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Part I The Musician's Experience and the Scientific Perspective |
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1 The Musician's Experience of Brass Instruments |
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3 | (28) |
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1.1 Creating Music from Lip Vibration: Labrosones Through the Ages |
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3 | (10) |
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1.1.1 Labrosones from Found Objects |
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4 | (2) |
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1.1.2 Early Metal Labrosones |
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6 | (3) |
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1.1.3 Labrosones in Renaissance and Baroque Music |
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9 | (3) |
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1.1.4 The Nineteenth-Century Labrosone Revolution |
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12 | (1) |
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1.2 The Musician's Interpretation of the Brass Playing Experience |
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13 | (12) |
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1.2.1 Musical Pitch Notation |
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13 | (1) |
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1.2.2 Natural Notes and Harmonics: The Musician's View |
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14 | (1) |
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1.2.3 Nominal Pitches of Brass Instruments |
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15 | (1) |
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16 | (1) |
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17 | (3) |
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20 | (1) |
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20 | (1) |
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1.2.8 Blowing Pressure and Air Flow |
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21 | (1) |
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1.2.9 Resistance and Playing Effort |
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22 | (1) |
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1.2.10 Responsiveness and Rapid Articulation |
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23 | (1) |
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1.2.11 Wrap, Directivity and Ergonomics |
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24 | (1) |
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1.3 Subjective and Objective Evaluation of Brass Instrument Quality |
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25 | (6) |
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1.3.1 Sound Quality and Payability |
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26 | (1) |
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1.3.2 Descriptive Terms Used by Musicians to Describe Brass Instrument Behaviour |
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27 | (1) |
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1.3.3 Biases in Quality Evaluation of Musical Instruments |
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28 | (3) |
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2 The Scientist's Perspective on Brass Instrument Behaviour |
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31 | (32) |
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2.1 Scientific Measurements of Brass Instrument Behaviour |
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31 | (16) |
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2.1.1 Sound Radiated from a Brass Instrument |
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33 | (3) |
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2.1.2 Sound Measured Inside a Trombone Mouthpiece |
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36 | (2) |
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2.1.3 Pressure Measured Inside a Brass Player's Mouth |
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38 | (3) |
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2.1.4 Lip Vibration and Air Flow: The Valve Effect Sound Source |
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41 | (2) |
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2.1.5 Is Air Row Through me Instrument Tube Important? |
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43 | (1) |
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2.1.6 Is Sound Radiation from the Vibrating Bell Important? |
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44 | (2) |
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2.1.7 Warming Up a Bras Instrument |
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46 | (1) |
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2.2 An Approach to Modelling Brass Instruments |
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47 | (16) |
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2.2.1 The Scientific Case for Simplified Models |
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48 | (2) |
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2.2.2 Coupled Systems and Feedback Loops |
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50 | (2) |
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2.2.3 Natural Notes and Harmonics: The Scientific View |
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52 | (5) |
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2.2.4 Self-Sustained Oscillations |
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57 | (1) |
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2.2.5 The Wind Instrument Paradox |
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58 | (5) |
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Part II Acoustical Modelling of Brass winds |
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3 Buzzing Lips: Sound Generation in Brass Instruments |
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63 | (38) |
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3.1 The Nature of Lip Vibration |
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63 | (16) |
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3.1.1 The Brass Player's Embouchure |
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63 | (2) |
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3.1.2 Experimental Studies of Vibrating Lips |
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65 | (1) |
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3.1.3 Time Dependence of the Lip Opening Area |
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66 | (4) |
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3.1.4 The Lip Opening Area-Height Function |
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70 | (2) |
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3.1.5 Two-Dimensional Motion of the Brass Player's Lips |
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72 | (4) |
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3.1.6 Experiments with Artificial Lips |
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76 | (3) |
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3.2 An Equation of Motion for the Lips |
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79 | (10) |
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3.2.1 A One-Mass Model of the Lips |
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79 | (2) |
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3.2.2 The Sliding Door Lip Model |
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81 | (2) |
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3.2.3 The Swinging Door Lip Model |
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83 | (2) |
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3.2.4 Inward-Striking and Outward-Striking Reeds |
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85 | (4) |
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3.3 The Mechanical Response of the Vibrating Lips |
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89 | (4) |
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3.3.1 Resonances of Artificial Lips |
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89 | (2) |
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3.3.2 Resonances of Human Lips |
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91 | (2) |
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3.4 Why Do the Lips Buzz? |
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93 | (3) |
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3.5 Volume Flow in Buzzing Lips |
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96 | (5) |
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3.5.1 Acoustic Volume Flow Through the Lip Aperture |
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96 | (2) |
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3.5.2 Acoustic Volume Flow Equation |
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98 | (3) |
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4 After the Lips: Acoustic Resonances and Radiation |
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101 | (116) |
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4.1 Internal Sounds in Brass Instruments |
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101 | (19) |
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4.1.1 Lumped and Distributed Resonators |
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102 | (2) |
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104 | (5) |
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109 | (3) |
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4.1.4 Frequency Domain and Time Domain |
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112 | (2) |
