The Physics of Music : Integrating the Technical and Artistic Aspects of Creating Music 1

This textbook is designed to help students and professionals understand the intimate connection between music and physics. The reader does not need prior background in music or physics, as the concepts necessary for understanding this connection are developed from scratch, using nothing more sophisticated than basic algebra which is reviewed for the reader. The focus is on connecting physics to the creation of music and its effect on humans. The reader will learn about the basic structure of music in relation to acoustics concepts, different musical instrument groups, how the room affects sound, and how sound travels from instruments to human ears to evoke an emotional reaction. Replete with exercises to hone students’ understanding, this book is ideal for a course on the physics of music and will appeal to STEM students as well as students, professionals, and enthusiasts in any field related to music and sound engineering. About the Author Gordon Ramsey is Emeritus Professor of Physics at Loyola University Chicago. He received a Ph.D. from the Illinois Institute of Technology in 1982 and began teaching at Loyola. Gordon was raised in a musical household. His father was a composer and jazz trumpet player and his mother was a church organist and classical pianist. His involvement in music began at five, when his mother gave him piano lessons while his father taught him chord structures. This paralleled his interest in mathematics, which combined well with music training. Gordon began studying the clarinet at ten and played in a championship high school band while in the eighth grade. At age fourteen, his father bought a tenor sax, which became an integral part of Gordon's musical experience. He has played in numerous theater orchestras and jazz bands. He enjoys doing physics and still having the pleasure of music without worrying about where the next "gig" is going to be. He has done musical acoustics research and published with students for the past 20 years. The Acoustical Society of America Acknowledgments Contents About the Author 1 Introduction 1.1 Overview of Book 1.1.1 General Introduction 1.1.2 Book Subjects and Structure 1.2 Role of Music in Society 1.3 Role of Physics in Society 1.3.1 STEM Definition and Societal Benefits 1.3.2 Connection Between Art and Science 1.4 Role of Physics in Acoustics 1.4.1 Waves in Modeling Physical Processes 1.4.2 Instrument Structure and Design 1.5 Discussion Topics 1.6 Problems References 2 Language, Structure and Function of Music 2.1 Language 2.1.1 Notes and Intervals 2.1.2 Frequencies and Wave Properties 2.1.3 Designation of Intervals 2.1.4 Scales and Chords 2.1.5 Blues and Other Scales 2.1.6 Structures Based on Circle of Fifths 2.2 Mathematics of Music 2.2.1 Powers and Logarithms 2.2.2 Logarithms 2.2.3 Cents Intervals and Equal Temperament Tuning 2.3 Basic Elements of Music 2.3.1 Other Key Elements of Music 2.3.2 Orchestration 2.3.3 Stages of Development in a Musical Piece-Revisited 2.4 Brief History of Musical Styles 2.5 Summary 2.6 Discussion Topics 2.7 Problems References 3 Physics Concepts 3.1 Physical Variables in Musical Acoustics 3.1.1 Units 3.1.2 Kinematics 3.1.3 Force and Pressure 3.1.3.1 Newton's Laws of Motion 3.1.3.2 Pressure 3.1.4 Energy and Power 3.1.4.1 Energy Conservation 3.1.4.2 Power 3.1.5 Periodic Motion 3.2 Wave Properties 3.2.1 Longitudinal and Transverse Waves 3.2.2 Superposition of Waves 3.2.3 Standing Waves 3.2.3.1 Pressure in Pipes 3.2.3.2 Standing Waves in Strings 3.2.4 Helmholtz Resonators 3.2.5 Waves in Instruments 3.3 Advanced Concepts 3.3.1 Doppler Effect 3.3.2 Sound Effects and Modulating Waves 3.3.3 Diffraction 3.3.4 Sensory Perception and the Ear 3.3.4.1 Energy Transfer in the Ear 3.3.4.2 Sensory Perception in the Ear 3.3.4.3 Physical Versus Psychological Variables: Psychoacoustics 3.4 Summary 3.5 Projects and Discussion 3.6 Lab Exercises 