bow. The results show considerable promise. None of the comparisons gives a perfect match to the measurements, but those measurements themselves show significant variation between nominal repeated runs using an automated bowing machine. It appears that a real bowed string is on the edge of chaotic behaviour, so that there are limits to what should be expected when comparing with simulations.

ABSTRACT. The main vibrational elements of a spring reverb tank are helical springs. The coupling between bending, longitudinal, and torsional oscillations in a single spring gives rise to complex vibrational behaviour characterised by several distinct echo patterns in measured impulse responses. For modelling purposes, a reduced representation that covers only the hearing range can be obtained by casting the equations in modal form. Previous attempts to explain the various features of measured impulse responses have largely focused on dispersion relation analysis. However, addressing open questions on driving, pick-up, and damping mechanisms requires also considering modal amplitudes. This work applies a pseudospectral method to a thin-spring version of Wittrick's twelve equations, framing an eigenvalue problem from which modal parameters are extracted. To investigate the influence of model parameters on the system response, we propose grouping modes across the wave number axis, which requires extracting wave numbers from mode shapes. This allows separate visualisation and analysis of the various echo patterns in the modelled impulse response. Preliminary results give new perspectives on how transition frequencies arise, and on the significance of specific mode groups.

ABSTRACT. The mechanical properties and geometry of violin top plates determine their vibrational behaviour. In this re-search, a finite element code simulation of the Stradivar-ius Titian violin top plate was modified according to the thickness and density of another experimental violin top plate made by the authors. Following, the simulation's mechanical properties were iteratively adjusted until reaching the desired vibratory modes of the experimental top plate. The elastic properties obtained in this way are in agreement with the expected values for spruce, so they were considered a good estimation of the real values for the experimental top plate. The goal of this research is not to replace traditional tuning and making for violin top plates, but to demonstrate how science can work towards arts being an important tool for students and professional violin makers.

ABSTRACT. The Ffowcs Williams-Hawkings (FW-H) acoustic analogy is applied to investigate the sound generation of a single-reed instrument. An FW-H formulation is derived using the one-dimensional Green's function for an infinitely long pipe, which estimates the outgoing acoustic pressure at an observer placed inside the instrument via a surface integral of hydrodynamic variables in the mouthpiece-reed system. The FW-H estimation is based on a two-dimensional computational aeroacoustic model developed with the lattice Boltzmann (LB) method, which computes the integrands in the FW-H formulation. The FW-H acoustic analogy is validated by comparing the estimated pressure at the observer to that simulated by the LB model and a good agreement is found. The outgoing pressure at the observer is further decomposed into contributions from monopole and dipole sources, which correspond to different terms in the FW-H formulation. The monopole sources come from the modulated jet flow entering the mouthpiece and the displacement flow induced by the moving reed, whereas dipole sources are produced by the unsteady force exerted on the fluid by the solid walls. Results show that dipole sources, particularly those associated to the long inclined mouthpiece baffle, dominate the observed pressure at the studied playing frequency of 230 Hz.

ABSTRACT. The Sheng (Chinese mouth-organ) is a family of free-reed instruments with over 3000 years of documented history and remains an integral member of many traditional East Asian musical ensembles. While the mechanics and acoustic response of individual free-reeds – which may be driven both by inhaling (draw) and exhaling (blow) – have been studied, we describe here the typical performance of the Sheng (as a system of free-reed + pipe resonators) to facilitate further documentation, improvement and propagation of the instrument’s de-sign, performance and pedagogy.

To map the typical performance parameter space (SPL vs pitch consistency) of a concert-grade ‘alto’ Sheng, an expert player sounded the instrument across its tessitura, at three dynamic levels, for both blow vs draw gestures. In terms of SPL, we identify the most efficient register of the instrument, the typical dynamic range available for each note, and the typical consistency expected when delivering a musical dynamic; three types of pressure-signal biases are also identified, regardless of direction of draw/blow. In terms of pitch, we note that (unlike other wind-instruments) intonation tends to flatten with in-creasing dynamic level. However, when performing the same musical dynamic, intonation is fairly consistent regardless of draw vs blow gestures, with the player delivering the best consistency in the upper register of the instrument.

ABSTRACT. The Chinese transverse flute Dízi, as a traditional instrument, is made from found organic material – bamboo. By carefully selecting bamboo blanks of ideal geometry and quality, expert makers fashion them into concert-grade instruments with seemingly minimal intervention (apart from boring embouchure- and finger- holes). We collaborated with a master Dízi-maker from Singapore and document the acoustic impedance spectra at various stages of fabrication, as simple bamboo blanks transform into concert-grade instruments. These measurements are interpreted in light of geometric, fabrication and material treatment considerations, including observations on the maker’s intuitive judgement and subjective assessment of the blanks and their quality. Finally, we present an online compendium of acoustic impedance spectra of one such completed Dízi for all standard (and non-standard) fingerings over the instrument’s standard tessitura.

