This paper is a collection of corrections and related thoughts for Bevil's thesis The Welsh Crwth, Its History and Its Genealogy.

Of the many waveforms the bowed string can assume, theso-called "Helmholtz motion" (Helmholtz 1862) gives the fullestsound in terms of power and overtone richness. The developmentof this steady-state oscillation pattern can take manydifferent paths, most of which would include noise caused bystick-slip irregularities of the bow-string contact. Of thefive papers included in the thesis, the first one shows, notsurprisingly, that tone onsets are considered superior when theattack noise has a very limited duration. It was found,however, that in this judgment thecharacterof the noise plays an important part, as thelistener’s tolerance of noise in terms of duration isalmost twice as great for "slipping noise" as for "creaks" or"raucousness" during the tone onsets. The three followingpapers contain analyses focusing on how irregular slip-sticktriggering may be avoided, as is quite often the case inpractical playing by professionals. The fifth paper describesthe triggering mechanism of a peculiar tone production referredto as "Anomalous Low Frequencies" (ALF). If properly skilled, aplayer can achieve pitches below the normal range of theinstrument. This phenomenon is related to triggering wavestaking "an extra turn" on the string before causing thestring’s release from the bow-hair grip. Since transverseand torsional propagation speeds are both involved, twodifferent sets of "sub-ranged" notes can be produced this way.In the four last papers wave patterns are analysed andexplained through the use of computer simulations. Key words: Key words: Bowed string, violin, musicalacoustics, musical transient, anomalous low frequencies,Helmholtz motion

<p>Of the many waveforms the bowed string can assume, theso-called "Helmholtz motion" (Helmholtz 1862) gives the fullestsound in terms of power and overtone richness. The developmentof this steady-state oscillation pattern can take manydifferent paths, most of which would include noise caused bystick-slip irregularities of the bow-string contact. Of thefive papers included in the thesis, the first one shows, notsurprisingly, that tone onsets are considered superior when theattack noise has a very limited duration. It was found,however, that in this judgment the<i>character</i>of the noise plays an important part, as thelistener’s tolerance of noise in terms of duration isalmost twice as great for "slipping noise" as for "creaks" or"raucousness" during the tone onsets. The three followingpapers contain analyses focusing on how irregular slip-sticktriggering may be avoided, as is quite often the case inpractical playing by professionals. The fifth paper describesthe triggering mechanism of a peculiar tone production referredto as "Anomalous Low Frequencies" (ALF). If properly skilled, aplayer can achieve pitches below the normal range of theinstrument. This phenomenon is related to triggering wavestaking "an extra turn" on the string before causing thestring’s release from the bow-hair grip. Since transverseand torsional propagation speeds are both involved, twodifferent sets of "sub-ranged" notes can be produced this way.In the four last papers wave patterns are analysed andexplained through the use of computer simulations.</p><p>Key words:</p><p>Key words:</p><p>Bowed string, violin, musicalacoustics, musical transient, anomalous low frequencies,Helmholtz motion</p>

In the early years of the nineteenth century, when bowed string instruments were assumed to have reached the apex of their development, there arose among antiquarians and scholars a widespread interest in tracing the ancestry of the violin and related members of the chordophone family. This task proved to be exceedingly formidable not only because of the enormous amount of often obscure evidence which had to be taken into consideration but also because of the manner in which many items of evidence seemed to contradict each other. The issue is still not resolved to the complete satisfaction of every party concerned. Literally scores of different and often conflicting arguments have been advanced, and it could perhaps be justly said that the only furtherance thus far realized has been that of the confusion rather than the resolution of the issue.

This thesis addresses sound production in bowed-string instruments from two perspectives: the physics of the bowed string, and bow control in performance. Violin performance is characterized by an intimate connection between the player and the instrument, allowing for a continuous control of the sound via the main bowing parameters (bow velocity, bow force and bow-bridge distance), but imposing constraints as well. In the four included studies the focus is gradually shifted from the physics of bow-string interaction to the control exerted by the player. In the first two studies the available bowing parameter space was explored using a bowing machine, by systematically probing combinations of bow velocity, bow force and bow-bridge distance. This allowed for an empirical evaluation of the maximum and minimum bow force required for the production of a regular string tone, characterized by Helmholtz motion. Comparison of the found bow-force limits with theoretical predictions by Schelleng revealed a number of striking discrepancies, in particular regarding minimum bow force. The observations, in combination with bowed-string simulations, provided new insights in the mechanism of breakdown of Helmholtz motion at low bow forces. In the second study the influence of the main bowing parameters on aspects of sound quality was analyzed in detail. It was found that bow force was totally dominating the control of the spectral centroid, which is related to the perceived brightness of the tone. Pitch flattening could be clearly observed when approaching the upper bow-force limit, confirming its role as a practical limit in performance. The last two studies were focused on the measurement of bowing gestures in violin and viola performance. A method was developed for accurate and complete measurement of the main bowing parameters, as well as the bow angles skewness, inclination and tilt. The setup was used in a large performance study. The analyses revealed clear strategies in the use of the main bowing parameters, which could be related to the constraints imposed by the upper and lower bow-force limits and pitch flattening. Further, it was shown that two bow angles (skewness and tilt) were systematically used for controlling dynamic level; skewness played an important role in changing bow-bridge distance in crescendo and diminuendo notes, and tilt was used to control the gradation of bow force. Visualizations and animations of the collected bowing gestures revealed significant features of sophisticated bow control in complex bowing patterns. / QC 20100809

