Chew / Childs / Chuan Mathematics and Computation in Music

Second International Conference, MCM 2009, New Haven, CT, USA, June 19-22, 2009. Proceedings
1. Auflage 2009
ISBN: 978-3-642-02394-1
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 38, 315 Seiten

Reihe: Communications in Computer and Information Science

This book constitutes the refereed proceedings of the Second International Conference on Mathematics and Computation in Music, MCM 2009, held in New Haven, CT, USA, in June 2009. The 26 revised full papers presented were carefully reviewed and selected from 38 submissions. The MCM conference is the flagship conference of the Society for Mathematics and Computation in Music. The papers deal with topics within applied mathematics, computational models, mathematical modelling and various further aspects of the theory of music. This year’s conference is dedicated to the honor of John Clough whose research modeled the virtues of collaborative work across the disciplines.

Autoren/Hrsg.

Chew, Elaine

Childs, Adrian

Chuan, Ching-Hua

Inhaltsverzeichnis

1;Preface;5
2;Organization;7
3;Foreword;10
4;Table of Contents;13
5;Hamiltonian Cycles in the Topological Dual of the Tonnetz;15
5.1;Introduction;15
5.2;Tone-Networks, the Tonnetz and Its Topological Dual;16
5.2.1;Definition;16
5.2.2;Definition;16
5.2.3;Definition;16
5.2.4;Theorem;16
5.2.5;Definition;17
5.2.6;Definition;17
5.2.7;Definition;17
5.2.8;Lemma;18
5.2.9;Theorem;19
5.3;Hamiltonian Cycles in $D(Ton)$;19
5.4;The Hamiltonian Cycle $#41$ and Beethoven's Ninth Symphony;21
5.4.1;Definition;21
5.4.2;Example;21
5.5;Hamiltonian Cycles as a Compositional Tool;23
5.6;References;24
6;The Continuous Hexachordal Theorem;25
6.1;Introduction;25
6.1.1;Basic Definitions;25
6.1.2;History;27
6.1.3;Outline;28
6.2;The Continuous Hexachordal Theorem;28
6.2.1;Weighted Rhythms;28
6.2.2;The Continuous Generalizations;29
6.2.3;Continuous Hexachordal Theorem and Proof;30
6.2.4;Discrete Theorem as Corollary;31
6.2.5;Double-Counting Diameter Intervals;32
6.2.6;Patterson’s First Theorem;33
6.3;OpenProblems;34
6.4;References;34
7;Speech Rhythms and Metric Frames;36
7.1;Introduction;36
7.2;Assessing Local Meter;37
7.3;Glued at the Subdivision;39
7.4;Beyond the Eighth-Note;41
7.5;The Tuplets;41
7.6;Conclusion;45
7.7;References;45
8;Temporal Patterns in Polyphony;46
8.1;Motivation;46
8.2;Relational Patterns;49
8.3;Humdrum;49
8.4;Structured Polyphonic Patterns;51
8.5;{\mathcal H} and {\mathcal SPP} are Distinct;52
8.6;The Common Denominator {\mathcal SPP}$_{seq}$;53
8.7;Discussion;55
8.8;References;55
9;Maximally Smooth Diatonic Trichord Cycles;57
9.1;Introduction;57
9.2;Maximally Smooth Cycles and Parsimonious Triads;57
9.3;Useful Scales;58
9.4;Trichord Species and Their Multiplicities;60
9.5;Trichord Cycles;62
9.6;Conclusions;69
9.7;References;70
10;Towards a Symbolic Approach to Sound Analysis;71
10.1;The Levels of Representation;71
10.2;Sound Types;73
10.2.1;Simple Type Theory;73
10.2.2;Models for Simple Type Theory;74
10.2.3;Low-Level Features and Audio-Indexing;75
10.2.4;The $Typed$ Model;76
10.2.5;Properties of Sound Types;78
10.3;Conclusions and Perspectives;78
10.4;References;78
11;Plain and Twisted Adjoints of Well-Formed Words;79
11.1;Geometrical Motivations;79
11.2;Well-Formed Words;81
11.3;Plain and Twisted Adjoints;84
11.4;Divider Incidence;88
11.5;Final Remarks;93
11.6;References;93
12;Regions and Standard Modes;95
12.1;Regions;95
12.1.1;$Ut-Re-Mi-Fa-Sol-La$;96
