Table of Contents
1. Introduction
1.1 Outline of the General Computational Theory
of Musical Structure
1.2 Uses of the General Computational Theory
of Musical Structure
1.3 Outline of thesis
2. Background and Related Work
2.1 Paradigmatic Analysis (Nattiez)
2.2 The Generative Theory of Tonal Music (Lerdahl
& Jackendoff)
2.3 The Implication-Realisation Model (Narmour)
2.4 Computational Models
2.4.1 Cypher (Rowe)
2.4.2 Experiments in Musical Intelligence
(Cope)
2.4.3 A Predictive Musical Model (Conklin
& Witten)
2.4.4 Humdrum (Huron)
2.5 General Comments and Problems
3. The General Computational Theory of
Musical Structure (GCTMS)
3.1 Musical Structure
3.2 Computational Theory
3.3 General Principles
3.4 Overview of the GCTMS
3.4.1 GCTMS: Musical Input
3.4.2 GCTMS: Output Analysis
3.4.3 GCTMS: Representations and Models
4. Logical and Cognitive Foundations
4.1 Basic Principles
4.2 Identity
4.3 Similarity
4.4 Categorisation
4.5 Similarity and categorisation bound together
4.6 Re-examining some psychological experiments
5. Representation of the Musical Surface
5.1 The Common Hierarchical Abstract Representation
for Music (CHARM)
5.2 Musical Surface
5.3 Pitch and Pitch Interval Representation
5.3.1 The General Pitch Interval Representation
(GPIR)
5.3.2 Applications and Uses of the GPIR
5.3.3 Transcription of melodies based on the
GPIR
6. Microstructural Module (Local Boundaries,
Accents, Metre)
6.1 Musical Rhythm
6.2 The Gestalt principles of proximity and
similarity in theories of rhythm
6.3 The Local Boundary Detection Model (LBDM)
6.3.1 The Identity-Change and Proximity Rules
6.3.2 Applying the ICR and PR rules on three
note sequences
6.3.3 Applying the ICR and PR rules on longer
melodic sequences
6.3.4 Further comments of the application
of the LBDM rules
6.3.5 The refined LBDM
6.4 Phenomenal Accentuation Structure
6.5 Metrical Structure
7. Macrostructural Module I (Musical Parallelism
and Segmentation)
7.1 Similarity and pattern-matching
7.2 Overlapping of patterns
7.3 Pattern-matching and pitch-interval representation
7.4 The String Pattern-Induction Algorithm
(SPIA)
7.5 The Selection Function
7.6 Segmentation based on musical parallelism
7.7 Interaction with microstructural module
8. Macrostructural Module II (Musical
Categories)
8.1 A working formal definition of similarity
and categorisation
8.2 The Unscramble Algorithm
8.3 An illustrative example
8.3.1 Category formation
8.3.2 Category membership prediction
8.4 A musical example
8.5 Relative merits of the Unscramble algorithm
9. Overall Model and Four Analyses
9.1 Overall model based on the GCTMS
9.1.1 Musical input
9.1.2 From melodic surface to segmentation
9.1.3 From segmentation to paradigmatic description
9.1.4 Manually performed tasks
9.2 Four melodic analyses
9.2.1 The Finale Theme of Beethoven's 9th
Symphony
9.2.2 L'Homme Arme
9.2.3 A melody from Webern's Lieder Op.3
9.2.4 A melody from Babbit's Du song cycle
10. Conclusion
10.1 Concluding remarks
10.2 Future developments
Bibliography