ABSTRACT. In this study, we consider the case of the trumpet to study the role of timbre quality from the perspectives of music pedagogy and music information retrieval. Prominent brass pedagogues have reported that the presence of excessive muscle tension and inefficiency in playing by a musician is reflected in the timbre quality of the sound produced, which is easily distinguished by an experienced ear. A technological tool that provides an automatic feedback on the tone quality can be of immense help for new learners to develop good playing habits during independent practice. To develop such a tool, an extensive dataset consisting of more than 19,000 tones played by 110 trumpet players of different expertise has been collected. We manually labelled a subset of 1,711 notes from this dataset with a grade on a scale of 1 to 4 based on the perceived efficiency of sound production. A classifier model with a mean 10-fold cross validation accuracy above 80\% was developed based on the extracted audio features to predict the level of efficiency. Finally, we present an interface for the application of this model in pedagogical contexts, in the framework of commercially available music education systems.

ABSTRACT. Stroboscopic digital image correlation allows to measure saxophone reed displacement and strain over the entire surface of the reed which is not covered by the lip. During the vibration cycle, at the moment where the reed touches the tip and side rails of the mouthpiece, the reed bends along the direction perpendicular to its long axis. Due to this bending, the center part of the reed tip is lower than its circumference, and compressive strain suddenly develops. This paper investigates the bending of a reed on a normal mouthpiece and a mouthpiece with a thin supporting ridge placed underneath the reed and parallel to the reed fibers so that it has minimal influence on the airstream. No vibration is obtained when the ridge is as high as the side rails. With a ridge 0.2 mm lower than the side rails, bending and strain were similar to the normal mouthpiece. However, an extra bounce effect of the reed on the mouthpiece was observed in the displacement curve. A professional player evaluated both mouthpieces. The high ridge mouthpiece was found to be unplayable. The mouthpiece with a slightly lower ridge influenced tone quality but was found to be playable. In conclusion, the transversal bending of the reed is an essential aspect of reed dynamics, and bidirectional elasticity parameters are important.

ABSTRACT. Apart from the obvious differences, there are interesting parallels between the trombone and the voice. Both instruments are air driven by lung pressure and excited by a valve mechanism of vibrating lips, with further downstream a tube or tract that can be considered to act like a filter. In this study, we used spectral Voice Range Profile (VRP) recording to characterize the similarities and differences in acoustic features in the singing voice of a professional baritone and a trombone. Selected maps are presented; together they demonstrate the differences in sound characteristics, that we try to relate to differences in the sound production in both instruments. Maximum sound levels for the trombone were not dependent on the fundamental frequency. In the trombone, we found considerably lower jitter values, when compared to the voice. Several metrics characterize the trombone waveform as less complex, consisting mostly of a single pulse. The spectrum balance and H2/H1 parameters mark the sudden introduction of high frequency energy around 100 dB SPL over the whole tonal range of the trombone.

ABSTRACT. The motion of a plucked harpsichord string is analysed with a numerical model during the time it is lifted at the plucking point. The attack wave is shown to be reflected from the fixed ends of the string back to the plucking point. Depending on the timing of the arrival of these reflections at the plectrum the force that the string exerts onto the plectrum can increase or diminish, leading to variations in the maximum amplitude at the moment of release. This timing is determined mainly by the frequency of the note. Based on simulations with the numerical model, a diagram is compiled that summarises the practical possibilities to obtain loudness variations over the keyboard range of the harpsichord. Understanding the workings of the reflected attack wave also allows for the compilation of a list of char- acteristics of the construction and regulation of a harpsi- chord that can conceivably influence a player’s ability to produce loudness effects on a particular instrument.

ABSTRACT. In this paper, we present a numerical method for solving the biharmonic equation using finite difference methods, which can be used for fast acoustic simulation with nonlinear plate dynamics. With the simply supported boundary condition, the linear system could be regarded as a composition of two Poisson's equations, and these Poisson's equations are solved by the Thomas algorithm for a series of tridiagonal systems after transpositions and linear transformations for vectors in the systems and all non-empty blocks of the Laplacian matrix. We also point out that the eigendecomposition used for these linear transformations has a closed-form formula, which is easy to be pre-computed and also space-saving. Furthermore, since this solver is computed block by block and does not need sparse matrix operations, this method is good for single instruction multiple data (SIMD) parallelization using advanced vector extensions (AVX) intrinsics on central processing units (CPUs), which makes it possible to execute at fast speeds for real-time music applications. We also show that this solver for the simply supported boundary condition can also be easily adapted for other boundary conditions using Woodbury matrix identity with a little extra complexity. Numerical experiments show that the C++ implementation of this method is faster than decomposition-based solvers (like LU or Cholesky decomposition) of some well-known C++ libraries at the scale of applications in the field of musical acoustics.

