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Session 01 Violins

The bowed string as we understand it today
Woodhouse, Jim
Cambridge University, Engineering, Cambridge, United Kingdom

The vibration of a bowed string has been studied since the 19th century, and today this problem is the only example of vibration excited by friction which can claim to be well understood. Today's theoretical models embody many of the complicating features of real strings, instruments and bows, and detailed comparisons with experimental studies are allowing fine tuning of the models to take place. The models can be used to explore questions directly relevant to instrument makers and players This lecture will review the history of bowed-string research, and highlight recent developments and current issues. Probably the main unresolved question at present concerns an accurate description of the frictional behaviour of rosin, since recent results have shown that none of the friction models used in the existing literature is entirely credible.

Generalized normal mode violin acoustics
G Bissinger
East Carolina U, Physics, Greenville, NC, United States

A constantly growing violin normal mode database presents significant opportunities to relate specific modal properties such as the 1st corpus bending mode frequencies to violin quality. Perhaps more interesting however is the prospect of extracting general aspects of violin sound related to quality classes such as "good" or "bad". Frequency-related trends for various measured properties, viz., total damping, radiation efficiency/damping, and internal damping, are of fundamental interest because of their connection to the vibratory energy expenditure of the violin. For example, (aggregate) violin internal damping obtained by subtracting radiation damping from total damping was surprisingly insensitive to violin quality, while the parent dampings were not. Because damping trendlines for each energy loss path are independent of excitation particulars, they provide insights into the spectral balance of radiation from the violin while sidestepping the role of the intermediate bridge-corpus energy transfer, i.e., a "bridge-less" violin. Computing the fraction-of-vibrational-energy-radiated from the radiation-total damping ratio up to 8 kHz reveals a mechanism related to the critical frequency for a "good" violin radiating more in the 3 kHz region relative to a "bad" violin. Finally some aspects of f-hole vs. structure contributions to the far-field radiation will be presented.

An acoustical comparison of flat- and round-backed double basses
A W Brown
University of Music and Dramatic Arts Vienna, Institut fuer Wiener Klangstil, Vienna, Austria

The form of the violin has prevailed as the standard for the violin, viola and violoncello, but not for the double bass. Surveys reveal that while some tendencies exist among instrument makers and musicians, opinions about the sound of the two main types of basses, flat- and round-backed, often conflict. Several new double basses of nearly identical form and extremely similar materials were created especially for this study, presenting a unique opportunity to define acoustical characteristics of flat-backed and round-backed basses. The pairs of instruments differ, in theory, only in the form of the back. Laser vibrometry, analysis of audio recordings made in an anechoic chamber, and listening test surveys were used to delineate differences between the types concerning radiation characteristics and timbre. A special flat back for an existing violoncello was also made, tested and compared to a similar instrument of the standard form. Room acoustics and psychoacoustical considerations are discussed along with experimental results to offer an explanation about why the double bass is the only modern bowed instrument in use that has a flat back.

Operating deflecting modes of five conventional and two unconventional violins recorded with TV-holography
A Buen¹, O J Løkberg²
¹Brekke & Strand akustikk as, Building acoustics, Oslo, Norway; ²The Norwegian University of Science and Technology, Institute of Physics, Trondheim, Norway

TV-holography has been used to study operating deflecting modes in seven violins including an old Italian. Two of these instruments were made of plywood with a special bar design, the patented "Hagetrø violin". Mode shapes, vibration phase, -frequencies, levels and Q-values were recorded for frequencies under 1400Hz. Generally corresponding modes of the seven violins looked similar, though differences were detected, especially in phase mappings of the vibrations. Combinations between modes were observed as the rule. The C3 and C4 modes appear as breathers in some instruments and as non-breathers in others. The Hagetrø violins were both breathing in these modes. All instruments had double or triple resonances where distinct modes appeared with similar vibration patterns at two or three maxima. This coupling effect was somewhat clearer in the higher quality instruments. Vibration velocity plots show clear differences in vibration levels among the violins. Playing tests in an echo free room indicated that the more intense sounding instruments are those with higher velocity levels. The modes were more damped in five varnished than in two unvarnished instruments.