L'étude par continuation des solutions périodiques et quasi-périodiques est appliquée à plusieurs modèles issus du violon. La continuation pour un modèle à un degré de liberté avec friction régularisée permet de montrer la préservation, par rapport à la friction de Coulomb, des bifurcations de cycle limite (une vitesse maximale et une force minimale permettant le mouvement de Helmholtz) et de propriétés globales de la branche de solution (croissance de l'amplitude avec la vitesse, décroissance de la fréquence avec la force normale). L'équilibrage harmonique est évalué sur la friction régularisée et a des propriétés de convergence intéressantes (erreur faible, monotone, à décroissance rapide). La continuation sur un modèle à deux modes donne accès aux solutions de registres supérieurs, dont la stabilité coïncide avec l'expérience. La valeur retenue pour l'inharmonicité peut modifier fortement le diagramme de bifurcation. Une nouvelle méthode de continuation des solutions quasi-périodiques est proposée. Elle associe l'EH étendu à deux pulsations avec la Méthode Asymptotique Numérique. Une attention particulière est portée à la rapidité des calculs, face à la croissance rapide de la taille des systèmes à inverser. Un modèle de friction prenant en compte la température au point de contact est reformulé à l'aide d'une dérivée fractionnaire. Nous proposons une méthode de continuation de solutions périodiques de systèmes contenant des dérivées ou intégrales fractionnaires. Nous établissons une condition suffisante pour que les cycles asymptotiques du cadre causal (Caputo) soient solutions du cadre que nous avons choisi. / The continuation of periodic and quasi-periodic solutions is performed on several models derived from the violin. The continuation for a one degree-of-freedom model with a regularized friction shows, compared with Coulomb friction, the persistence of limit cycle bifurcations (a maximum bow speed and a minimum normal force allowing Helmholtz motion) and of global properties of the solution branch (increase of amplitude with respect to the bow speed, decrease of frequency with respect to the normal force). The Harmonic Balance Method is assessed on this regularized friction system and shows interesting convergence properties (the error is low, monotone and rapidly decreasing). For two modes the continuation shows higher register solutions with a plausible stability. A stronger inharmonicity can greatly modify the bifurcation diagram. A new method is proposed for the continuation of quasi-periodic solutions. It couples a two-pulsations HBM with the Asymptotic Numerical Method. We have taken great care to deal efficiently with large systems of unknowns. A model of friction that takes into account temperature of the contact zone is reformulated with a fractional derivative. We then propose a method of continuation of periodic solutions for differential systems that contain fractional operators. Their definition is usually restricted to causal solutions, which prevents the existence of periodic solutions. Having chosen a specific definition of fractional operators to avoid this issue we establish a sufficient condition on asymptotically attractive cycles in the causal framework to be solutions of our framework.