ABSTRACT. The concert kantele is a trapezoidal plucked string instrument initially developed by Paul Salminen in Finland and in the US in the early 20th century to extend the repertoire of the traditional kantele. The concert kantele features a lever mechanism similar to that of the concert harp to raise and lower the pitch of each of the 40 strings by a semitone. The concert kantele is characterised by a bright beating tone with a long sustain. It is also a rather quiet instrument. In this paper, the acoustics of the concert kantele are discussed with measurements of several instrument specimens by the same maker, and with the help of some modelling.

ABSTRACT. The woodblock is generally regarded as an idiophone. It is similar to a large slit drum on a smaller scale, usually made from a single block of wood, and widely employed in concert music, pop bands, percussion ensembles, Latin American music, and other genres. It is called a "pitched instrument", with a rather clear tonal sound. Each woodblock is finely adjusted to match a given note and delivered with a label to identify its pitch. In spite of an established classification by organologists and percussionists as an idiophone, a careful analysis will indicate that the woodblock's nominal pitch is directly related to the acoustical resonance of the instrument cavity. If it is so, one might consider the woodblock as an air chamber with a wooden flexible layer that is excited by the striking of a mallet, thus, relocating it to the category of the aerophones, or, at least, declaring it as belonging to both categories. We present a model for the prediction of the pitch of a woodblock and compare the experimental data obtained from commercial instruments, expecting that the conclusions might foster the dialog between acoustics, organology, and musical pedagogy.

ABSTRACT. Playing a musical instrument to convey a convincing and engaging performance requires mastering several musical and technical aspects of playing the instrument. Timing and loudness of notes are recognised as important components of conveying musical expression, but also important are finer aspects such as the timbre of notes, how rapidly a note starts as well as fine variations of loudness and pitch within the note. An expert musician acquires a subtle control (often subconscious) of the gestures needed to produce these sound results, but they are usually difficult to observe or communicate. This presentation introduces the MIPCAT, a hardware and software toolbox that can be used to record simultaneously the sound and the action of a musician: the variables that directly affect the sound such as (in the example of a reed instrument) blowing pressure and bite force, but also body gestures or mouth-mouthpiece geometry, captured via general-purpose cameras. The toolbox also facilitates data processing and analysis in a semi-automatic way. To demonstrate the potential use of the MIPCAT in pedagogy, we show measurements of the gestures of a beginner clarinettist in comparison with those of a panel of expert players.

ABSTRACT. Instrumental music has the fascinating capacity to communicate emotions, sometimes with subtlety. Most previous research has mainly focused on comparing features of recordings (e.g. sound level, tempo and timbre) of music conveying different emotions, rather than detailed gestures that musicians use during music playing, which would be useful for music students, teachers and music researchers. This paper reports an experimental study on how expert clarinet players express six different emotions when playing the same pieces of music: happy, sad, expressive, angry, fearful and lacklustre. Parameters showing musicians’ continuous control of blowing pressure, reed displacement and embouchure details were measured, as well as variables mentioned above in the recorded music; all were analysed semi-automatically using an innovative toolbox developed for this study. The results show how the emotions can be differentiated not only by the variables in the music, but also the details of how musicians controlled the instrument to produce them. These results also have potential applications in training musicians in expressive playing.

ABSTRACT. Vibrato is a central component of western classical singing technique. As such, it is important for singers to have an understanding of the acoustic characteristics of vibrato and how those features could develop over a course of study.

Vibrato rate and extent were calculated automatically from recordings of sustained tones for 141 voice majors from the Hochschule für Musik Carl Maria von Weber Dresden, collected at the beginning and conclusion of university studies over a period from 2002 to 2021.

Median vibrato extent for all students increased from 19 cents, interquartile range (IQR) (12, 33) to 32 cents, IQR (20, 51). The median vibrato rate increased from 5.44 Hz, IQR (5.01, 5.78) to 5.59 Hz, IQR (5.08, 6.09) while the standard deviation of vibrato rate decreased from the initial recording to the final recording at graduation: 0.20 Hz IQR (0.09, 0.58) to 0.11 Hz, IQR (0.07, 0.28).

The classical voice majors considered in this study exhibited increased vibrato extent and vibrato rate stability during sustained tones at the conclusion of conservatory studies.

ABSTRACT. We examined the impact of the perception of singing togetherness, as indexed by the spectral envelope of the sound, and task complexity on choristers’ body motion, as they performed in duo with a pre-recorded tune presented over a loudspeaker. Fifteen experienced choral singers first manipulated the spectral filter settings of the tune in order to identify the re-cordings they felt most and not at all together with. Then, they sang the tune in unison and canon along with the recordings featuring the chosen filter settings. Audio and motion capture data of the musicians' upper bodies during repeated performances were collected. Results demonstrate that wrist motion was more peri-odic, singer posture more open, and the overall quantity of body motion higher when singing in unison than in canon; singing togetherness did not impact body motion. The current findings suggest that some body movements may support choral performance, depending on the complexity of the task condition.