ON THE ART AND SCIENCE OF ACOUSTIC INSTRUMENTS
Buy now at Amazon.com and AbeBooks.com.
© 2000–2025 Cris Forster
* * * * *
The following M.M. pages:
(1) the Table of Contents,
(2) the Foreword by Dr. David R. Canright,
(3) the Introduction and Acknowledgments,
(4) a Tone Notation graphic,
(5) the List of Symbols,
(6) the First Pages of all the chapters,
and the
(7) Bibliography & (8) Index may be downloaded here:
* * * * *
Musical Mathematics — Online PDF Citations
CONTENTS
| Foreword by David R. Canright | v | |
| Introduction and Acknowledgments | vii | |
| Tone Notation | ix | |
| List of Symbols | xi | |
| CHAPTER 1 | MICA MASS | 1 |
| Part I | Principles of force, mass, and acceleration | 1 |
| Part II | Mica mass definitions, mica unit derivations, and sample calculations | 14 |
| Notes | 24 | |
| CHAPTER 2 | PLAIN STRING AND WOUND STRING CALCULATIONS | 27 |
| Part I | Plain strings | 27 |
| Part II | Wound strings | 36 |
| Notes | 41 | |
| CHAPTER 3 | FLEXIBLE STRINGS | 44 |
| Part I | Transverse traveling and standing waves, and simple harmonic motion in strings | 44 |
| Part II | Period and frequency equations of waves in strings | 54 |
| Part III | Length, frequency, and interval ratios of the harmonic series on canon strings | 59 |
| Part IV | Length, frequency, and interval ratios of non-harmonic tones on canon strings | 69 |
| Part V | Musical, mathematical, and linguistic origins of length ratios | 79 |
| Notes | 94 | |
| CHAPTER 4 | INHARMONIC STRINGS | 98 |
| Part I | Detailed equations for stiffness in plain strings | 98 |
| Part II | Equations for coefficients of inharmonicity in cents | 108 |
| Part III | General equations for stiffness in wound strings | 113 |
| Notes | 115 | |
| CHAPTER 5 | PIANO STRINGS VS. CANON STRINGS | 118 |
| Part I | Transmission and reflection of mechanical and acoustic energy | 118 |
| Part II | Mechanical impedance and soundboard-to-string impedance ratios | 120 |
| Part III | Radiation impedance and air-to-soundboard impedance ratios | 126 |
| Part IV | Dispersion, the speed of bending waves, and critical frequencies in soundboards | 130 |
| Part V | Methods for tuning piano intervals to beat rates of coincident string harmonics | 135 |
| Part VI | Musical advantages of thin strings and thin soundboards | 141 |
| Notes | 143 | |
| CHAPTER 6 | BARS, RODS, AND TUBES | 147 |
| Part I | Frequency equations, mode shapes, and restoring forces of free-free bars | 147 |
| Part II | Free-free bar tuning techniques | 160 |
| Part III | Frequency equations, mode shapes, and restoring forces of clamped-free bars | 174 |
| Part IV | Clamped-free bar tuning techniques | 176 |
| Notes | 178 | |
| CHAPTER 7 | ACOUSTIC RESONATORS | 182 |
| Part I | Simple harmonic motion of longitudinal traveling waves in air | 182 |
| Part II | Equations for the speed of longitudinal waves in solids, liquids, and gases | 186 |
| Part III | Reflections of longitudinal traveling waves at the closed and open ends of tubes | 189 |
| Part IV | Acoustic impedance and tube-to-room impedance ratio | 196 |
| Part V | Longitudinal pressure and displacement standing waves in tubes | 200 |
| Part VI | Length and frequency equations of tube resonators | 203 |
| Part VII | Theory of cavity resonators | 212 |
| Part VIII | Cavity resonator tuning techniques | 219 |
| Notes | 223 | |
| CHAPTER 8 | SIMPLE FLUTES | 227 |
| Part I | Equations for the placement of tone holes on concert flutes and simple flutes | 227 |
