Item Details

Fractals in Music: Introductory Mathematics for Musical Analysis

Charles Madden
Format
Book
Published
Salt Lake City : High Art Press, 1999.
Edition
1st ed
Language
English
Series
InMusic
InMusic (Salt Lake City, Utah)
ISBN
0967172756
Contents
  • Chaos Theory 3
  • Fractal Geometry 9
  • 2. Self-Similarity 19
  • Elements of Self-Similarity 19
  • Similarity Transforms 21
  • Similarity Transforms Applied to a Motive 22
  • Self-Similarity in the Resulting Melody 25
  • Octave Sequence 27
  • Harmonic Sequence 29
  • Self-Similarity in the Harmonic Sequence 31
  • Scales 33
  • Equal Temperament 34
  • Logarithmic Transforms 36
  • More Mathematics 38
  • Rhythm, Meter, and Dynamics 39
  • Larger Structures 39
  • 3. Attractors 41
  • What is an Attractor? 41
  • Pitches and Keys 43
  • Application to Atonality 47
  • Attractors: Schenker, Schoenberg, and Stravinsky 49
  • Other Musical Attractors 54
  • 4. Fib and Phi 57
  • Fibonacci Numbers 57
  • Phi: The Golden Mean 59
  • Organicism 61
  • Fib [characters not producible] Phi, But 63
  • Working Procedure 66
  • Music 67
  • Varese 67
  • Schoenberg 68
  • Bartok 68
  • Schillinger 70
  • Stockhausen 70
  • Debussy 72
  • Beethoven 72
  • Bach 73
  • Liber Usualis 74
  • Webster 74
  • 5. Resonance 77
  • Self-Organization 77
  • Mode Locking 78
  • Impedance 81
  • Formants 84
  • Tuning 86
  • Undertones 87
  • Multiphonics 89
  • Acoustic Feedback 92
  • 6. Randomicity 97
  • Noise 98
  • Scatter Diagrams 103
  • Voss: Music from 1/f Noise 107
  • Xenakis: Eonta 112
  • Schubert: Who is Sylvia? 112
  • Gregorian Chant 113
  • Dodge: Brown Music 115
  • Stewart: Chaotic Music 115
  • 7. Dimension 119
  • Fractal Dimensions 119
  • Scatter Plots 121
  • Uniform Noise 121
  • Gaussian Noise 122
  • Pink Noise 124
  • Brown Noise 125
  • Dodge: Brown Music 126
  • Gregorian Music 127
  • Schubert: Who is Sylvia? 129
  • Voss: White Music 131
  • Voss: Pink Music 132
  • Voss: Brown Music 133
  • Xenakis: Eonta 135
  • 8. Statistics 139
  • Statistical Parameters 140
  • Range 140
  • Midpoint 140
  • Median 140
  • Mean 141
  • Variance 141
  • Standard Deviation 141
  • Spreadsheets and Distribution Plots 142
  • Musical Analysis 148
  • Correlation 151
  • Applications to the Music 155
  • Other Applications 158
  • Databases 159
  • 9. Transforms 163
  • Fundamentals of Signal Processing 163
  • Fourier Series 170
  • Fourier Transform 175
  • Inverse Fourier Transform 178
  • Application to Nonperiodic Waveforms, i.e., Music 179
  • Final Conclusions 189.
Description
xiv, 210 p. : ill. ; 23 cm.
Notes
Includes bibliographical references (p. [191]-204) and index.
Series Statement
InMusic ; no. 1
InMusic (Salt Lake City, Utah) ; no. 1
Technical Details
  • Access in Virgo Classic

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    a| xiv, 210 p. : b| ill. ; c| 23 cm.
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    t| Chaos Theory g| 3 -- t| Fractal Geometry g| 9 -- g| 2. t| Self-Similarity g| 19 -- t| Elements of Self-Similarity g| 19 -- t| Similarity Transforms g| 21 -- t| Similarity Transforms Applied to a Motive g| 22 -- t| Self-Similarity in the Resulting Melody g| 25 -- t| Octave Sequence g| 27 -- t| Harmonic Sequence g| 29 -- t| Self-Similarity in the Harmonic Sequence g| 31 -- t| Scales g| 33 -- t| Equal Temperament g| 34 -- t| Logarithmic Transforms g| 36 -- t| More Mathematics g| 38 -- t| Rhythm, Meter, and Dynamics g| 39 -- t| Larger Structures g| 39 -- g| 3. t| Attractors g| 41 -- t| What is an Attractor? g| 41 -- t| Pitches and Keys g| 43 -- t| Application to Atonality g| 47 -- t| Attractors: Schenker, Schoenberg, and Stravinsky g| 49 -- t| Other Musical Attractors g| 54 -- g| 4. t| Fib and Phi g| 57 -- t| Fibonacci Numbers g| 57 -- t| Phi: The Golden Mean g| 59 -- t| Organicism g| 61 -- t| Fib [characters not producible] Phi, But g| 63 -- t| Working Procedure g| 66 -- t| Music g| 67 -- t| Varese g| 67 -- t| Schoenberg g| 68 -- t| Bartok g| 68 -- t| Schillinger g| 70 -- t| Stockhausen g| 70 -- t| Debussy g| 72 -- t| Beethoven g| 72 -- t| Bach g| 73 -- t| Liber Usualis g| 74 -- t| Webster g| 74 -- g| 5. t| Resonance g| 77 -- t| Self-Organization g| 77 -- t| Mode Locking g| 78 -- t| Impedance g| 81 -- t| Formants g| 84 -- t| Tuning g| 86 -- t| Undertones g| 87 -- t| Multiphonics g| 89 -- t| Acoustic Feedback g| 92 -- g| 6. t| Randomicity g| 97 -- t| Noise g| 98 -- t| Scatter Diagrams g| 103 -- t| Voss: Music from 1/f Noise g| 107 -- t| Xenakis: Eonta g| 112 -- t| Schubert: Who is Sylvia? g| 112 -- t| Gregorian Chant g| 113 -- t| Dodge: Brown Music g| 115 -- t| Stewart: Chaotic Music g| 115 -- g| 7. t| Dimension g| 119 -- t| Fractal Dimensions g| 119 -- t| Scatter Plots g| 121 -- t| Uniform Noise g| 121 -- t| Gaussian Noise g| 122 -- t| Pink Noise g| 124 -- t| Brown Noise g| 125 -- t| Dodge: Brown Music g| 126 -- t| Gregorian Music g| 127 -- t| Schubert: Who is Sylvia? g| 129 -- t| Voss: White Music g| 131 -- t| Voss: Pink Music g| 132 -- t| Voss: Brown Music g| 133 -- t| Xenakis: Eonta g| 135 -- g| 8. t| Statistics g| 139 -- t| Statistical Parameters g| 140 -- t| Range g| 140 -- t| Midpoint g| 140 -- t| Median g| 140 -- t| Mean g| 141 -- t| Variance g| 141 -- t| Standard Deviation g| 141 -- t| Spreadsheets and Distribution Plots g| 142 -- t| Musical Analysis g| 148 -- t| Correlation g| 151 -- t| Applications to the Music g| 155 -- t| Other Applications g| 158 -- t| Databases g| 159 -- g| 9. t| Transforms g| 163 -- t| Fundamentals of Signal Processing g| 163 -- t| Fourier Series g| 170 -- t| Fourier Transform g| 175 -- t| Inverse Fourier Transform g| 178 -- t| Application to Nonperiodic Waveforms, i.e., Music g| 179 -- t| Final Conclusions g| 189.
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