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4.1.5 Impulse Response and Reflection Function |
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114 | (2) |
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116 | (4) |
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4.2 Measuring Input Impedance |
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120 | (6) |
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4.2.1 Capillary-Based Methods |
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120 | (3) |
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4.2.2 Complementary Cavity Methods |
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123 | (1) |
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4.2.3 Wave Separation Methods |
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123 | (2) |
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4.2.4 Acoustic Pulse Reflectometry |
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125 | (1) |
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4.3 Bore Profiles of Brass Instruments |
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126 | (33) |
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4.3.1 Different Parts of the Bore |
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126 | (2) |
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128 | (4) |
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132 | (4) |
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4.3.4 Equivalent Fundamental Pitch and Equivalent Cone Length |
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136 | (2) |
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4.3.5 The Mouthpiece as a Helmholtz Resonator |
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138 | (4) |
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4.3.6 Mouthpiece Effects on Intonation and Timbre |
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142 | (5) |
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4.3.7 Sound Waves in Flaring Bells |
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147 | (3) |
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4.3.8 A Theoretical Example: The Bessel Horn |
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150 | (5) |
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4.3.9 A Practical Example: The Complete Trombone |
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155 | (2) |
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4.3.10 Instruments with Predominantly Expanding Bore Profiles |
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157 | (2) |
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159 | (5) |
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164 | (15) |
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165 | (2) |
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4.5.2 Effects of Internal Resonances in the Straight Mute |
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167 | (3) |
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170 | (2) |
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4.5.4 Plunger and Cup Mutes |
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172 | (2) |
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174 | (4) |
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4.5.6 Hand Technique on the Horn |
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178 | (1) |
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4.6 Radiation of Sound from Brass Instruments |
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179 | (18) |
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4.6.1 Near Field and Far Field |
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180 | (1) |
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181 | (2) |
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4.6.3 Transition from Internal to External Sound Fields |
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183 | (2) |
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4.6.4 Mapping the Radiation Fields of Brass Instruments |
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185 | (2) |
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4.6.5 Visualising Wavefronts with Schlieren Optics |
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187 | (4) |
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4.6.6 Far Field Directivity in Brass Instruments |
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191 | (6) |
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4.7 Going Further: Calculating Input Impedance |
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197 | (17) |
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4.7.1 Analytical Calculations |
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197 | (3) |
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4.7.2 Lossless Plane Wave TMM Calculations |
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200 | (3) |
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4.7.3 Including Losses in TMM Calculations |
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203 | (2) |
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4.7.4 TMM with Non-Cylindrical Elements |
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205 | (2) |
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4.7.5 Radiation Impedance |
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207 | (2) |
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4.7.6 Multimodal Calculations |
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209 | (3) |
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4.7.7 Bends in Brass Instruments |
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212 | (2) |
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4.8 Going Further: The Wogram Sum Function |
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214 | (3) |
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5 Blow That Horn: An Elementary Model of Brass Playing |
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217 | (54) |
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5.1 The Three Equations of the Brass Instrument Model |
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218 | (4) |
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5.1.1 The First Constituent Equation: Lip Dynamics |
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220 | (1) |
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5.1.2 The Second Constituent Equation: Flow Conditions |
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221 | (1) |
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5.1.3 The Third Constituent Equation: Instrument Acoustics |
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222 | (1) |
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5.2 Crossing the Threshold: Small Amplitude Oscillating Solutions |
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222 | (10) |
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5.2.1 Phase Relationships in the Lip Valve |
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223 | (5) |
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5.2.2 Silence or Sound? Stability Analysis of Brass Instruments |
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228 | (4) |
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5.3 Beyond Pianissimo: Modelling Realistic Playing Amplitudes |
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232 | (8) |
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5.3.1 Analysis of Brass Performance Using Simulations |
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233 | (4) |
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5.3.2 Bifurcation Diagrams |
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237 | (3) |
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5.4 Going Further: From Linearl tability Analysis to Oscillation Regimes |
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240 | (31) |
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5.4.1 Introduction: A Van der Pol Self-Sustained Oscillator |
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241 | (5) |
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5.4.2 State-Space Representations of the Elementary Brass Playing Model |
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246 | (5) |
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5.4.3 Linear Stability Analysis Applied to Brass Instruments |
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251 | (4) |
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5.4.4 The Trombone Pedal Note Regime |
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255 | (2) |
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5.4.5 Bifurcation Diagrams of Reed and Brass Instruments |
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257 | (7) |
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264 | (7) |
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6 Shocks and Surprises: Refining the Elementary Model |
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271 | (66) |
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6.1 Why Brass Instruments Sound Brassy |
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271 | (16) |
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6.1.1 Brassy Sounds in Music |
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272 | (2) |
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6.1.2 Experimental Evidence for Shock Waves in Brass Instruments |
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274 | (2) |
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6.1.3 To Infinity and Beyond: Nonlinear Propagation in Tubes |
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276 | (4) |
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6.1.4 The Brassiness Potential Parameter |