3.7 Problems Appendix References 4 Introduction to the Instrument Groups 4.1 Common Features of All Instruments 4.2 Characteristics of the Specific Instrument Groups 4.2.1 Brass 4.2.2 Strings 4.2.3 Woodwinds 4.2.4 Percussion 4.2.5 Electronic 4.2.6 Voice 4.3 Musical Considerations 4.4 Discussion Topics and Problems References 5 Brass Instrument Group 5.1 History of Brass Instruments 5.2 Summary of Key Properties 5.3 Description of Operation 5.3.1 Source of Sound 5.3.2 Body Structure and Function 5.3.3 Interface 5.4 Unique Characteristics of Brass Instruments 5.4.1 Trumpets 5.4.2 French Horn 5.4.3 Trombone 5.4.4 Tuba, Sousaphone and Other Brass Instruments 5.5 Summary 5.6 Discussion Topics and Problems 5.7 Demonstrations and Experiments Appendix References 6 Stringed Instrument Group 6.1 History of Stringed Instruments 6.1.1 Strummed Instruments 6.1.2 Bowed Instruments 6.1.3 Keyboard Instruments 6.2 Summary of Key Properties 6.3 Description of Operation 6.3.1 Source of the Sound 6.3.1.1 String Properties 6.3.1.2 Vibrations of Plucked, Bowed and Picked Strings 6.3.2 Use of Strings to Create Musical Effects 6.3.3 Body and Interface Structure and Function 6.4 Unique Characteristics of Stringed Instruments 6.4.1 The Violin Family 6.4.2 Plucked Instruments 6.4.3 Pianos 6.5 Discussion Topics and Problems References 7 Woodwind Instrument Group 7.1 History of Woodwind Instruments 7.2 Summary of Key Properties 7.3 Description of Operation 7.3.1 Source of Sound 7.3.2 Body Structure and Function 7.3.3 Interface 7.4 Unique Characteristics of Woodwind Instruments 7.4.1 Flutes and Recorders 7.4.2 Single Reed Instruments 7.4.2.1 Clarinets 7.4.2.2 Saxophones 7.4.3 Double Reed Instruments 7.4.3.1 Oboes 7.4.3.2 Bassoons 7.4.4 Free Reed Instruments 7.4.5 Harmonica 7.4.6 Accordion 7.5 Discussion Topics and Problems 7.6 Demonstrations and Experiments References 8 Percussion Instrument Group 8.1 History of Percussion Instruments 8.1.1 Two Dimensional Sources 8.1.2 Three Dimensional Idiophones 8.2 Key Properties and Operation 8.2.1 Two Dimensional Percussion Sources 8.2.2 Three Dimensional Percussion Idiophones 8.3 Unique Characteristics of Percussion Instruments 8.3.1 Snare Drum 8.3.2 Other Stretched Membrane Drums 8.3.3 Timpani 8.3.4 Cymbals and Triangles 8.3.5 Gongs and Tamtams 8.3.6 Bar Instruments: Idiophones 8.3.7 Chimes 8.3.8 Bells 8.3.9 Steelpans 8.4 Discussion Topics and Problems 8.5 Demonstrations and Experiments References 9 Electronic Instrument Group 9.1 History of Electronic Instruments 9.2 Summary of Properties and Operation 9.2.1 Properties 9.2.1.1 Electronics Terminology 9.2.1.2 Creating Waveforms 9.2.2 Operation 9.3 Unique Characteristics of Electronic Instruments 9.3.1 Electric Guitars and Amplified Instruments 9.3.2 Sound Recording 9.3.3 Organs 9.3.4 Synthesizers and MIDI 9.4 Summary 9.5 Discussion Topics and Problems 9.6 Demonstrations and Experiments References 10 The Voice Group 10.1 Summary of Key Properties 10.2 Description of Operation 10.2.1 The Vocal Tract Source 10.2.2 Vocal Tract Function 10.2.3 Interface 10.3 Unique Characteristics of Singing Voices 10.4 Summary 10.5 Discussion Topics and Problems References 11 Room Acoustics 11.1 Introduction 11.2 Sound Propagation 11.3 Room Acoustics Standards 11.4 Physical Requirements for Appropriate Sound 11.4.1 Venue Design Parameters 11.4.2 Venue Design Examples 11.5 Summary of Room Acoustics 11.6 Discussion Topics and Problems 11.7 Demonstrations and Experiments References 12 Epilog: Connecting the Concepts 12.1 Summary of Musical Topics 12.2 Overview of Technical Concepts 12.3 Revisiting the Science and Art Connection 12.4 Individual Project and Group Work 12.5 Final Thoughts References A Frequencies of a Wide Range of Musical Notes B Fourier Transforms and Acoustic Spectra C Powers, Logarithms and Decibels C.1 Introduction C.2 Powers and Logarithms C.2.1 Powers C.2.2 Logarithms C.3 Decibels References D Frequencies and Notes on a Piano Glossary Glossary Index