In this thesis a method to implement the radiation characteristics of musical instruments in wave field synthesis systems is developed. It is applied and tested in two loudspeaker systems.Because the loudspeaker systems have a comparably low number of loudspeakers the wave field is synthesized at discrete listening positions by solving a linear equation system. Thus, for every constellation of listening and source position all loudspeakers can be used for the synthesis. The calculations are done in spectral domain, denying sound propagation velocity at first. This approach causes artefacts in the loudspeaker signals and synthesis errors in the listening area which are compensated by means of psychoacoustic methods. With these methods the aliasing frequency is determined by the extent of the listening area whereas in other wave field synthesis systems it is determined by the distance of adjacent loudspeakers. Musical instruments are simplified as complex point sources to gain, store and propagate their radiation characteristics. This method is the basis of the newly developed “Radiation Method” which improves the matrix conditioning of the equation system and the precision of the wave field synthesis by implementing the radiation characteristics of the driven loudspeakers. In this work, the “Minimum Energy Method” — originally developed for acoustic holography — is applied for matters of wave field synthesis for the first time. It guarantees a robust solution and creates softer loudspeaker driving signals than the Radiation Method but yields a worse approximation of the wave field beyond the discrete listening positions. Psychoacoustic considerations allow for a successfull wave field synthesis: Integration times of the auditory system determine the spatial dimensions in which the wave field synthesis approach works despite different arrival times and directions of wave fronts. By separating the spectrum into frequency bands of the critical band width, masking effects are utilized to reduce the amount of calculations with hardly audible consequances. By applying the “Precedence Fade”, the precedence effect is used to manipulate the perceived source position and improve the reproduction of initial transients of notes. Based on Auditory Scene Analysis principles, “Fading Based Panning” creates precise phantom source positions between the actual loudspeaker positions. Physical measurements, simulations and listening tests prove evidence for the introduced methods and reveal their precision. Furthermore, results of the listening tests show that the perceived spaciousness of instrumental sound not necessarily goes along with distinctness of localization. The introduced methods are compatible to conventional multi channel audio systems as well as other wave field synthesis applications. / In dieser Arbeit wird eine Methode entwickelt, um die Abstrahlcharakteristik von Musikinstrumenten in Wellenfeldsynthesesystemen zu implementieren. Diese wird in zwei Lautsprechersystemen umgesetzt und getestet. Aufgrund der vergleichsweise geringen Anzahl an Lautsprechern wird das Schallfeld an diskreten Hörpositionen durch Lösung eines linearen Gleichungssystems resynthetisiert. Dadurch können für jede Konstellation aus Quellen- und Hörposition alle Lautsprecher für die Synthese verwendet werden. Hierzu wird zunächst in Frequenzebene, unter Vernachlässigung der Ausbreitungsgeschwindigkeit des Schalls gerechnet. Dieses Vorgehen sorgt für Artefakte im Schallsignal und Synthesefehler im Hörbereich, die durch psychoakustische Methoden kompensiert werden. Im Vergleich zu anderen Wellenfeldsyntheseverfahren wird bei diesem Vorgehen die Aliasingfrequenz durch die Größe des Hörbereichs und nicht durch den Lautsprecherabstand bestimmt. Musikinstrumente werden als komplexe Punktquellen vereinfacht, wodurch die Abstrahlung erfasst, gespeichert und in den Raum propagiert werden kann. Dieses Vorgehen ist auch die Basis der neu entwickelten “Radiation Method”, die durch Einbeziehung der Abstrahlcharakteristik der verwendeten Lautsprecher die Genauigkeit der Wellenfeldsynthese erhöht und die Konditionierung der Propagierungsmatrix des zu lösenden Gleichungssystems verbessert. In dieser Arbeit wird erstmals die für die akustische Holografie entwickelte “Minimum Energy Method” auf Wellenfeldsynthese angewandt. Sie garantiert eine robuste Lösung und erzeugt leisere Lautsprechersignale und somit mehr konstruktive Interferenz, approximiert das Schallfeld jenseits der diskreten Hörpositionen jedoch schlechter als die Radiation Method. Zahlreiche psychoakustische Überlegungen machen die Umsetzung der Wellenfeldsynthese möglich: Integrationszeiten des Gehörs bestimmen die räumlichen Dimensionen in der die Wellenfeldsynthesemethode — trotz der aus verschiedenen Richtungen und zu unterschiedlichen Zeitpunkten ankommenden Wellenfronten — funktioniert. Durch Teilung des Schallsignals in Frequenzbänder der kritischen Bandbreite wird unter Ausnutzung von Maskierungseffekten die Anzahl an nötigen Rechnungen mit kaum hörbaren Konsequenzen reduziert. Mit dem “Precedence Fade” wird der Präzedenzeffekt genutzt, um die wahrgenommene Schallquellenposition zu beeinflussen. Zudem wird dadurch die Reproduktion transienter Einschwingvorgänge verbessert. Auf Grundlage von Auditory Scene Analysis wird “Fading Based Panning” eingeführt, um darüber hinaus eine präzise Schallquellenlokalisation jenseits der Lautsprecherpositionen zu erzielen. Physikalische Messungen, Simulationen und Hörtests weisen nach, dass die neu eingeführten Methoden funktionieren und zeigen ihre Präzision auf. Auch zeigt sich, dass die wahrgenommene Räumlichkeit eines Instrumentenklangs nicht der Lokalisationssicherheit entspricht. Die eingeführten Methoden sind kompatibel mit konventionellen Mehrkanal-Audiosystemen sowie mit anderen Wellenfeldsynthesesystemen.