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280 | (5) |
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6.1.5 Elephants, Exhausts and Angels: Some Surprising Sources of Brassy Sounds |
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285 | (2) |
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6.2 Going Further: Nonlinear Propagation |
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287 | (9) |
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6.2.1 From the Fundamental Fluid Dynamic Equations to the Nonlinear Wave Propagation Equation |
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288 | (3) |
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6.2.2 The Burgers Equations |
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291 | (3) |
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6.2.3 Brassiness of Flaring Bells |
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294 | (2) |
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296 | (6) |
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6.3.1 Coupling of Upstream and Downstream Resonances |
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296 | (2) |
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6.3.2 Tuning of Windway Impedance Peaks |
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298 | (1) |
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6.3.3 Other Effects of the Player's Windway |
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299 | (2) |
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6.3.4 Respiratory Control |
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301 | (1) |
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6.4 Improving the Lip Model |
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302 | (6) |
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6.4.1 Evidence from Mechanical Response Measurements |
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302 | (1) |
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6.4.2 Evidence from Measurements of Threshold Playing Parameters |
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303 | (5) |
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6.4.3 Models with More Than One Degree of Freedom |
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308 | (1) |
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6.5 Playing Frequencies of Brass Instruments |
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308 | (3) |
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6.6 The Influence of Wall Material on Brass Instrument Performance |
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311 | (15) |
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6.6.1 Factors Affecting the Choice of Wall Material |
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312 | (1) |
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6.6.2 Experimental Studies of Brass Instrument Wall Vibrations |
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312 | (4) |
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6.6.3 Pathological Wall Vibration Effects in Wind Instruments |
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316 | (1) |
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6.6.4 Frequency-Localised and Broadband Effects of Structural Resonances in Brass Instruments |
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317 | (8) |
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6.6.5 Mechanical Vibration at the Lip-Mouthpiece Interface |
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325 | (1) |
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6.7 Going Further: Analytical Modelling of Vibroacoustic Coupling in Ducts |
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326 | (11) |
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6.7.1 Basic Vibroacoustic Theory |
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327 | (2) |
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6.7.2 Effect of Vibroacoustic Coupling on Input Impedance |
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329 | (3) |
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6.7.3 Some Experimental Tests of Vibroacoustic Modelling |
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332 | (5) |
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Part III Historical Evolution and Taxonomy of Brass Instruments |
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7 The Amazing Diversity of Brass Instruments |
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337 | (54) |
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7.1 What Are Important Features of Brass Instruments? |
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337 | (3) |
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7.1.1 Taxonomic Labels Based on Tube Length |
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338 | (1) |
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7.1.2 Bore Profile and Brassiness |
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339 | (1) |
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7.2 The Different Kinds of Brass Instrument |
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340 | (26) |
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7.2.1 Instruments with the Shortest Tube Lengths |
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342 | (1) |
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7.2.2 Instruments with Very Short Tube Lengths in C and Bb |
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343 | (2) |
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7.2.3 Instruments with Short Tube Lengths in G, F, Eb and D |
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345 | (4) |
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7.2.4 Instruments with Short Tube Lengths in C and Bb |
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349 | (2) |
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7.2.5 Instruments with Medium Tube Lengths in G, F, Eb and D |
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351 | (4) |
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7.2.6 Instruments with Long Tube Lengths in C and Bb |
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355 | (4) |
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7.2.7 Instruments with Long Tube Lengths in G, F, Eb and D |
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359 | (5) |
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7.2.8 Instruments with Very Long Tube Lengths in C and Bb |
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364 | (1) |
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7.2.9 Instruments with Very Long Tube Lengths in G, F, Eb and D |
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365 | (1) |
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366 | (3) |
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369 | (2) |
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7.5 Going Further: Trumpets and Cornets--Are They Different? |
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371 | (3) |
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7.6 Going Further: Alternative Taxonomies |
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374 | (1) |
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7.7 Going Further: Mouthpiece Parameters |
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375 | (3) |
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7.8 Going Further: The Bass Brass Instruments of Berlioz |
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378 | (13) |
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380 | (2) |
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382 | (3) |
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385 | (1) |
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386 | (2) |
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7.8.5 Berlioz and Pedal Notes |
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388 | (3) |
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8 How Brass Instruments Are Made |
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391 | (10) |
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391 | (1) |
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392 | (1) |
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393 | (3) |
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396 | (2) |
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398 | (3) |
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9 Looking Back and Looking Forward |
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401 | (18) |
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9.1 Brass Instruments in the Ancient World |
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402 | (6) |
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9.1.1 Etruscan Cornu and Lituus |
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402 | (3) |
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405 | (3) |
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9.2 Brass Instruments in the Digital World |
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408 | (11) |
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9.2.1 Optimisation in Instrument Design |
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409 | (2) |
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9.2.2 Modification of Instruments Using Active Control |
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411 | (2) |
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9.2.3 Live Electronics and Augmented Instruments |
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413 | (5) |
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418 | (1) |
References |
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419 | (16) |
Index |
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435 | |