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Music and Schema Theory
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Music is an important domain of application for scema theory. The perceptual structure for pitch and timbre have been mapped via schemata, with results that have contributed to a better undestanding of music perception. This text asks the questions, "How does a schema come into existence?", and "How does it function in a particular perception task?". It provides a foundation for the understanding of emergence and functionality of schemata by means of computer-based simulations of tone centre perception. It is about how memory structures self-organize and how they use contextual information to guide perception.
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Table of Contents

1. Introduction.- 2. Tone Semantics.- 2.1 The Problem of Tone Semantics.- 2.2 Historical Background.- 2.3 Consonance Theory.- 2.4 Cognitive Structuralism.- 2.5 The Static vs. Dynamic Approach.- 2.6 Conclusion.- 3. Pitch as an Emerging Percept.- 3.1 The Two-Component Theory of Revesz.- 3.2 Attribute Theory Reconsidered.- 3.3 The Shepard-Tone.- 3.4 Paradoxes of Pitch Perception.- 3.5 The Shepard-Illusion.- 3.6 Ambiguous Stimuli.- 3.7 Conclusion.- 4. Defining the Framework.- 4.1 The Computer Model.- 4.2 Representational Categories.- 4.2.1 Signals.- 4.2.2 Images.- 4.2.3 Schemata.- 4.2.4 Mental Representations.- 4.3 Conclusion.- 5. Auditory Models of Pitch Perception.- 5.1 The Missing Fundamental.- 5.2 Auditory Models.- 5.3 SAM: A Simple Model.- 5.3.1 SAM - The Acoustical Representation.- 5.3.2 SAM - The Synthetic Part.- 5.4 TAM: A Place Model.- 5.4.1 TAM - The Analytic Part.- 5.4.2 TAM - The Synthetic Part.- 5.4.3 TAM - Examples.- 5.5 VAM: A Place-Time Model 53.- 5.5.1 VAM - The Analytic Part.- 5.5.2 VAM - The Synthetic Part.- 5.5.3 VAM - Examples.- 5.6 Conclusion.- 6. Schema and Learning.- 6.1 Gestalt Perception.- 6.2 Tone Semantics and Self-Organization.- 6.2.1 Self-Organization as Learning.- 6.2.2 Self-Organization as Association.- 6.3 SOM: The Self-Organizing Map.- 6.3.1 Reduction of Dimensionality.- 6.3.2 Analogical and Topological Representations.- 6.3.3 Statistical Modeling.- 6.4 Architecture.- 6.5 Dynamics.- 6.6 Implementation.- 6.7 Conclusion.- 7. Learning Images-out-of-Time.- 7.1 SAMSOM.- 7.1.1 Selection of Data.- 7.1.2 Preprocessing.- 7.1.3 Network Specifications.- 7.1.4 Aspects of Learning.- 7.1.5 Ordering and Emergence.- 7.1.6 Conclusion.- 7.2 TAMSOM.- 7.2.1 Selection of Data and Preprocessing.- 7.2.2 Network Specifications.- 7.2.3 Ordering and Emergence.- 7.3 VAMSOM.- 7.3.1 Selection of Data and Preprocessing.- 7.3.2 Network Specifications.- 7.3.3 Ordering and Emergence.- 7.3.4 Tone Center Relationships.- 7.4 Conclusion.- 8. Learning Images-in-Time.- 8.1 Temporal Constraints in Tonality Perception.- 8.2 Tone Images-in-Time.- 8.3 Tone Context Images.- 8.4 Determination of the Integration Period.- 8.5 TAMSOM.- 8.5.1 Selection of Data and Preprocessing.- 8.5.2 Network Specifications.- 8.5.3 Aspects of Learning.- 8.5.4 Aspects of Ordering and Emergence.- 8.6 VAMSOM.- 8.6.1 Selection of Data and Preprocessing.- 8.6.2 Network Specifications and Aspects of Learning.- 8.6.3 Aspects of Ordering and Emergence.- 8.7 Conclusion.- 9. Schema and Control.- 9.1 Schema-Based Dynamics.- 9.2 TCAD: Tone Center Attraction Dynamics.- 9.2.1 Schema Responses as Semantic Images.- 9.2.2 Images as States.- 9.3 TCAD - Stable States.- 9.4 TCAD - Recognition.- 9.5 TCAD - Interpretation.- 9.6 The TCAD Model.- 9.6.1 Definitions.- 9.6.2 Dynamics.- 9.7 TCAD - At Work.- 9.8 Conclusion.- 10. Evaluation of the Tone Center Recognition Model.- 10.1 Overview of Other Models.- 10.2 TCAD-Based Tone Center Analysis.- 10.3 The Evaluation Method.- 10.4 Bartok - Through the Keys.- 10.4.1 Analysis.- 10.4.2 Discussion.- 10.5 Brahms - Sextet No. 2.- 10.5.1 Analysis.- 10.5.2 Discussion.- 10.6 Chopin - Prelude No. 20.- 10.6.1 Analysis.- 10.6.2 Discussion.- 10.7 The Effect of Phrase - Re-evaluation of Through the Keys.- 10.8 Conclusion.- 11. Rhythm and Timbre Imagery.- 11.1 Models of Rhythm Perception.- 11.2 VRAM: A Rhythm Analysis Model.- 11.2.1 Detection of Periodicities.- 11.2.2 VRAM - Analysis.- 11.2.3 VRAM - Examples.- 11.2.4 VRAM - Discussion.- 11.3 The Analysis of Timbre.- 11.4 Conclusion.- 12. Epistemological Foundations.- 12.1 Epistemological Relevance.- 12.2 Neurophysiological Foundations.- 12.2.1 Foundations of Images.- 12.2.2 Foundations of Schemata.- 12.3 Modular Organization.- 12.4 Relevance for a Theory of Meaning.- 12.4.1 Expressive Meaning and Analogical Thinking.- 12.4.2 Expressive Meaning and Virtual Self-movement.- 12.5 Music Semantics and Meaning Formation.- 12.6 Epistemological Principles.- 12.6.1 Atomism vs. Continuity.- 12.6.2 Cartesian Dualism vs. Monism.- 12.6.3 Computational Formalism vs. Complex System Dynamics.- 12.6.4 Representational Realism vs. Naturalism.- 12.6.5 Methodological Solipsism vs. Methodological Ecologism.- 12.6.6 Cognitivism vs. Materialism.- 12.7 Conclusion.- 13. Cognitive Foundations of Systematic Musicology.- 13.1 Cognitive Musicology, AI and Music, and Systematic Musicology.- 13.2 Historical-Scientific Background.- 13.3 New Developments in the 1960s.- 13.4 A Discipline of Musical Imagery.- 13.5 A Psycho-morphological Account of Musical Imagery.- 13.6 Interdisciplinary Foundations.- 13.7 General Conclusion.- A. Orchestra Score in CSOUND.- A.l The Orchestra File.- A. 2 The Score File.- B. Physiological Foundations of the Auditory Periphery.- B.1 The Ear.- B.1.1 The Outer Ear.- B.1.2 The Middle Ear.- B.1.3 The Inner Ear.- B.2 The Neuron.- B.2.1 Architecture.- B.2.2 Analysis of Neuronal Activity.- B.3 Coding.- B.3.1 Spatial Coding.- B.3.2 Temporal Coding.- B.3.3 Intensity.- B. 4 The Brain Stem and Cortex.- C. Normalization and Similarity Measures.- C. l Similarity Measures.- C.2 Towards a Psychoacoustic-Based Similarity Measure.- References.

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