Numerical optimization of violin bows with varying densities of the wood material
P Carlsson, M Tinnsten
Mid Sweden University, Information Technology and Media, Ostersund, Sverige

The wood material for violin Bows from the Pernambuk tree (Guilandina echinata) has large individual variations in the density. For high quality bows, the higher densities are preferred, but since the Pernambuk is rather rare and expensive, it is of interest to investigate if it is possible to compensate for density variations in the wood material, at the same time as the first eigenfrequencies, the total mass and location of the center of gravity of the bow is unchanged. The mechanical calculations of the bow is made with a numerical model in the finite element program ANSYS, and in this first approach, the calculations considers only the elastic properties of the bow, damping is not included. In order to perform automatic optimization of the geometry of the bow, the FEM-program ANSYS is coupled to an external optimization routine. The stochastic Simulated Annealing method (SA) is used as optimization routine, and the routine has showed good performance in similar problems with several local minima.

Experiments with an automatic bowing machine
P M Galluzzo, J Woodhouse
Cambridge University, Engineering, Cambridge, United Kingdom

In order to validate and develop theoretical models of the action of a bowed string, careful experimental work is needed. It is already known that current models predict behaviour which is qualitatively plausible, but can they predict accurately the details of the transient response to specific bowing gestures? A computer-controlled bowing machine has been developed which allows reproducible gestures to be made, in which the velocity and force waveforms can be specified. This allows systematic experiments to be made in which a portion of parameter space is explored by varying parameters in small steps. These results can be compared directly to corresponding simulated results, and the identical automatic processing of the string transients can be applied to both so that the comparison is fair. This comparison reveals that some aspects of behaviour are quite well captured by current models, but that other features are not reproduced. Careful study of the results can guide further development of the theoretical models.

Psychoacoustic investigations on the possibility of aurally identical violins
P Geissler¹, O Martner¹, C Zerbs¹, M Schleske²
¹Müller-BBM, Schalltechnisches Beratungsbüro, Planegg, Germany; ²Meisteratelier für Geigenbau, Munich, Germany

"Is it possible to make sound copies of violins?" To answer this question one needs to know the ingredients which make two violins being judged by musicians to be aurally identical. Using a questionnaire among 50 musicians verbal attributes related to the sound characteristics of violins were collected and ranked. Subjective listening tests were carried out to check which verbal attributes are suitable and do evoke the same meaning in different persons. Useful attributes for the ranking could be found using statistical measures for consistency and concordance. Additionally, it was found that the measurement uncertainty of frequency response measurements today is smaller than the analysis resolution of the human ear in regard to frequency and amplitude in the frequency range important for the hearing sensation and for room acoustic situations typical for a violin maker's workshop. The results give strong indications that the psychoacoustic characteristics of the human ear and the vibroacoustic characteristics of the violin body in combination with the attributes judged to be important for violin sound quality will in principle allow for the idea of making sound copies of a given violin.

The influence of vibrato and noise on the assessment of violin tone
C Gough
University of Birmingham, School of Physics and Astronomy, Birmingham, United Kingdom

We investigate the influence of vibrato and noise on the perception of the tonal quality of a violin in two ways. First, we consider recorded sound of both high and poor quality violins. By continuous repetition of single period waveforms, we remove the frequency, amplitude, and noise fluctuations introduced by the performer playing the instrument, whilst retaining the sampled spectral information relating to resonances of the particular violin being played. Audio demonstrations demonstrate the importance of the fluctuations in frequency, amplitude and spectral timbre in identifying the sound as that of a violin. We therefore argue that such fluctuations must be equally important in any subjective assessment of the quality of a violinīs tone. To investigate such correlations, we have developed computational models, which enable the listener to judge the influence of vibrato amplitude and frequency on the tone of an idealised multi-resonant violin. In particular, we also demonstrate how the influence of vibrato depends critically on the Q-values and density of the vibrational modes excited. Such factors are clearly correlated with the "quality" of the wood used in a violinīs construction and the thicknesssing of plates by the luthier.

Bow speed or bowing position - which one influences spectrum the most?
K Guettler¹, E Schoonderwaldt², A Askenfelt²
¹Norwegian Academy of Music, Oslo, Norway; ²KTH, Dept. of Speech, Music and Hearing, Stockholm, Sweden

Raman and Schelleng analysed waveform properties of the bowed string as function of bow speed, bow force, and bow position (the distance between bow and bridge). Schelleng also described spectral changes caused by alterations of the bow force alone. This phenomenon was later explained by Cremer, and referred to as "rounding of the Helmholtz corner". In this study it is shown that of the remaining two parameters, it is the bow's speed rather than its position that bears a potential of changing the shape of the string's spectral envelope. This contrasts to the popular belief that by bringing the bow closer to the bridge, the sound automatically becomes more brilliant.

