Mathematics and Computation in Music
Third International Conference, MCM 2011, Paris, France, June 15-17, 2011. Proceedings
Published on 18. June 2011
XV, 375 pages
978-3-642-21590-2 (ISBN)
Description
This book constitutes the refereed proceedings of the Third International Conference on Mathematics and Computation in Music, MCM 2011, held in Paris, France, in June 2011. The 24 revised full papers presented and the 12 short papers were carefully reviewed and selected from 62 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. This year's conference aimed to provide a multi-disciplinary platform dedicated to the communication and exchange of ideas amongst researchers involved in mathematics, computer science, music theory, composition, musicology, or other related disciplines. Areas covered were formalization and geometrical representation of musical structures and processes; mathematical models for music improvisation and gestures theory; set-theoretical and transformational approaches; computational analysis and cognitive musicology as well as more general discussions on history, philosophy and epistemology of music and mathematics.
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Carlos Agon | Emmanuel Amiot | Moreno Andreatta
Mathematics and Computation in Music
Third International Conference, MCM 2011, Paris, France, June 15-17, 2011. Proceedings
Book
06/2011
1st Edition
Springer
€53.49
Shipment within 7-9 days
Content
- Title
- Preface
- Organization
- Table of Contents
- Long Papers
- Subsumption of Vertical Viewpoint Patterns
- Motivation
- Relational Patterns
- Vertical Viewpoints
- Subsumption for Vertical Viewpoints
- Discussion
- References
- Building Topological Spaces for Musical Objects
- Introduction
- PresentationoftheMGS Programming Language
- Topological Collections
- Transformations
- Self-assembly
- All-Interval Series
- Presentation of AIS
- Enumeration of All-Interval Series
- A Spatial Classification of AIS
- Conclusion and Future Work
- References
- A Model for Collective Free Improvisation
- Introduction
- Definitions and Model
- Time Scales
- Signal and Information
- Signal and Intention
- Objective
- Results and Discussion
- Collective Sequences and Their Articulation
- Contributing Factors to CFI's Structuring in Collective Sequences
- Future Plans
- References
- On a Class of Locally Symmetric Sequences:\\The Right Infinite Word $\Lambda_{\theta}$
- Introduction
- A Right Infinite Word on an Infinite Alphabet
- Each Letter Appears a Calculably Finite Number of Times
- Palindromes in $\Lambda_{\theta}$
- Regions
- Successive Letter Palindromes
- A Factoring by Nuclear Palindromes
- The Fibonacci Lambda Word
- Conclusions
- References
- Sensitive Interval Property for Scales as Words in the Free Group F2
- Introduction: Scale Theory and Word Theory
- Word Theory and Modes
- Into the Free Group F2, and Sensitive Intervals
- References
- Commuting Groups and the Topos of Triads
- Introduction
- Dual Groups and Cayley's Theorem
- Sub Dual Groups
- Hexatonic Systems
- Octatonic Systems
- The Topos of Triads and the neo-Riemannian $PLR$-Group
- Appendix on Topos Theory
- References
- Spelled Heptachords
- Spelled Pitch Classes
- Spelled Pitch-Class Sets
- Spelled Heptachords
- Applications to Chromatic Harmony
- References
- Fundamental Passacaglia: Harmonic Functions and the Modes of the Musical Tetractys
- Tonal Perspectives of the Harmonic Underworld
- Fifths and Minor Thirds Revisited
- Identifying the Fundamental Bass
- Functional Modes: The $T$ - $S$ - $D$Constellation Revisited
- Combinatorics of the Tetractys Modes
- The Structural Scale
- The Tesserachordon - Authentic and Plagal Tetractys Modes
- Modulation between Tetractys Modes
- Exploring the World of Functional Modes
- Lines, Foldings and Duality
- Essential vs. Accidental Alteration of Fundaments
- "Double Star", Hierarchy, Modulation and Sequence
- Conclusion
- References
- Musical Tonality, Neural Resonance and Hebbian Learning
- Introduction
- TonalTheory
- Theories of Musical Tonality
