Spectral Analysis of Musical Sounds with Emphasis on the Piano

Contents

• Part 1: Some Basic Sound Waves and Some Simple Tools
• 1 An Introduction to Some Elementary Waves
• 2 The Basic Tools of Spectral Analysis
• 3 Analysis of Several Common Musical Instruments
• 4 Harmonics in Musical Sounds
• Part 2: A Visual Analysis of Vibrating Objects (Strings, Membranes, Bars, Plates)
• 5 The Vibrating String
• 6 The Vibrating Bar
• 7 The Vibrating Membrane
• 8 The Vibrating Plate
• Part 3: The Piano
• 9 An Introduction to Pianos
• 10 Some Individual Piano Notes and Interactions Between Them
• 11 The Missing Fundamental
• 12 Octave Stretching, Inharmonicity and Railsback Curves
• 13 Beating, Unisons and Tuning
• 14 Two Dimensional Graphical Metrics
• 15 Three Dimensional Graphical Metrics
• 16 An Investigation into Hammer Knock and Key Striking
• 17 Evaluation of a Wapin Bridge Conversion
• 18 Similarities between Pianos and Repeatability of Data Gathering Methods
• 19 Two Metrics Applied to Other Instruments
• 20 Use of the Metrics in Production and Development
• 21 Comments by Delwin Fandrich
• Appendix 1. Mathematical Basis for Part One
• Appendix 2. Mathematical Basis for Part Two
• Appendix 3. Mathematical Basis for Part Three
• Appendix 4. Experimental Setup
• Appendix 5. A Brief Exposure to Matlab