| Part II | Equations for analyzing the tunings of existing flutes | 242 |
| Part III | Suggestions for making inexpensive yet highly accurate simple flutes | 246 |
| Notes | 248 | |
| CHAPTER 9 | THE GEOMETRIC PROGRESSION, LOGARITHMS, AND CENTS | 253 |
| Part I | Human perception of the harmonic series as a geometric progression | 253 |
| Part II | Logarithmic processes in mathematics and human hearing | 257 |
| Part III | Derivations and applications of cent calculations | 265 |
| Part IV | Logarithmic equations for guitar frets and musical slide rules | 271 |
| Notes | 276 | |
| CHAPTER 10 | WESTERN TUNING THEORY AND PRACTICE | 280 |
| Part I | Definitions of prime, composite, rational, and irrational numbers | 281 |
| Part II | Greek classifications of ratios, tetrachords, scales, and modes | 284 |
| Part III | Arithmetic and geometric divisions on canon strings | 291 |
| Part IV | Philolaus, Euclid, Aristoxenus, and Ptolemy | 299 |
| Part V | Meantone temperaments, well-temperaments, and equal temperaments | 334 |
| Part VI | Just intonation | 365 |
| Notes | 460 | |
| CHAPTER 11 | WORLD TUNINGS | 485 |
| Part I | Chinese Music | 485 |
| Notes | 504 | |
| Part II | Indonesian Music: | 508 |
| Java | 508 | |
| Bali | 522 | |
| Notes | 535 | |
| Part III | Indian Music: | 540 |
| Ancient Beginnings | 540 | |
| South India | 564 | |
| North India | 587 | |
| Notes | 600 | |
| Part IV | Arabian, Persian, and Turkish Music | 610 |
| Notes | 774 | |
| CHAPTER 12 | ORIGINAL INSTRUMENTS | 788 |
| Stringed Instruments: | ||
| Chrysalis I — and Chrysalis II for a future 2nd ed. | 788 | |
| Harmonic/Melodic Canon | 790 | |
| Bass Canon | 800 | |
| Just Keys | 808 | |
| Percussion Instruments: | ||
| Diamond Marimba II — and Diamond Marimba I for a future 2nd ed. | 824 | |
| Bass Marimba | 826 | |
| Friction Instrument: | ||
| Glassdance | 828 | |
| Wind Instruments: | ||
| Simple Flutes | 833 | |
| CHAPTER 13 | BUILDING A LITTLE CANON | 834 |
| Parts, materials, labor, and detailed dimensions | 834 | |
| Epilog by Heidi Forster | 839 | |
| Plate 1: Chrysalis I | 845 | |
| Plate 2: Harmonic/Melodic Canon | 846 | |
| Plate 3: Bass Canon | 847 | |
| Plate 4: String Winder (machine) | 848 | |
| Plate 5: String Winder (detail) | 849 | |
| Plate 6: Just Keys | 850 | |
| Plate 7: Diamond Marimba | 851 | |
| Plate 8: Bass Marimba | 852 | |
| Plate 9: Glassdance | 853 | |
| Plate 10: Glassdance (back) | 854 | |
| Plate 11: Simple Flutes | 855 | |
| Plate 12: Little Canon | 856 | |
| Plate 13: Cris Forster with Chrysalis I | 857 | |
| Plate 14: Heidi Forster playing Glassdance | 858 | |
| Plate 15: David Canright, Heidi Forster, and Cris Forster | 859 | |
| Plate 16: Chrysalis Foundation Workshop | 860 | |
| Bibliography for Chapters 1-9 | 861 | |
| Bibliography for Chapters 10 | 866 | |
| Bibliography for Chapters 11 | 871 | |
| Bibliography for Chapters 12 | 877 | |
| Appendix A: Frequencies of Eight Octaves of 12-Tone Equal Temperament | 879 | |
| Appendix B: Conversion Factors | 880 | |
| Appendix C: Properties of String Making Materials | 882 | |
| Appendix D: Spring Steel Music Wire Tensile Strength and Break Strength Values | 884 | |
| Appendix E: Properties of Bar Making Materials | 885 | |
| Appendix F: Properties of Solids | 888 | |
| Appendix G: Properties of Liquids | 890 | |
| Appendix H: Properties of Gases | 892 | |
| Index | 895 | |