- Some Issues with Modern Tonal Theory
- Dynamical Model of Auditory Processing
- A Learning Experiment
- Conclusions
- References
- Interval Cycles, Affinity Spaces, and Transpositional Networks
- Introduction
- Homogeneous T-Nets and Affinity Spaces
- Homogeneous T-Nets
- Affinity Spaces
- Progressive T-Nets
- DynamicT-Nets
- Conclusion
- References
- Two-Dimensional Visual Inspection of Pitch-Space, Many Time-Scales and Tonal Uncertainty over Time
- Introduction
- Background
- Tonal Cognition and Toroidal Spaces
- Multidimensional Unfolding and Tonal Centroids
- The SOM Approach
- Representation over Time and Temporal Multi-scale
- ProposedModel
- Signal Segmentation and Key Estimation
- Mapping Key Estimations into Pitch-Space
- Time vs. Time-Scale Representation
- Geometrical Colourspace
- Colouring Strategy
- Discussion
- Formal Analysis
- Tonal Mining in More Dimensions
- Other Aspects of Tonal Ambiguity
- Conclusions and Future Work
- References
- Musical Composition and Gestural Diagrams
- Introduction
- Preliminaries on Gesture Categories
- Form Diagrams
- Gesturally Defined Form Diagrams
- Bruhat Decomposition for Gestural Diagrams
- A New Perspective on Musical Composition
- The Process Diagram of a Score
- Integrating Satellite Structures with Dynamic Notes
- General Score Operations in Process Diagrams
- Outlook: Navigating and Changing the History of a Composition
- References
- Tonal Scales and Minimal Simple Pitch Class Cycles
- Introduction
- Minimal Simple Pitch Class Cycles
- Minimal Simple Pitch Class Cycles and the Tonal Scale Sets
- Minimal Simple Cycle Sets and Interval Set Inversion
- Minimal Simple Cycle Sets and the Diatonic Spectra
- $\minsimcycsets(\mathcal D)$ and Contradictions
- The Anhemitonic Pentatonic Scale and the Major Dominant Ninth Chord
- $\minsimcycsets(\mathcal D)$, $\minsimcycsets(\mathcal P)$ and Rothenberg's Concept of Propriety
- $\mathcal T$, $\minsimcycsets(\mathcal P)$ and Carey's Coherence Quotient
- Measuring the Evenness of a Pitch Class Set
- Summary of Main Results
- References
- Scratching the Scale Labyrinth
- Introduction
- Some Properties of MOS/Well-Formed Scales
- The Stern-Brocot Tree
- Reading the Interactive Labyrinths
- Fourier Scratching as a Performance Technique
- Automatic Adaption of Sound Color
- Discussion
- Conclusion
- References
- $N^th$ Roots of Pitch-Class Inversion
- Introduction
- $n$th-Root Inclusive Models of Inversion in Pitch-Class Spaces
- Inversion in Pitch-Class Spaces of Order 2$m$
- Inversion in Pitch-Class Spaces of Order 2$m$+1
- $n$th Roots of Inversion in the Models
- The Existence of nth Roots in Moduli 2$m$ and 2$m$+1
- Multiplicities of the $n$th Roots
- Conclusions and Future Work
- References
- Cardinality Transformations in Diatonic Space
- Introduction
- Filtered Point-Symmetry
- Graphic Transformations with Scalar Contexts
- Cardinality Transformations
- Partially Symmetric Distribution
- Relatively Even Sets
- Harmonic Relationships
- Cardinality Transformations
- Conclusion
- References
- Indeterminate Music and Probability Spaces: The Case of John Cage's Number Pieces
- Introduction
- Introduction and Model
- Definitions
- The Probability Space of a Single Time-Bracket
- Sound Lengths in a Single Time-Bracket
- Multiple Time-Brackets and Point Processes
- Conclusions
- References
- Voice-Leading Prototypes and Harmonic Function in Two Chorale Corpora
- Introduction
- Methods
- Results
- Five Clusters
- Thirty-Four Clusters
- Comparison of the Corpora
- Conclusions
- References
- Emergent Formal Structures of Factor Oracle-Driven Musical Improvisations
- Introduction
- The Mimi System
- Procedure
- Recording of Human-Machine Improvisations
- Annotation of Performances
- Comparison of Annotations
- Results
- Annotation of Performances
- Comparison of Annotations
- Formal Structures
- Discussion and Conclusion
- References
- Open Form and Two Combinatorial Musical Models: The Cases of $Domaines$ and $Duel$
- Introduction
- The Common Structure
- Methodology