The BH-hill and tonal quality of the violin
E V Jansson
KTH, TMH, Stockholm, Sweden

In the frequency range of maximum sensitivity of the ear the so-called BH-hill can be found. The BH-hill is not confined to the violin bridge only. A normal bridge and a bridge plate (a bridge with only feet tips but no cutting outs as heart, ear etc) give mainly the same BH-hills. The same bridge on a Stradivarius violin and a new violin gives differently shaped BH-hills.
A couple of forces (two forces in opposite directions) one at each bridge foot gives a BH-hill, both for a normal bridge and a bridge plate. A momentum applied at the central line of the top plate gives no BH-hill.
The BH-hill is much affected by the distance between the two feet, i.e. between the two forces of the couple. The cross-stiffness of the top plate also gives a large influence.
The importance of the bridge hill will be demonstrated by playing two violins, one with a normal BH-hill and another violin with no BH-hill.
Thus it will be demonstrated that the BH-hill is very important and that it is mainly set by the bridge feet distance and the top plate properties at the bridge feet.

Unsupervised machine learning methods in timbral violin characteristics visualization
E Lukasik, R Susmaga
Poznan University of Technology, Institute of Computing Science, Poznan, Poland

We apply a mixture of unsupervised learning and statistical methods to find and illustrate similarity and dissimilarity factors in the timbre of violin voices. Our data come from the AMATI sound database that contains digitized recordings of 70 musical instruments presented at the Henryk Wieniawski 10th International Violinmakers Competition in Poznan, Poland, 2001. The raw sound data served to extract various sets of features, including harmonic based parameters (e.g. brightness, tristimulus, even and odd harmonics content), spectral parameters (e.g. energy, moments of various order), mel and linear scale cepstral coefficients, spectral envelope features (maxima and minima) and human ear auditory model features (the Lyon's model). We demonstrate machine ability to perceive the differences of violin timbre by applying multidimensional scaling (MDS) paradigm to the results of both classic and enhanced clustering methods. The MDS-based visualization leads to better perception and comprehension of the analyzed multi-dimensional space of the timbre characteristics. The ultimate MDS result is finally enhanced by the introduction of Voronoi diagrams, which can be displayed in form of both planar and spherical maps.

AMATI: A multimedia database of violin sounds
E Lukasik
Poznan University of Technology, Institute of Computing Science, Poznan, Poland

We present a database AMATI, entirely devoted to the violin voices. The instruments recorded are master quality and represent international schools of violinmaking. They were competitors of the 10th International Henryk Wieniawski Violinmaker Competition, held in Poznan in autumn 2001. There are 17 000 sound files gathered in the database. The collection of sounds comprise material similar to the one that the jury of musicians examined during the audition. It includes open string bowed and pizzicato sounds, the entire range of notes across a chromatic scale on each string, a range of notes of diatonic scale and a fragment of J.S. Bach's work. For each instrument the basic information is provided, including a photo, an emblem, the violinmaker's nationality, etc. The averaged scores of musical jury judgements constitute the unique and important element of the database, making search for relationships between objective and subjective measure possible. The database contains harmonics based parameters for each sound. Parameter values may be visualized and compared in multiple configurations using a variety of charts created on-line. Signal waveforms, spectra and spectrograms are also available. Numerical values of parameters may be exported and used for further study. The database is an open source product (My SQL) and may be distributed among researchers.

Logarithmic damping decrement as the characteristic of physical acoustics for quality estimation of violin wedges
E Rajcan, S Urgela, M Culik
Technical University Zvolen, Zvolen, Slovakia

The quality evaluation of elements assessed for bowed instruments making is important for forest economists, wood businessman as well as for music instrument makers. In order to get the more complex data for violin wedges evaluation, to the trinity of characteristics of physical acoustics, measured in previous experiments (the density, modulus of elasticity, acoustical constant) the measurement of logarithmic damping decrement was added. After construction and evaluation of experimental violins made from the samples investigated, the more close linkage between materials characteristics and quality of instruments should be expected.

