- 6 -Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory 
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1 Introduction
2 OpenMusic description
 2.1 Patches
 2.2 The Musical Framework
 2.3 Music editors
3 Mixing visual programming and music notation
 3.1 Scores integrating visual programs
 3.2 Visual programs integrating Scores
4 Maquettes
5 Conclusion
1 Introduction
2 Some musical CSPs
 2.1 CSPs in Computer Assisted Composition
 2.2 CSPs in computer assisted musical analysis
3 Special features of these CSP
 3.1 About composition problems
 3.2 About analysis
 3.3 General features
4 Resolution
 4.1 Adaptive search
 4.2 Algorithm
 4.3 Use of this algorithm for musical CSPs
5 Conclusion
1 Introduction
 1.1 Roles in Software Development and Configuration for Music Research
 1.2 Kinds of Configuration
 1.3 Integration Preconditions
2 Humdrum: Basic Score Processing
 2.1 User and Programming Levels
 2.2 A Distributed Support Model
3 Rubato: Interactive Theory Testing
 3.1 Configuration Levels
 3.2 User and Developer Resources of Support
4 OpenMusic: Composing
 4.1 User Levels and Roles in Configuration and Programming
 4.2 Support at IRCAM
5 OHR: Software Integration
 5.1 An OpenMusic, Humdrum, and Rubato Integration Example
 5.2 Interprocess Communication Routing
 5.3 Language Mappings
 5.4 Configuring an Interpreter Mapping in OpenMusic
 5.5 Examples of Mixing Programming Languages in OpenMusic
 5.6 Wrapping up Functionality
 5.7 User Gains of Existing Integration Components
6 Conclusion
1 Introduction
2 Traditional vs. Distributed Rubato
3 Implementation in Java
 3.1 Communication using Denotators over RMI
4 Forms, Denotators, and Modules
5 The Rubette Interface
6 Designing a Rubette
7 Interfacing with other Software
8 Spatialization
 8.1 Folding n -Space
 8.2 Folding Denotators
 8.3 Folding Matrix
 8.4 Simple Denotator Folding
 8.5 Limit
 8.6 Colimit
 8.7 Powerset
 8.8 Greeking
9 Visualization
 9.1 Satellites
 9.2 Cockpits
10 Conclusion
1 Introduction
2 Inner metric analysis
3 Second Symphony
 3.1 First movement
 3.2 Second movement
 3.3 Third Movement
 3.4 Fourth movement
 3.5 Summary Second Symphony
4 Third Symphony
 4.1 First movement
 4.2 Third movement
 4.3 Summary Third Symphony
5 Conclusion
1 Introduction
2 Motivic Spaces
3 Presence, Content, and Weight Functions
4 The Flow Chart for the Calculations in the MeloTopRUBETTE
5 RUBATO’s MeloTopRUBETTE vs Melo-
RUBETTE
6 Acknowledgments
1 Introduction
2 The Mathematical Model
3 Numerical Characteristics
4 Hausdorff Distance and Melodic Weight
5 Combinatorial Characteristics
6 Concluding Remarks
1 Introduction
 1.1 Homogeneity and Temperament
 1.2 Chords as Tone-Sets
 1.3 Anchors in American >Set Theory<
 1.4 Anchors in >Neo-Riemannian Theory<
 1.5 Circle Chords -- a Motivating Observation
2 Basic Investigations
 2.1 Tone Perspectives
 2.2 Tone Symmetries
 2.3 Chords and their Perspectives
3 Harmonic Morphology
 3.1 Harmonic Morphemes
 3.2 Internal Logics of a Morpheme
 3.3 Towards Enumeration of Harmonic Morphemes
 3.4 Harmonic Topology
4 Bridges to Hugo Riemann
 4.1 Consonant and dissonant Tone Perspectives
 4.2 Bigeneric Morphemes
5 Experiments with the Program jMorph
 5.1 Construction of Morphemes with the Morpheme Browser
 5.2 Presence of a Morpheme in a Chord Sequence
6 Perspectivic Approach to Voice Leadings
1 Paths in Harmonic Spaces
 1.1 Chords, Harmonic Loci, and Harmonic Analyses
 1.2 Interpretation of Harmonic Path Analyses and Refinements
 1.3 Quantification of Harmonic Transition
 1.4 Evaluation of Harmonic Analyses
 1.5 Formulas for transV al and locusV al
2 Riemann Logics
 2.1 General Morphology of Chords
 2.2 Tone Profiles
 2.3 Perspectival Morpho-Logic
 2.4 Concrete Tone Spaces
3 HarmoRubette and Re-Design
 3.1 Harmonic Configuration Space in the >Classic< HarmoRubette
 3.2 Riemann Logic in the >Classic< HarmoRubette
 3.3 Aspects of the Re-Design
4 Elaine Chew’s Spiral Array
 4.1 Tone-, Chord- and Keyspirals
 4.2 Tuning of the Free Parameters
 4.3 Proposal for a Riemann Function Space
 4.4 Center-Of-Effect-Generator
5 Fred Lerdahl’s model of Chordal/Regional Space
 5.1 Intra-Regional Distance
 5.2 Inter-Regional Distance
 5.3 Hybrid Space: Hierarchy versus Shortest Path
 5.4 Reduced Chordal/Regional Space
 5.5 Lerdahl versus Lerdahl: The Faith-motive
 5.6 Diatonic Triad Stratifications
1 Introduction
2 Analysis of Co-occurrence
 2.1 Correspondence Analysis
3 Circle of Fifths in the Keyscape
 3.1 Circle of Fifths from Score
 3.2 Circle of Fifths in Performance
4 Stylescapes Based on Key Preference
5 Discussion
6 Appendix
 6.1 Technical Details of Correspondence Analysis
 6.2 Details of Chew’s Model with Choice of Parameters

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- 6 -Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory