Mathematics and Computation in Music

Table of Contents

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   Book Overview
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   Chapter 1 Primal-Circular Substitutions
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   Chapter 2 On the Group of Transformations of Classical Types of Seventh Chords
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   Chapter 3 Pairwise Well-Formed Modes and Transformations
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   Chapter 4 Homometry in the Dihedral Groups: Lifting Sets from $$ \mathbb {Z}_{n}$$ Z n to $$ D_{n}$$ D n
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   Chapter 5 A Symmetric Quantum Theory of Modulation in $$Z\!\!Z_{20}$$ Z Z 20
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   Chapter 6 Almost Difference Sets in Transformational Music Theory
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   Chapter 7 Algebra of Harmony: Transformations of Just Consonances
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   Chapter 8 Developing Software for Dancing Tango in Compás
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    Chapter 9 Using Inharmonic Strings in Musical Instruments
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    Chapter 10 Real-Time Compositional Procedures for Mediated Soloist-Ensemble Interaction: The Comprovisador
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    Chapter 11 Strange Symmetries
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    Chapter 12 Interval Content vs. DFT
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    Chapter 13 Probing Questions About Keys: Tonal Distributions Through the DFT
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    Chapter 14 Abstract Gestures: A Unifying Concept in Mathematical Music Theory
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    Chapter 15 Mathematical Music Theory and the Musical Math Game—Two Creative Ontological Switches
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    Chapter 16 Hamiltonian Graphs as Harmonic Tools
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    Chapter 17 New Investigations on Rhythmic Oddity
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    Chapter 18 Polytopic Graph of Latent Relations
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    Chapter 19 Dynamic Time Warping for Automatic Musical Form Identification in Symbolical Music Files
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    Chapter 20 Identification and Evolution of Musical Style I: Hierarchical Transition Networks and Their Modular Structure
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    Chapter 21 A Fuzzy-Clustering Based Approach for Measuring Similarity Between Melodies
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    Chapter 22 The Evolution of Tango Harmony, 1910–1960
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    Chapter 23 Determination of Compositional Systems Through Systemic Modeling
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    Chapter 24 A Cluster Analysis for Mode Identification in Early Music Genres
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    Chapter 25 Cross Entropy as a Measure of Coherence and Uniqueness
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    Chapter 26 Complementary Collections in Ligeti’s Désordre
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    Chapter 27 Probabilistic Generation of Ragtime Music from Classical Melodies
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    Chapter 28 Using Probabilistic Parsers to Support Salsa Music Composition