Effect of the width of the bow hair on the violin string spectrum
E Schoonderwaldt¹, K Guettler², A Askenfelt¹
¹KTH, Dept. of Speech, Music and Hearing, Stockholm, Sweden; ²Norwegian Academy of Music, Oslo, Norway

Violinists often claim that tilting the bow provides greater brilliance. By tilting, the effective width of the bow hair is reduced and the bow force distribution across the bow hair ribbon is changed. Considering that the width of the bow hair of a violin bow is roughly 1/32 of the string length (about 10 mm), and that the relative bow-bridge distance in playing typically varies between 1/8 and 1/32, an effect of the width of the hair on the slip-stick process seems reasonable. Pitteroff has reported simulations and measurements showing that the slipping intervals become progressively shorter as the width of the bow hair ribbon is decreased. [Pitteroff & Woodhouse et al, acta acustica - Acustica 84, 929-946]. However, the effect, which mainly was attributed to a faster transition from stick to slip at release, was small. In this study, evidence gained in experiments using a bowing machine are presented, showing that a decrease of the width of the bow hair may boost the string spectrum considerably for higher harmonics. A gain in partial amplitudes of 3 - 6 dB has been observed above harmonic #20. Besides increased brilliance, it is clear that there are several other reasons for violinists to tilt the bow. For example, tilting the bow hair facilitates gentle note attacks due to a gradual buildup in string contact.

Modeling Savart 's trapezoidal violin using a digital waveguide mesh
S Serafin¹, F Fontana²
¹CCRMA, Music, Stanford, United States; ²University of Padova
Department of Information Engineering, Padova, Italy

An important element of a violin is its body, which filters vibrations that propagate from the string through the bridge. In real-time synthesis of a violin, there is some difficulty in modeling the body because of a tradeoff between accuracy and computational cost. If all the resonances of the body are accounted for by modeling each one with its own pair of filter poles, the computational cost is too high. On the other hand, one cannot implement too few filter poles and neglect the large number of resonances, because the complex filtering of the body contributes strongly to the characteristic timbre of the violin. The complexity of the spectrum of a violin's body is due to the complexity of the shape of the instrument, which is the result of centuries of developments. In the 19th century, Savart proposed a simplification of this shape building a trapezoidal violin. Documents of the period report that, even if the violin was never adopted, its sonorities were perceptually equivalent to the ones of the traditionally shaped violin. In this paper we propose a digital implementation of Savart's trapezoidal violin using a three dimensional waveguide mesh. The dimensions of the mesh are chosen in order to match the dimensions of the instrument as built by Savart. Digital waveguide filters have been used to simulate damped boundary reflection of the acoustic waves against the violin body. Advantages and limitations of Savart's trapezoidal violin are discussed.

Bowed string simulation using an elasto-plastic friction model
S Serafin¹, F Avanzini², D Rocchesso³
¹CCRMA, Department of Music, Stanford, United States; ²University of Padua, D.E.I., Padua, Italy; ³University of Verona, Computer Science, Verona, Italy

The interaction of a bow exciting a string is a complex phenomenon that belongs to the larger field of frictional induced vibrations. In the past, theoretical models of the bow-string interaction assumed that the frictional force at the contact point depends only on the relative sliding velocity between the bow and the string. Recently, Smith and Woodhouse observed that rosin exhibits plastic deformation at the contact point. For this reason, they proposed a model called plastic, in which friction has a dependence on the temperature variations in the interfacial rosin layer. This model exhibits an hysteresis loop in the velocity versus force plane. In robotics and haptics, in order to better predict friction phenomena, dynamic friction models have been proposed, in which the dependence of friction on the relative sliding velocity is given by a differential equation. In this paper we apply the state of the art dynamic friction models. i.e. the elasto-plastic friction models, to the simulation of a bow exciting a string, proposing an accurate yet efficient numerical implementation. Comparisons between Smith and Woodhouse's plastic model and the dynamic friction models are described, which show that an accurate choice of the control's parameters in the dynamic models allow to obtain an hysteresis loop in the friction versus velocity plane similar to the one produced by the plastic model.

Bowed string physical model validation through use of a bow controller and examination of bow strokes
S Serafin¹, D Young 2
¹Stanford University, CCRMA, Stanford, CA, United States; ²Massachusetts Institute of Technology, Media Lab, Cambridge, MA, United States

Bowed string physical models have achieved a level of completeness that allows their performance to be favorably compared to that of their real instrument counterparts. These comparisons are facilitated by the use of refined bow controllers that detect all the subtle changes in motion and force that are experienced by a bow while in contact with a string and give expressive playing its characteristic sound. In this paper we use a real-time bowed string physical model and a wireless bow controller to reproduce the bow strokes that are most fundamental to the right hand technique of an accomplished bowed string player, such as legato, detaché staccato, spiccato, and balzato. We discuss the integration of the two components of these experiments and illustrate how the bow controller is used to control the physical model of the violin in order to faithfully reproduce these strokes. Moreover, we compare the range of input parameters that determine these strokes in the model with the values for these parameters measured on real violins, showing how synthetic instruments may present the same playability regions as real instruments.

