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Visualisation of the Lip Motion of Brass Instrument Players, and Investigations of an Artificial Mouth As a Tool for Comparative Studies of Instruments

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Visualisation of the Lip Motion of Brass Instrument Players, and Investigations of an Artificial Mouth As a Tool for Comparative Studies of Instruments Visualisation of the Lip Motion of Brass Instrument Players, and Investigations of an Artificial Mouth as a Tool for Comparative Studies of Instruments I V N E R U S E I T H Y T O H F G E R D I N B U Seona Bromage A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the University of Edinburgh 2007 Abstract When playing a brass instrument the lips of the player fulfil a similar role to the cane reeds of wood-wind instruments. The nature of the motion of this lip-reed determines the flow of air through the lips, between the player's mouth and the instrument. It is a complicated feedback system in which the motion of the lips controls the air flow, which itself affects the behaviour of the lips. In recent years several designs of artificial mouth have been developed; these model the human lips using latex rubber tubes filled with water. These artificial mouths are increasingly used in experiments rather than enlisting the services of a musician as they have many advantages including greater accessibility and the stability of the embouchure. In this thesis factors affecting the reproducibility of the embouchure of one such artificial mouth are investigated with reference to the measured resonances of the lips. Using these results, procedures and practical design improvements are suggested. Two examples of comparative studies of historic instruments are presented. In order to provide detailed information on the behaviour of the lips of brass players high speed digital photography is used to image the self-oscillating lip- reed. Variation in the lip opening, over a wide range of notes and different players, is investigated, providing experimental evidence to aid the process of refining physical models of the behaviour of the brass player's lips. Particular attention is paid to the relationship between the area and height of the lip opening. Results suggest that during extremely loud playing the lip motion is qualitatively similar to that in quieter notes and therefore is not the origin of the dramatic increase in the levels of the high harmonics of the radiated sound. Investigation of the behaviour at the start of a note has shown evidence relating the lip motion to the transient in the mouthpiece pressure waveform. Comparison is made between the behaviour of the artificial lips and that of the lips of musicians providing evidence of the suitability of the use of the artificial mouth as a model for real brass players. Results show that although differences exist, particularly when looking at behaviour over a wide range of dynamic levels, the general features of behaviour are reproduced by the artificial mouth. i Declaration I do hereby declare that this thesis was composed by myself and that the work described within is my own, except where explicitly stated otherwise. Seona Bromage April 2007 ii Acknowledgements Firstly I would like to thank Murray Campbell for all the help support and guidance I have received. I would also like to thank Clive Greated who along with Murray introduced me to the field of musical acoustics ten years ago. Without their enthusiasm for the subject I probably would not have even started this work. I would like to acknowledge the assistance provided by those with whom I have collaborated. Thanks to Jo¨el Gilbert for his invaluable input on much of this work and for tolerating my lack of ability to speak French. Thank you to Arnold Myers for many useful suggestions and for providing the historic instruments. Thanks to John Chick for assistance with the transient and brassy measurements. I would like to acknowledge the assistance provided by Alistair Braden with the BIAS measurements, Sandra Carral and Felicien Vallet for the discussions and help with the spectral centroid results, and Michael Newton for providing the input response of the horn. Special thanks to Catherine Archbold for her help with some of the filming. To all those who volunteered their lips for investigation (Murray, Jo¨el, AlistairJ, Tim, Sunil, Mike, Arnold, AlistairB, John, Anne) - I could not have done it without you. Extra special thanks to Orlando Richards for all his help and support over the last ten years and for introducing me to his rubber lips. Thanks to Steve Tonge for being lovely and very helpful and to Alan Woolley, Calum Gray, Rob MacDonald and all the other