This thesis treats the control of sound synthesis of bowed string instruments based on physical modelling. The work followed two approaches: (a) a systematic exploration of the influence of control parameters (bow force, bow velocity, and bow-bridge distance) on the output of a physical model of the violin, and (b) measurements and analyses of the bowing parameters in real violin playing in order to model and parameterize basic classes of bowing patterns for synthesis control.First a bowed-string model based on modal solutions of the string equation is described and implemented for synthesis of violin sounds. The behaviour of the model is examined through simulations focusing on playability, i.e. the control parameter space in which a periodic Helmholtz motion is obtained, and the variations of the properties of the simulated sound (sound level and spectral centroid) within this parameter space. The response of the model corresponded well with theoretical predictions and empirical expectations based on observations of real performances. The exploration of the model allowed to define optimal parameter regions for the synthesis, and to map sound properties on the control parameters.A second part covers the development of a sensor for measuring the bow force in real violin performance. The force sensor was later combined with an optical motion capture system for measurement of complete sets of bowing parameters in violin performance.In a last part, measurements of the control parameters for basic classes of bowing patterns (sautillé, spiccato, martelé, tremolo) are analyzed in order to propose a realistic control of the sound synthesis. The time evolution of the bowing parameters were modelled by analytical functions, which allowed to describe and control simulated bowing patterns by a limited set of control parameters. For sustained bowing patterns such as détaché, control strategies for basic elements in playing (variations in dynamic level, bow changes) were extracted from exemplary measurements, and simple rules deduced, which allowed extrapolation of parameters to modified bow strokes with other durations and at different dynamic levels. / Denna avhandling behandlar styrning av syntes av stråkinstrument med tillämpningar inom fysikalisk modellering av musikinstrument. Problemet har angripits i två steg, först genom en systematisk undersökning av inflytandet av styrparametrarna i violinspel (stråkkraft, stråkhastighet, och avstånd stråke-stall) på utsignalen från en fysikalisk modell, följt av mätningar och analyser av stråkningsparametrarna i normalt violinspel med syfte att modellera och parameterisera grundläggande klasser av stråkarter för styrning av syntesen. En modell av interaktionen mellan stråke-sträng har utvecklats baserad på modal syntes och modellen har implementerats för syntes av violintoner. Modellen har utforskats genom simuleringar inriktade dels på spelbarheten, dvs. gränserna för den parameterrymd inom vilken en periodisk Helmholtz-rörelse erhålls, och dels på variationerna hos det syntetiserade ljudets egenskaper (ljudnivå och spektral centroid) inom detta parameterområde. Modellens egenskaper motsvarade väl de teoretiska prediktionerna och förväntade resultat från observationer av violinster. Utforskningen av modellen gjorde det möjligt att definiera optimala parameterområden för styrning av syntesen, och även avbilda ljudens egenskaper på styrparametrarna. En sensor för mätning av stråkkraften utvecklades för att kunna genomföra mätningar under normalt spel. Sensorn kombinerades senare med ett optiskt system för rörelseanalys vilket gjorde det möjligt att mäta kompletta uppsättningar av stråkparametrar under spel. Uppmätta styrparametrar för grundläggande klasser av stråkarter (sautillé, spiccato, martelé, tremolo) analyserades för att ge tillgång till realistiska styrförlopp av syntesen. Stråkningsparametrarna modellerades med analytiska funktioner, för att kunna beskriva och styra simulerade stråkningsförlopp med ett begränsat antal modellparametrar. För stråkarter med uthållna toner som détaché utvecklades styrstrategier för grundläggande element i spelet, som ändringar i styrkegrad och stråkväxlingar, utifrån mätningar på typfall. Enkla regler formulerades för att kunna extrapolera parametrarna till modifierade stråk med andra durationer och styrkegrader. / Cette thèse porte sur le contrôle de la synthèse sonore par modélisation physique des instruments à corde frottée. Il se base, d’une part, sur l’exploration systématique de l’influence des paramètres de contrôle (pression d’archet, vitesse de l’archet et distance au chevalet) sur le comportement du modèle, et d’autre part, sur la mesure et l’analyse du contrôle effectif qu’exerce l’instrumentiste afin de modéliser et paramétriser des modes de jeu typiques pour le contrôle de la synthèse. Un modèle de corde frottée basé sur la résolution modale de l’équation de la corde est d’abord présenté et implémenté pour la synthèse sonore du violon. Le comportement du modèle physique est ensuite examiné en effectuant un grand nombre de simulations et se concentre sur deux aspects : la “jouabilité", c’est-à-dire l’espace des paramètres de contrôle dans lequel un mouvement de Helmholtz périodique est obtenu, et les variations des propriétés du son synthétisé (niveau sonore et centroïde spectral) à l’intérieur de cet espace de paramètres. Un très bon accord a été trouvé entre, d’une part, le résultat des simulations et, d’autre part, les prédictions théoriques ou empiriques basées sur l’expérience des instrumentistes. Cette exploration systématique a permis de définir des régions optimales pour le jeu dans l’espace des paramètres de contrôle et de décrire quantitativement la correspondance entre les propriétés sonores pertinentes et les paramètres de contrôle. La deuxième partie de ce travail concerne la mise au point d’un capteur pour mesurer la force d’appui de l’archet sur la corde dans un contexte de jeu réel. Le capteur est ensuite combiné avec un système optique de capture du mouvement afin de mesurer les paramètres de jeu du violoniste. La dernière partie présente l’analyse des mesures de ces paramètres de contrôle pour des modes de jeu typiques (sautillé, spiccato, martelé, tremolo), afin de proposer un contrôle réaliste de la synthèse sonore. L’évolution temporelle des paramètres de jeu est modélisée par des fonctions analytiques, ce qui permet de décrire et de simuler différents modes de jeu par un nombre limité de paramètres. Pour les modes de jeu soutenus tels que le détaché, les mesures permettent de décrire des stratégies de contrôle pour des tâches typiques (variation de niveau sonore, changement de direction d’archet), et des procédures simples ont été déduites, permettant d’extrapoler les paramètres de contrôle afin de changer le niveau sonore ou la durée des coups d’archet. / QC 20100714. Gemensam forskarutbildning KTH och Universite Pierre et Marie Curie (Paris VI).