1. Introduction. - 2. Sound-Based Synthesis Methods. - 1 Wavetable synthesis. - 2 Granular synthesis. - 3 Additive synthesis. - 4 Subtractive synthesis. - 5 FM synthesis. - 6 Combinations of sound-based synthesis methods. - 3. Physical Description of Musical instruments. - 1 General notation. - 2 Subdivision of a musical instrument into vibration generators and a resonant body. - 3 Physical description of string vibrations. - 4 Physical description of membrane vibrations. - 5 Physical description of resonant bodies. - 6 Chapter summary. - 4. Classical Synthesis Methods Based on Physical Models. - 1 Finite difference method. - 2 Digital waveguide method. - 3 Modal synthesis. - 4 Chapter summary. - 5. Functional Transformation Method. - 1 Fundamental principles of the FTM. - 2 Application of the FTM to vibrating strings. - 3 Application of the FTM to vibrating membranes. - 4 Application of the FTM to resonant bodies. - 5 Chapter summary. - 6. Comparison of the Ftm with the Classical Physical Modeling Methods. - 1 Comparison of the FTM with the FDM. - 2 Comparison and combination of the FTM with the DWG. - 3 Comparison of the FTM with the MS. - 4 Chapter conclusions. - 7. Summary Conclusions and Outlook. Language: English