- $Domaines$ (1961-1968) by Pierre Boulez
- Description
- Combinatorics
- Permutations
- Some Case Studies
- Analyses of Real Performances of $Domaines$
- Other Elements of $S_6$ in the Clarinet $Cahiers$
- Practical Problems of Performance
- $Duel$ (1959) by Iannis Xenakis
- Description
- Game Theory
- Practical Problems of Performance (I)
- Computer Simulations of the Game
- Practical Problems of Performance (II)
- Conclusion
- References
- Exploding the Monochord: An Intuitive Spatial Representation of Microtonal Relational Structures
- Background
- Microtonality
- Diagrams
- The Proposed Model
- Numerical Conventions
- Displacement in Two Dimensions
- Projection in Two Dimensions
- Displacement and Projection in Three Dimensions
- Implications
- Conclusion
- References
- Music between Hearing and Counting (A Historical Case Chosen within Continuous Long-Lasting Conflicts)
- The Conflicts
- Hermann von Helmholtz, Bernhard Riemann, Johannes Brahms, and Joseph Joachim
- Max Planck
- TheMoral
- References
- Mazzola's Model of Fuxian Counterpoint
- Introduction
- Mazzola's Description of Fux's First-Species Rules
- Mazzola's Derivation of the Rules
- Conclusion
- References
- Introduction to Scale Theory over Words in Two Dimensions
- Preliminaries
- Words
- (Unpitched) Generated Tone Systems
- Conceptual Framework
- Quasi Pairwise Well-Formed Words
- Product Words
- Interval Variety
- Generating Patterns
- MainResults
- Generalization of Myhill's Property
- Necessary Condition for Generating Patterns
- Sufficient Condition for Generating Patterns
- References
- Short Papers (Poster Sessions)
- The Planet-4D Model: An Original Hypersymmetric Music Space Based on Graph Theory
- Symmetry
- Mathematical Background
- Vizualisation
- Applications and Perspectives
- References
- Motivic Topologies: Mathematical and Computational Modelling in Music Analysis
- Introduction
- The Mathematical and Computational Models
- Motivic Spaces: The Mathematical Model
- OM-Melos: The Computational Model
- Related Issues in Computational Music Analysis
- Theoretical Implications and Conclusions
- References
- Exploring Rameau and Beyond: A Corpus Study of Root Progression Theories
- Introduction and Motivation
- Method
- Results
- Discussion and Conclusions
- References
- Melodic Morphing Algorithm in Formalism
- Introduction
- Time-Span Trees in Feature Structures
- Calculus in Melody Lattice
- Melodic Morphing Algorithm
- Conclusion
- References
- From 2D to 3D: Using Geometry and Group Theory to Model Motivic Structure in Musical Composition
- Motivation
- $Torus$
- $12 Variations on a Dodecahedron$
- The Group of Rotational Symmetries of the Dodecahedron
- Establishing an Edge Labelling of the Dodecahedron
- Representing the Dodecahedron in $12 Variations$
- Conclusion
- Reference
- Clustering and Classification of Music by Interval Categories
- Introduction
- Interval Categories
- Composer Clustering
- Tonal - Atonal Classification
- Beethoven's Three Periods
- Conclusions
- References
- Plactic Classification of Modes
- The Plactic Congruences
- The Pentatonic Modes
- The Plactic Modal Classes
- References
- Feature Extraction Using Pitch Class Profile Information Entropy
- Introduction
- The Proposed Approaches
- Results
- Concluding Remarks
- References
- Catastrophe Theory: An Enhanced Structural and Ontological Space in Music Composition
- Introduction
- Methodological Background
- Case Study: $Diathlassis$ for Flute Solo
- Conclusion
- References
- Enriched Score Access for Computer Assisted Composition in PWGL
- Introduction
- The New Expression Access Scheme
- An Example of Basic Expression Access
- Conclusions
- References
- Historical Development of Tonal Syntax: Counting Pitch-Class Sets in 13^th-16^th Century Polyphonic Vocal Music
- Introduction
- Method
- Corpus and Transcription
- Analysis
- Results
- Conclusions
- References
- Surveying Musical Form through Melodic-Motivic Similarities
- Introduction
- TheMethod
- Sample Analysis
- Future Directions
- References
- Author Index
