This book presents a new approach to computational musicology in which music becomes a computational entity based on human cognition, allowing us to calculate music like numbers. Does music have semantics? Can the meaning of music be revealed using symbols and described using language? The authors seek to answer these questions in order to reveal the essence of music.
Chapter 1 addresses a very fundamental point, the meaning of music, while referring to semiotics, gestalt, Schenkerian analysis and cognitive reality. Chapter 2 considers why the 12-tone equal temperament came to be prevalent. This chapter serves as an introduction to the mathematical definition of harmony, which concerns the ratios of frequency in tonic waves. Chapter 3, “Music and Language,” explains the fundamentals of grammar theory and the compositionality principle, which states that the semantics of a sentence can be composed in parallel to its syntactic structure. In turn, Chapter 4 explains the most prevalent score notation – the Berklee method, which originated at the Berklee School of Music in Boston – from a different point of view, namely, symbolic computation based on music theory. Chapters 5 and 6 introduce readers to two important theories, the implication-realization model and generative theory of tonal music (GTTM), and explain the essence of these theories, also from a computational standpoint. The authors seek to reinterpret these theories, aiming at their formalization and implementation on a computer. Chapter 7 presents the outcomes of this attempt, describing the framework that the authors have developed, in which music is formalized and becomes computable. Chapters 8 and 9 are devoted to GTTM analyzers and the applications of GTTM. Lastly, Chapter 10 discusses the future of music in connection with computation and artificial intelligence.This book is intended both for general readers who are interested in music, and scientists whose research focuses on music information processing. In order to make the content as accessible as possible, each chapter is self-contained.
Author(s): Keiji Hirata, Satoshi Tojo, Masatoshi Hamanaka
Publisher: Springer
Year: 2022
Language: English
Pages: 263
City: Singapore
Preface
Acknowledgements
Contents
1 Machine that Computes the Meaning of Music
1.1 Music Theory that Enjoys the Benefits of Computers
1.2 A Short History of Program Music
1.3 Understanding Music from a Gestalt Point of View
1.4 Attribution of Meaning to Melody by Semiotics
1.5 Categorization of Musical Meaning
1.6 Reduction Hypothesis and Schenkerian Analysis
1.7 Analysis of Retrograde
1.8 Understanding Music that Imitates Understanding Language
1.9 Cognitive Reality
References
2 The Mathematics of Ebony and Ivory Keys
2.1 Scale with 2 and 3
2.2 Revised Pythagoras Scale
2.3 Just Intonation—Introduction of 5
2.4 Eitz's Notation
2.5 What Is Overtone?
2.6 Meantone
2.7 Issue on Modulation
2.8 Equal Temperament
2.9 Scale, Mode, and Key
2.10 History of 12-Tone Equal Temperament
2.11 Symmetry
References
3 Music as Formal Language
3.1 Chomsky and Generative Grammar
3.2 Formal Language and Automata
3.3 Human Language in the Hierarchy
3.4 Language Class of Chord Progression
3.4.1 Context-Free Syntax of Cadence
3.4.2 Generative Syntax Model
3.4.3 Probabilistic Context-Free Grammar
3.4.4 Head-Driven Phrase Structure Grammar
3.4.5 Combinatorial Category Grammar
3.4.6 Parsing Algorithms
References
4 Berklee Method
4.1 Berklee Method
4.2 Degree
4.3 Chords
4.4 Chord Names and Rules of Functions
4.5 Historical Significance
4.6 Merits and Demerits of Symbolization
4.7 Virtualization
4.8 Jazz, Classical and Pop Music
References
5 Implication-Realization Model
5.1 The Implication-Realization Model
5.2 Gestalt that Appears in Music
5.3 The Principles of the Implication-Realization Model
5.4 Basic Implication-Realization Patterns
5.5 Carlsen's Experiment and the Validity of the Implication-Realization Model
References
6 GTTM and TPS
6.1 Introduction to GTTM
6.1.1 Grouping Analysis
6.1.2 Metrical Analysis
6.1.3 Introduction to Reduction
6.1.4 Time-Span Reduction
6.1.5 Prolongational Reduction
6.2 Tonal Pitch Space
6.2.1 Tonal Tension and Attraction
References
7 Formalization of GTTM
7.1 Putting Intention into Music
7.2 GTTM Analysis and Rendering
7.3 Formalization of Time-Span Trees
7.4 Reduction Distance
7.5 Experiment to Assess the Validity of the Time-Span Tree
7.6 Melody Morphing by Time-Span Tree
7.7 Concluding Remarks
References
8 Implementation of GTTM
8.1 Introduction of Implementing GTTM
8.2 Previous Work on Implementing a Music Theory
8.3 Implementing GTTM on a Computer
8.3.1 Problems in Implementing GTTM
8.3.2 Solution: Proposal of exGTTM
8.4 Grouping Analysis
8.4.1 Application of Grouping Preference Rules
8.4.2 Acquisition of Hierarchical Grouping Structure
8.5 Metrical Analysis
8.5.1 Application of MPRs
8.5.2 Acquisition of Hierarchical Metrical Structure
8.6 Generation of Time-Span Tree
8.6.1 Application of Time-Span Reduction Preference Rules
8.6.2 Generation of Time-Span Tree
8.7 Automatic Time-Span Tree Analyzer (ATTA)
8.7.1 XML-Based Data Structure
8.7.2 Implementation in Perl
8.7.3 Java-Based GUI
8.8 Experimental Results
8.8.1 Evaluation Data
8.8.2 Parameter Tuning
8.8.3 Acquisition of Low-Level Grouping Boundary
8.8.4 Acquisition of Hierarchical Grouping Structure
8.8.5 Acquisition of Metrical Structure
8.8.6 Acquisition of Time-Span Tree
8.9 Concluding Remarks
References
9 Application of GTTM
9.1 Basic Algorithm of Melodic Morphing
9.1.1 Ideas of Melodic Morphing
9.1.2 Partial Melody Reduction
9.1.3 Combining Two Melodies
9.2 Implementation of Melodic Morphing Algorithm
9.2.1 Two Solutions to the Two Problems
9.2.2 Melodic Morphing Based on Ternary-Branching Tree
9.2.3 Automating Melodic Morphing by Prioritization of Branches
9.3 Experimental Results
9.3.1 Subject Evaluation with Melodic Morphing Based on Ternary-Branching Tree
9.3.2 Automating Melodic Morphing by Prioritization of Branches
9.4 Concluding Remarks
References
Epilogue
Appendix Appendix
1Pitch, Note Name and Interval
2Scale and Mode
3Key
4Melody and Counterpoint
5Chords and Functional Harmony
6Beat and Rhythm
Index