12.1.2;Central Words;98
12.1.3;Duality for Central Words;99
12.2;Standard Modes;101
12.2.1;$Do-Re-Mi-Fa-Sol-La-Ti-(Do')$;101
12.2.2;Standard Pairs and Their Duality;103
12.3;References;105
13;Compatibility of the Different Tuning Systems in an Orchestra;107
13.1;Introduction;107
13.2;Some Concepts and Notation;108
13.3;Introducing Fuzzy Logic;109
13.4;Fuzzy Musical Notes;111
13.5;Measuring Compatibility;112
13.6;Computational Results;114
13.7;Conclusions;116
13.8;References;116
14;Formal Diatonic Intervallic Notation;118
14.1;Introduction;118
14.2;Quality Modifiers;119
14.3;Group Structures;121
14.4;Group Actions;123
14.5;Generalized Interval Systems;125
14.6;Coda;126
14.7;References;127
15;Determining Feature Relevance in Subject Responses to Musical Stimuli;129
15.1;Introduction;129
15.2;Prior Work;130
15.3;Feature Relevance Measured by Polynomial Least-Mean Square Estimation;131
15.4;Extension to General Nonlinear Estimators and Probabilistic Models;134
15.5;Kullback-Leibler Distance;136
15.6;Experimental Results;138
15.6.1;Data Set;138
15.6.2;Results;138
15.7;References;142
16;Sequential Association Rules in Atonal Music;144
16.1;Introduction;144
16.1.1;Atonal Music and Pitch Class Set Theory;145
16.2;Pitch Class Set Categories in Atonal Music;146
16.3;Sequential Association Rules;148
16.3.1;The Method;148
16.4;Results;149
16.5;Concluding Remarks;151
16.6;References;152
17;Badness of Serial Fit Revisited;153
17.1;Introduction;153
17.2;Badness of Serial Fit and Partial Orders;154
17.3;Logarithmic BSF and the Metric;155
17.4;Transformational Similarity and Presortedness of Permutations;157
17.5;Conclusions;159
17.6;References;159
18;Estimating the Tonalness of Transpositional Type Pitch-Class Sets Using Learned Tonal Key Spaces;160
18.1;Introduction;160
18.2;Low Dimensional Tonal Key Space;162
18.3;Mapping Tn-Type Sets to the Tonal Key Space;163
18.4;Evaluation;164
18.5;Conclusions;166
18.6;References;166
19;Musical Experiences with Block Designs;168
19.1;t-Designs: A Brief Survey;168
19.2;Drawingt-Designs;170
19.3;Cyclic Representations;172
19.4;Pcsets and Designs;175
19.5;A Compositional Application;176
19.6;References;178
20;A Generalisation of Diatonicism and the Discrete Fourier Transform as a Mean for Classifying and Characterising Musical Scales;180
20.1;Introduction;180
20.2;The Diatonic Bell;181
20.2.1;Input Parameters;181
20.2.2;Find All Scales;182
20.2.3;Find All Centred Scales;182
20.2.4;Find the Reference Scale;182
20.2.5;Find the Reference Mode;183
20.2.6;Find All Centred Modes;183
20.2.7;Construct All Representations;184
20.2.8;Order All Scales;185
20.2.9;Modal Transposition;186
20.3;The DFT Analysis of Scales;187
20.3.1;Phases;189
20.3.2;Modules;190
20.3.3;Periodicity;190
20.3.4;Chord Quality;191
20.4;Conclusion;192
20.4.1;Symmetry;192
20.4.2;Measuring the Diatonic Character of a Scale;192
20.5;References;193
21;The Geometry of Melodic, Harmonic, and Metrical Hierarchy;194
21.1;General Characteristics of Musical Hierarchy;194
21.2;Harmonic, Melodic, and Metrical Forms of Hierarchy;196
21.2.1;Harmonic Hierarchy;196
21.2.2;Melodic Hierarchy;197
21.2.3;Metric Hierarchy;198
21.3;Musical Realizations of the Stasheff Polytope;198
21.4;Relating Hierarchies on Different Musical Parameters;201
21.4.1;Conflict between Melodic and Metric Structures;201
21.4.2;Melodic Structures in Counterpoint;203
21.4.3;Relationships between Melodic and Harmonic Structure;203
21.5;Conclusion;205
21.6;References;205
