Computational Mechanics of the Classical Guitar describes a new dynamic paradigm in instrument acoustics based on time-dependent transient analysis and simulation of complete musical instruments. It describes the current state of theoretical and experimental research into the guitar for engineers, instrument makers and musicians. This includes a summary of the basic equations for the mechanics of vibrating bodies and a presentation of the FDM (finite difference method) model with which the true vibrational behaviour of the instrument as an entire system can be understood for the first time. This monograph presents various new theoretical and experimental results and insights into guitar playing such as the coupling between the strings and the top plate or a description of the finger noise made when the fingers slide over the strings before plucking.
Author(s): Rolf Bader
Edition: 1
Year: 2005
Language: English
Pages: 182
Contents......Page 7
1.1 General Remarks......Page 14
1.2 Brief Summary......Page 18
2 Musical Transient-Modeling Software MTMS......Page 19
2.1 Part of the MTMS Program for Plates......Page 21
2.2 MTMS Software for Guitar Parts......Page 22
2.3 Software WAVELET......Page 29
2.4 The MAS Program as a Signal-Processing Tool for Music......Page 30
3.1.1 Strong Formulation......Page 35
3.1.3 Action Principle......Page 36
3.2 Overview of Continuum Mechanics......Page 39
3.2.1 Definition of the Variables......Page 40
3.2.2 Mechanical Laws......Page 41
3.3 Discrete Mechanics......Page 43
4 Studies of the Guitar To Date......Page 45
4.1.1 Transverse Movement......Page 46
4.1.2 Longitudinal Movement......Page 47
4.2 Strings and Corpus Impedance......Page 49
4.3 Guitar Body Modes......Page 50
4.4 Nonlinearities and Transient Analyses......Page 55
4.5 Discrete Instrument Models......Page 61
5 The Discrete Guitar Model......Page 62
5.1.1 Coupling within Top and Back Plate......Page 63
5.1.3 Mass Distribution of the Top and Back Plate......Page 64
5.3 The Neck of the Guitar......Page 66
5.6 Sound Radiation of the Guitar Body......Page 67
5.7 The String Movement and Its Discrete Form......Page 69
5.8 Longitudinal Waves and Their Discrete Form......Page 70
5.9 Bending Waves and Their Discrete Form......Page 73
5.10 Boundary Conditions......Page 76
5.10.1 Boundary Conditions with Longitudinal Boundaries......Page 77
5.10.2 Boundary Condition of Bending Movements......Page 80
6 Bending, Damping and Coupling......Page 84
6.1.1 LT – First Type Coupling......Page 85
6.1.2 LT – Second Type Coupling......Page 94
6.2 Time-Stepping Method......Page 104
6.3 Energy Conservation......Page 108
6.4 Spacial-Temporal Differences in Discrete and Continues Mechanics......Page 113
6.5 Results for the Plate......Page 120
6.6.1 Velocity Term as Damping Term with the Harmonic Oscillator......Page 128
6.6.2 Force Term as Damping Term with Bending Waves......Page 130
6.7 Coupling......Page 139
7 Results......Page 142
7.1 Parameters of the Guitar Model......Page 143
7.2 Sounds of the Individual Parts of the Guitar......Page 145
7.4 Spectra of the Parts of the Guitar......Page 146
7.5 Development of the Initial Transient......Page 154
7.6 Aural Evaluation of the Calculated Sounds of the Parts of the Guitar......Page 167
7.7 Coupling of the String to the Top Plate......Page 170
7.8 Pre-Scratch......Page 172
8 Summary and Outlook......Page 178
B......Page 183
E......Page 184
H......Page 185
K......Page 186
M......Page 187
R......Page 188
T......Page 189
Z......Page 190
Audio Files and Videos on the Web......Page 191
