Fractals in Music: Introductory Mathematics for Musical Analysis

a| 99090421

a| 0967172756

a| (Sirsi) i0967172756

a| (OCoLC)42729532

a| DLC c| DLC d| OTC d| MRY d| OCL d| MvI

a| MT6.M14 b| F73 1999

a| 781.1

a| Madden, Charles q| (Charles B.)

a| Fractals in music : b| introductory mathematics for musical analysis / c| Charles Madden.

a| 1st ed.

a| Salt Lake City : b| High Art Press, c| 1999.

a| xiv, 210 p. : b| ill. ; c| 23 cm.

a| InMusic ; v| no. 1

a| Includes bibliographical references (p. [191]-204) and index.

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.

a| 12

a| Music theory x| History y| 20th century.

a| Musical analysis.

a| Fractals.

a| InMusic (Salt Lake City, Utah) ; v| no. 1.

a| MT6 .M14 F73 1999 w| LC i| X004545306 l| STACKS m| MUSIC t| BOOK