The bassoon is a conical woodwind instrument blown with a double-reed mouthpiece. The sound is generated by the periodic oscillation of the mouthpiece which excites the air column. The fundamental frequency of this oscillation is determined to a large extent by the resonances of the air column. These can be varied by opening or closing tone-holes. For any given tone hole setting a fine-tuning in pitch is necessary during playing. Musicians adjust the slit opening of the double-reed by pressing their lips against the opposing reed blades. These so-called embouchure corrections are required to tune the pitch, loudness and sound color of single notes. They may be tedious, especially if successive notes require inverse corrections. However, such corrections are essential: Due to the very high frequency sensitivity of the human ear playing in tune is the paramount requirement when playing music. This implies, that embouchure actions provide an important insight into a subjective quality assessment of reed wind instruments from the viewpoint of the musician: An instrument requiring only small corrections will be comfortable to play. Theoretical investigations of the whole system of resonator, reed, and musician by use of a physical model nowadays still seem insufficient with respect to the required precision. Therefore the path of well-described artificial mouth measurements has been chosen here. For the separate treatment of the resonator and the double-reed, existing classical models have been used. Modifications to these models are suggested and verified experimentally. The influence of the musician is incorporated by the lip force-dependent initial reed slit height. For this investigation a measurement setup has been built that allows precise adjustment of lip force during playing. With measurements of the artificial mouth parameters blowing pressure, mouthpiece pressure, volume-flow rate and axial lip position on reed, the experiment is fully described for a given resonator setting represented by an input impedance curve. By use of the suggested empirical model the adjustment parameters can be turned into model parameters. A large data set from blowing experiments covering the full tonal and dynamical range on five modern German bassoons of different make is given and interpreted. The experimental data presented with this work can be a basis for extending the knowledge and understanding of the interaction of instrument, mouthpiece and player. On the one hand, they provide an objective insight into tuning aspects of the studied bassoons. On the other hand the experiments define working points of the coupled system by means of quasi-static model parameters. These may be useful to validate dynamical physical models in further studies. The experimental data provide an important prerequisite for scientific proposals of optimizations of the bassoon and other reed wind instruments. It can further serve as a fundament for the interdisciplinary communication between musicians, musical instrument makers and scientists.