acoustics people past and present, especially Sam Stevenson and Mike Newton - the lips are in your hands. Cheers to Darren Hendrie for all the disk quota and entertainment. Without my husband David this would either have been finished ages ago or not at all. Thank you for everything including lots of Matlab support, making my dinner and for all the lovely love. I would like to thank my sister Kathy her for all her patience and for being so wonderful. Finally I would like to thank my mum and dad for making me in the first place and and for cultivating my love of Edinburgh. Financial support was provided by EPSRC. iii Nomenclature Musical notes and equivalent frequencies Below are given approximate frequencies for some commonly referred to notes of the equal-tempered chromatic scale based on A4 = 440Hz (\Middle C" is C4). B[1 58.3 Hz B[2 116.5 Hz F3 174.6 Hz D4 293.7 Hz F4 349.2 Hz Musical dynamics p piano \softly" mf mezzo-forte \moderately-loud" f forte \loudly" or \strong" ff fortissimo \very loudly" Lip parameters mlip mass of lip !lip natural resonant (angular) frequency of lip Qlip quality factor of lip resonance F driving force on lip (also used to denote some general function) h lip separation h0 time averaged lip separation h(!) oscillating component of lip opening ∆P (!) oscillating pressure difference across the lips S area of lip opening q exponent in the area-height relationship iv General symbols z specific acoustic impedance Z acoustic impedance ! angular frequency p acoustic pressure P pressure u acoustic particle velocity S cross sectional area U acoustic volume flow ν frequency n harmonic number l effective length v Contents 1 Introduction 1 1.1 Context and Motivation . 1 1.2 Aims . 2 1.3 Content . 3 2 Brass instrument acoustics 5 2.1 Overview . 5 2.2 The air column in the instrument . 6 2.2.1 Impedance . 6 2.2.2 The instrument as a simple resonator . 7 2.2.3 The shape of real brass instruments . 8 2.3 The lips - mechanical oscillator . 10 2.3.1 One mass model . 11 2.3.2 Pressure controlled valve . 13 2.4 The air flow - nonlinearity . 15 2.4.1 Harmonic generation . 16 2.4.2 The brassy sound . 17 2.4.3 Co-operative regimes of oscillation . 18 2.5 Modelling the Brass player's lips . 19 vi 3 Reproducibility and control of the artificial mouth 21 3.1 Introduction . 21 3.1.1 The lip response . 23 3.2 Design of the artificial mouth . 24 3.2.1 Characteristic parameters of the embouchure . 24 3.3 Experimental method . 25 3.3.1 Setup . 25 3.3.2 Speaker mounting . 27 3.3.3 Measurement procedure . 28 3.4 Measurements of repeatability and reproducibility . 31 3.4.1 Unavoidable variations - repeatability . 32 3.4.2 Resetting the embouchure control parameters . 35 3.4.3 Reconnecting mouthpiece and instrument . 37 3.4.4 Lip position . 37 3.4.5 Summary . 38 3.5 Recommendations . 39 3.5.1 Mouthpiece holder . 40 3.5.2 Lip-guides . 40 3.6 Conclusions . 41 4 Visualisation of the self-oscillating lips of musicians and the ar- tificial mouth 42 4.1 Introduction and motivation . 42 4.2 Experimental investigation of lip motion . 44 4.2.1 Experimental procedure . 44 4.2.2 Analysis procedure . 47 4.2.3 The definition of height . 49 vii 4.2.4 Accuracy . 50 4.3 Describing the lip opening . 53 4.3.1 Time-averaged behaviour . 53 4.3.2 Variation of lip opening with time . 56 4.3.3 Summary . 62 4.4 The area-height function - towards a more realistic model . 63 4.4.1 Sensitivity of results to analysis procedure . 65 4.4.2 Results - single straight line fit . 69 4.4.3 Variations within one cycle of oscillation . 75 4.4.4 Summary . 81 4.5 Extremely loud playing - the `brassy' sound . 81 4.5.1 Background and motivation . 81 4.5.2 Method . 82 4.5.3 The area-height function . 88 4.5.4 Discussion . 88 4.6 Conclusions . 89 5 Transient behaviour 91 5.1 Experimental procedure . 92 5.1.1 The instrument . 93 5.1.2 Data acquisition . 95 5.1.3 Analysis procedure . 96 5.2 Results . 97 5.2.1 Input impulse response measurements . 98 5.2.2 Amplitude . 99 5.2.3 Frequency . 101 viii 5.3 Conclusions and future work . 103 6 Example experiments using the artificial mouth for comparative studies of historic instruments 105 6.1 Background and motivation . 106 6.2 The ophicleide and the saxhorn . 106 6.2.1 Motivation and aims . 106 6.2.2 Instruments . 106 6.2.3 Notes played . 107 6.2.4 Data acquisition . 108 6.2.5 Method . 108 6.2.6 Threshold pressure . 109 6.2.7 Pitch variation with pressure . 110 6.2.8 Variation with fingerings and valve combination . 111 6.2.9 Discussion - embouchure suitability . 114 6.2.10 Conclusions . 115 6.3 The bass trumpet . 116 6.3.1 Instruments . 116 6.3.2 Experimental setup . 117 6.3.3 Improvements to mouth-piece holder .
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