Published 2019
Table of Contents:
“…Preface xiii -- Acknowledgements xvii -- List of Figures xix -- List of Tables xxv -- 1 Elements and Philosophy of Music 1 -- 1.1 The Logic of Sound 1 -- 1.2 The Audio and the Video 3 -- 1.3 Made of Sound and Silence 5 -- 1.4 The Quantum Nature of Music 7 -- 1.5 The Sound Perception 10 -- 1.6 The Material and the Virtual 12 -- 1.7 The Organized Sound 14 -- 1.8 Music and Poetry 16 -- 2 History and Evolution of Music 21 -- 2.1 Music of the Evolution 21 -- 2.2 The Pre-Historic Antiquity 22 -- 2.3 Music Eras 24 -- 2.3.1 Middle Ages 24 -- 2.3.2 Renaissance 25 -- 2.3.3 Baroque 26 -- 2.3.4 Classic 26 -- 2.3.5 Romantic 26 -- 2.3.6 Modern Era 27 -- 2.3.7 Neoclassicism 28 -- 3 Music and Mathematics 29 -- 3.1 Music in Theory 29 -- 3.1.1 Equal Temperament 30 -- 3.1.2
Just Intonation 31 -- 3.2 The First Studies of Musical Consonance 34 -- 3.3 Mathematicians and Music 36 -- 3.4 The Decomposition of Music 41 -- 4 Signal Analysis 47 -- 4.1 Basic Fourier Analysis 47 -- 4.1.1 The Trigonometric Fourier Series 49 -- 4.1.2 The Compact Fourier Series 55 -- 4.1.3 The Exponential Fourier Series 56 -- 4.2 Convergence to Fourier Transform 58 -- 5 Fourier Transform Applications 61 -- 5.1 Fourier Transform 61 -- 5.1.1 Fourier Transform of the Impulse Function 61 -- 5.1.2 Transform of the Unit Step Function 63 -- 5.1.3 Transform of the Constant Function 64 -- 5.1.4 The Exponential Signal 65 -- 5.1.5 Bilateral Exponential Signal 67 -- 5.1.6 Transform of the Gate Function 68 -- 5.1.7 Fourier Transform of the Sine and Cosine Functions 70 -- 5.1.8 Fourier Transform of the Complex Exponential 70 -- 5.1.9 Fourier Transform of a Periodic Function 71 -- 6 Properties of the Fourier Transform 73 -- 6.1 Properties of the Fourier Transform 73 -- 6.1.1 Linearity the Fourier Transform 73 -- 6.1.2 Scaling Property 74 -- 6.1.3 Symmetry of Fourier Transform 75 -- 6.1.4 Time Domain Shift 76 -- 6.1.5 Frequency Domain Shift 76 -- 6.1.6 Differentiation in the Time Domain 76 -- 6.1.7 Integration in the Time Domain 77.…”
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