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
- Staff View
LEADER 03469cam a2200337Ia 4500001 u3707411003 SIRSI005 20010409120722.0008 990408s1999 utua b 001 0 enga| 99090421a| 0967172756a| (Sirsi) i0967172756a| (OCoLC)42729532a| DLC c| DLC d| OTC d| MRY d| OCL d| MvIa| MT6.M14 b| F73 1999a| 781.1a| 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. 1a| 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| 12a| 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
Availability
Library | Location | Map | Availability | Call Number |
---|---|---|---|---|
Music | Stacks | N/A | Available |
MT6 .M14 F73 1999 |