Music: A Mathematical Offering

Contents

• Preface
• Introduction
• Acknowledgements
• 1. Waves and harmonics
• 2. Fourier theory
• 3. A mathematician's guide to the orchestra
• 4. Consonance and dissonance
• 5. Scales and temperaments: the fivefold way
• 6. More scales and temperaments
• 7. Digital music
• 8. Synthesis
• 9. Symmetry in music
• Appendix A. Bessel functions
• Appendix B. Equal tempered scales
• Appendix C. Frequency and MIDI chart
• Appendix D. Intervals
• Appendix E. Just, equal and meantone scales compared
• Appendix F. Music theory
• Appendix G. Recordings
• Bibliography
• Index.