The bassoon is a conical woodwind instrument blown with a double-reed mouthpiece. The sound is generated by the periodic oscillation of the mouthpiece which excites the air column. The fundamental frequency of this oscillation is determined to a large extent by the resonances of the air column. These can be varied by opening or closing tone-holes. For any given tone hole setting a fine-tuning in pitch is necessary during playing. Musicians adjust the slit opening of the double-reed by pressing their lips against the opposing reed blades. These so-called embouchure corrections are required to tune the pitch, loudness and sound color of single notes. They may be tedious, especially if successive notes require inverse corrections. However, such corrections are essential: Due to the very high frequency sensitivity of the human ear playing in tune is the paramount requirement when playing music. This implies, that embouchure actions provide an important insight into a subjective quality assessment of reed wind instruments from the viewpoint of the musician: An instrument requiring only small corrections will be comfortable to play. Theoretical investigations of the whole system of resonator, reed, and musician by use of a physical model nowadays still seem insufficient with respect to the required precision. Therefore the path of well-described artificial mouth measurements has been chosen here. For the separate treatment of the resonator and the double-reed, existing classical models have been used. Modifications to these models are suggested and verified experimentally. The influence of the musician is incorporated by the lip force-dependent initial reed slit height. For this investigation a measurement setup has been built that allows precise adjustment of lip force during playing. With measurements of the artificial mouth parameters blowing pressure, mouthpiece pressure, volume-flow rate and axial lip position on reed, the experiment is fully described for a given resonator setting represented by an input impedance curve. By use of the suggested empirical model the adjustment parameters can be turned into model parameters. A large data set from blowing experiments covering the full tonal and dynamical range on five modern German bassoons of different make is given and interpreted. The experimental data presented with this work can be a basis for extending the knowledge and understanding of the interaction of instrument, mouthpiece and player. On the one hand, they provide an objective insight into tuning aspects of the studied bassoons. On the other hand the experiments define working points of the coupled system by means of quasi-static model parameters. These may be useful to validate dynamical physical models in further studies. The experimental data provide an important prerequisite for scientific proposals of optimizations of the bassoon and other reed wind instruments. It can further serve as a fundament for the interdisciplinary communication between musicians, musical instrument makers and scientists.:1 Introduction 1 1.1 Motivation 1 1.2 Scientific Approaches to Woodwind Musical Instruments 3 1.3 Organization of the Thesis 6 2 Acoustical Properties of the Bassoon Air Column 7 2.1 Wave propagation in tubes 7 2.1.1 Theory 7 2.1.2 Transmission Line Modeling 8 2.1.3 Implementation 18 2.1.4 Remarks on Modeling Wall Losses in a Conical Waveguide 19 2.2 Input Impedance Measurement 23 2.2.1 Principle 23 2.2.2 Device 23 2.2.3 Calibration and Correction 24 2.3 Comparison of Theory and Experiment 27 2.3.1 Repeatability and Measurement Uncertainty 27 2.3.2 Comparison of numerical and experimental Impedance Curves 32 2.4 Harmonicity Analysis of the Resonator 35 2.4.1 The Role of the Resonator 35 2.4.2 The reed equivalent Volume 35 2.4.3 Harmonicity Map 36 2.5 Summary 38 3 Characterization of the Double Reed Mouthpiece 41 3.1 Physical Model of the Double-Reed 41 3.1.1 Working Principle 41 3.1.2 Structural Mechanical Characteristics 42 3.1.3 Fluid Mechanical Characteristics 44 3.2 Measurement of Reed Parameters 49 3.2.1 Quasi-stationary Measurement 49 3.2.2 Dynamic Measurement 50 3.3 Construction of an Artificial Mouth 52 3.3.1 Requirements Profile 52 3.3.2 Generic Design 53 3.3.3 The artificial Lip 54 3.3.4 Air Supply 55 3.3.5 Sensors and Data Acquisition 57 3.3.6 Experimental setup 59 3.4 Summary 59 4 Modeling Realistic Embouchures with Reed Parameters 61 4.1 Reed Channel Geometry and Flow Characteristics 61 4.1.1 The Double-Reed as a Flow Duct 61 4.1.2 Bernoulli Flow-Model with Pressure Losses 65 4.1.3 Discussion of the Model 68 4.2 Quasi-static Interaction of Flow and Reed-Channel 72 4.2.1 Pressure-driven Deformation of the Duct Intake 72 4.2.2 Reed-Flow Model including Channel Deformation 75 4.2.3 Influence of Model Parameters 76 4.2.4 Experimental Verification 78 4.3 Effect of the Embouchure on the Reed-Flow 81 4.3.1 Adjustment of the Initial Slit Height 81 4.3.2 Quasi-static Flow in the Deformed Reed-Channel 83 4.3.3 Simplified empirical Model including a Lip Force 85 4.4 Summary 93 5 Survey of Performance Characteristics of the Modern German Bassoon 5.1 Experimental Procedure and Data Analysis 95 5.1.1 Description of the Experiment 95 5.1.2 Time Domain Analysis 97 5.1.3 Spectral Analysis – Period Synchronized Sampling 98 5.1.4 Spectral Centroid and Formants 99 5.1.5 Embouchure parameters 100 5.2 Observations on the Bassoon under Operating Conditions 105 5.2.1 Excitation Parameter Ranges 106 5.2.2 Characteristics of the radiated Sound 110 5.2.3 Reed Pressure Waveform Analysis 115 5.2.4 Summarizing Overview 118 5.3 Performance Control with the Embouchure 120 5.3.1 Register-dependent Embouchure Characteristics 120 5.3.2 Intonation Corrections 123 5.3.3 Sound Color Adjustments 127 5.3.4 Relation to the acoustical Properties of the Resonator 129 5.4 Summary 137 6 Conclusion 139 6.1 Summary 139 6.2 Outlook 141