Inferring decision rules from jurys' ranking of competing violins
R Slowinski, J Jelonek
Poznan University of Technology, Institute of Computing Science, Poznan, Poland

We present results of analyses carried out for violins that were submitted to the 10th International Henryk Wieniawski Violinmakers Competition. In the analyses we were especially interested in reconstructing the relationship between some pre-defined characteristics of the instruments and the verdict reached by the jury. Taking into account the following criteria: volume of sound, timbre of sound, ease of sound emission, equal sound volume of strings, accuracy of assembly and individual qualities of the instrument, the jury ranked the instruments from the best down to the worst. On the base of this ranking we attempt to infer a preference model that is supposed to re-construct the preference of the jury. We use inductive supervised learning methods that include a preference-modeling tool called Dominance-based Rough Set Approach. The analysis starts with constructing a rough approximation of the preference relation underlying the final ranking. This allows inducing decision rules in terms of criteria considered by the jury but also in terms of other criteria, including various acoustic characteristics of the violins. In both cases, the rules can serve to: (i) explain the decision policy of the jury, (ii) build new rankings for new sets of violins, either evaluated on the jury's criteria or characterized by acoustic features. The approach is especially useful in discovering subsets of acoustic features that are relevant to producing rankings of violins.

Determination of important wood properties for blanks for violin tops by the use of numerical optimization
M Tinnsten, P Carlsson
Mid Sweden University, Information Technology and Media, Ostersund, Sverige

In the strive of understanding how different parameters affects the vibration properties and the characteristics of the sound emanating from a violin, i.e. what makes a good violin good, numerical methods as FEM (finite element method) and BEM (boundary element method) are used. Numerical models of whole violins and/or part of it is created and studied. Crucial for the results from these studies is the correctness of the input data for the numerical analysis. One important group of input data is the wooden material parameters for the part of the violin subjected to analysis. In this study a new method for determining these important material parameters for blanks for violin tops is proposed. In the proposed method a FEM-code is linked together with a stochastic optimization algorithm in order to, in an automatic fashion, determine the material parameters. The method requires the geometrical dimensions, the density, and measured normal modes for the blank and it consider the fact that the Young's modulus in the longitudinal direction varies in the radial direction.

Wireless sensor system for measurement of violin bowing parameters
D Young
Massachusetts Institute of Technology, Media Lab, Cambridge, MA, United States

We present a new system to measure the position and force parameters most relevant to violin bowing technique. It is stable and reliable, and as it allows players to perform without impediment and consists of minimal equipment, it is also suitable for use in professional performance settings. This measurement system, implemented on a carbon fiber bow, relies on an electromagnetic field sensing technique for detecting both transverse bow position and bow-bridge distance and foil strain gauges for downward force measurement. The position data is collected using an antenna that is located behind the bridge and mounted from the tailpiece of an acoustic violin. The strain gauges are permanently mounted around the midpoint of the bow stick, and the force data is collected and sent to a remote computer via a wireless transmitter mounted at the frog. The resultant bow remains wireless, and the placement of the sensors and electronics ensures a balance point that remains within the normal range for traditional bows. We describe several experiments illustrating the usefulness of this system for continued studies of bowing parameters, as well as inspection of musical performance style and pedagogical applications.

The admittance matrix of a cello
J Woodhouse, P Courtney
Cambridge University, Engineering, Cambridge, United Kingdom

The 3x3 admittance matrix at the centre of a cello bridge has been measured directly, using a miniature impulse hammer and laser vibrometer. This contrasts with earlier work, in which the matrix was determined (for a violin) by ingenious but indirect means. Data exhibiting good coherence and correct reciprocal behaviour has been obtained up to 3 kHz (corresponding to 9 kHz on the violin). Results will be shown, and the interpretation will be discussed of some unusual features appearing in the admittances for excitation parallel to the strings. Out-of-plane resonances of the bridge are seen, together with an apparently new vibration mode of the cello structure at about 400 Hz.

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