22;A Multi-tiered Approach for Analyzing Expressive Timing in Music Performance;207
22.1;Introduction;207
22.2;Related Previous Research;208
22.3;Tempo Curve Calculation Using a Non-parametric Regression Model;209
22.4;The Hierarchy of Metric Deviations;212
22.5;Conclusions and Future Directions;212
22.6;References;218
23;HMM Analysis of Musical Structure: Identification of Latent Variables Through Topology-Sensitive Model Selection;219
23.1;Introduction;219
23.2;HMM Training and Topology Identification;221
23.3;Case Study I: Statistical Segmentation of Symbolic Sequences;222
23.4;Case Study II: Meter Induction from Rhythmic Patterns;224
23.5;Conclusions;227
23.6;References;231
24;A Declarative Language for Dynamic Multimedia Interaction Systems;232
24.1;Introduction;232
24.2;Preliminaries;234
24.3;A Model for Dynamic Interactive Scores;235
24.4;A Model for Music Improvisation;238
24.5;Concluding Remarks;240
24.6;References;241
25;Generalized Voice Exchange;242
25.1;Introduction;242
25.1.1;Connection to Contextual Inversion;243
25.2;Generalized Voice Exchange;243
25.2.1;Generalized Chromatic Voice Exchange: The Variable $i \epsilon {\mathbb Z}_{12}$;244
25.2.2;Permutations of the Orbits: The Variable $p \epsilon {\mathbb Z}_{5}$;246
25.2.3;Initial Harmonic Intervals: The Variable $q \epsilon {\mathbb Z}_{12}$;247
25.3;Conclusions: The Group $R$ and Transformational Networks;248
25.4;References;249
26;Representing and Estimating Musical Expression in Melody;250
26.1;Introduction;250
26.2;The Theremin;252
26.3;Representing Musical Interpretation;252
26.4;From Labeling to Audio;253
26.5;Does the Labeling Capture Musicality?;254
26.6;Estimating the Interpretation;255
26.7;Results;256
26.8;References;258
27;Evaluating Tonal Distances between Pitch-Class Sets and Predicting Their Tonal Centres by Computational Models;259
27.1;Introduction;259
27.2;Algorithmic Models;261
27.2.1;Training the Weights of a Linear Polynomial with Tonal Constraints;261
27.2.2;Circle-of-Fifths-Based Algorithm;262
27.2.3;Training a Neural Network with Empirical Results;263
27.2.4;The Tonal Profile of a PCS as a Weighted Mean of KK-Profiles;265
27.3;Comparing and Combining Predictions;266
27.4;Is Alban Berg’s $Invention on a Key$ in D Minor?;267
27.5;Conclusions;269
27.6;References;269
27.7;APPENDIX A;270
27.8;APPENDIX B;270
27.9;APPENDIX C;271
28;Three Conceptions of Musical Distance;272
28.1;Introduction;272
28.2;Voice-Leading Lattices and Acoustic Affinity;275
28.3;Tuning Lattices as Approximate Models of Voice Leading;278
28.4;Voice Leading, “Quality Space,” and the Fourier Transform;281
28.5;Conclusion;285
28.6;References;286
29;Pairwise Well-Formed Scales and a Bestiary of Animals on the Hexagonal Lattice;287
29.1;Well-Formed Scales;287
29.2;Pairwise Well-Formed Scales;287
29.3;Animals on the Hexagonal Lattice—The Heptatonic Case;289
29.4;Three-Stepped Animals on the Tonnetz of Fifths and Thirds;290
29.5;Pwwf Animals on the $Tonnetz$ of Fifths and Thirds;290
29.6;Pwwf Animals on Other Lattices;293
29.7;Arbitrary Heptatonic Pwwf Scales;296
29.8;Pwwf Scales of Other Cardinalities;298
29.9;References;299
30;Generalized $Tonnetz$ and Well-Formed GTS: A Scale Theory Inspired by the Neo-Riemannians;300
30.1;Inspirations;300
30.2;Generalized $Tonnetz$;301
30.3;Unpitched Generated Tone System;303
30.4;Generated Tone System;305
30.5;The Main Theorem;309
30.6;A Case Study: The System of $\'{S}rutis$;309
30.7;References;312
31;Author Index;313