Klouche / Noll Mathematics and Computation in Music

First International Conference, MCM 2007, Berlin, Germany, May 18-20, 2007. Revised Selected Papers
1. Auflage 2010
ISBN: 978-3-642-04579-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 37, 546 Seiten

Reihe: Communications in Computer and Information Science

This book constitutes the refereed proceedings of the First International Conference on Mathematics and Computation in Music, MCM 2007, held in Berlin, Germany, in May 2007. The 51 papers presented were carefully reviewed and selected from numerous 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 verious further aspects of the theory of music.

Autoren/Hrsg.

Klouche, Timour

Noll, Thomas

Inhaltsverzeichnis

1;Preface;5
2;Table of Contents
;6
3;Rhythm and Transforms, Perception and Mathematics
;11
3.1;1 What Is Rhythm?;11
3.2;2 Auditory Perception;12
3.3;3 Transforms;13
3.4;4 Adaptive Oscillators;14
3.5;5 Statistical Models;14
3.6;6 Automated Rhythm Analysis;15
3.7;7 Beat-Based Signal Processing;16
3.8;8 Musical Composition and Recomposition;18
3.9;9 Musical Analysis via Feature Scores;19
3.10;10 Conclusions;19
3.11;References;20
4;Visible Humour – Seeing P.D.Q. Bach's Musical Humour Devices in The Short-Tempered Clavier on the Spiral Array Space
;21
4.1;1 Introduction;21
4.2;2 MuSA.RT and Visualization
;22
4.2.1;2.1 Seeing Style Differences;22
4.3;3 Expectations Violated;24
4.3.1;3.1 The Jazz Ending;24
4.3.2;3.2 Improbable Harmonies;25
4.3.3;3.3 Excessive Repetition;26
4.4;4 Conclusions;27
4.5;Acknowledgements;27
4.6;References;28
5;Category-Theoretic Consequences of Denotators as a Universal Data Format
;29
5.1;1 Introduction;29
5.2;2 Diagrams in Category Theory;30
5.3;3 Limits;30
5.4;4 Colimits;32
5.5;5 Integration in RUBATO COMPOSER;33
5.6;References;34
6;Normal Form, Successive Interval Arrays, Transformations and Set Classes: A Re-evaluation and Reintegration
;35
6.1;References;59
6.2;Appendix Rahn/Morris/Scotto Normal Form Algorithm
;59
7;A Model of Musical Motifs;62
7.1;1 Introduction;62
7.2;2 The Formal Model;63
7.3;3 AnExample;65
7.4;4 Discussion;67
7.5;References;68
8;Melodic Clustering within Motivic Spaces: Visualization in OpenMusic and Application to Schumann’s Träumerei ;69
8.1;1 Introduction;69
8.2;2 Topological Model of Motivic Structure
;70
8.2.1;2.1 Melodic Clustering within Motivic Spaces;71
8.3;3 Model Implementation and Visualization in OpenMusic;71
8.4;4 Application to Schumann’s Traumerei
;74
8.5;References;76
9;Topological Features of the Two-Voice Inventions;77
9.1;1 Introduction;77
9.2;2 The Similarity Neighbourhood Model;78
9.3;3 Inheritance Property;80
9.4;4 Redundant Melodies;81
9.5;5 Finding Subsequences;82
9.6;6 Melodic Topologies;84
9.6.1;6.1 Melodic Topologies on the Syntagms;85
9.6.2;6.2 Investigation of the Inventions;85
9.7;7 Conclusion;86
9.8;References;87
10;Comparing Computational Approaches to Rhythmic and Melodic Similarity in Folksong Research
;88
10.1;1 Introduction;88
10.2;2 Two Computational Approaches to Rhythmic Similarity
;89
10.2.1;2.1 Transportation Distances;89
10.2.2;2.2 Inner Metric Analysis;89
10.2.3;2.3 Defining Similarity Based on Inner Metric Analysis;91
10.3;3 Evaluation of the Rhythmic Similarity Approaches
;92
10.3.1;3.1 A Detailed Comparison on the Melody Group Deze Morgen;93
10.3.2;3.2 Summary of Further Results;96
10.4;4 Conclusion;96
10.5;References;96
11;Automatic Modulation Finding Using Convex Sets of Notes
;98
11.1;1 Introduction;98
11.2;2 Probability of Convex Sets in Music;98
11.2.1;2.1 Finding Modulations by Means of Convexity;102
11.3;3 Results;104
11.4;4 Conclusions;105
11.5;Acknowledgments;105
11.6;References;105
12;On Pitch and Chord Stability in Folk Song Variation Retrieval
;107
12.1;1 Introduction;107
12.1.1;Overview;107
12.2;2 Modifications of the Retrieval System;108
12.3;3 Pitch Stability;109
12.3.1;3.1 Metrical Levels;109
12.3.2;3.2 Evaluation of Pitch Stability;110
12.3.3;3.3 Query Formulation;110
12.4;4 Implied Chord Stability;111
12.4.1;4.1 Harmonization;111
12.4.2;4.2 Evaluation of Implied Chord Stability;111
12.4.3;4.3 Contextualization;112
12.5;5 Excerpts from the Variation Group ‘Frankrijk B1’;113
12.6;6 Summary;115
12.7;Acknowledgements;116
12.8;References;116
13;Bayesian Model Selection for Harmonic Labelling
;117
13.1;1 Introduction;117
13.2;2 Previous Work;118
13.3;3 Model;120
13.3.1;3.1 Dirichlet Distributions;120
13.3.2;3.2 The Chord Model;120
13.3.3;3.3 Bayesian Model Selection;121
13.4;4 Experiment;122
13.4.1;4.1 Parameter Estimation;122
13.4.2;4.2 Results;123
13.5;5 Conclusions;125
13.6;References;125
14;The Flow of Harmony as a Dynamical System;127
14.1;1 Dynamical Systems Applied to Harmony;127
14.2;2 Dynamical Systems Applied to Counterpoint;129
14.3;3 The Composer
;130
14.4;4 Summary;131
14.5;References;131
15;Tonal Implications of Harmonic and Melodic Tn-Types;134
15.1;Tn-types of cardinality 3;135
15.2;The harmonic profile;137
15.3;The tonal profile;142
15.4;Perceptual profiles, consonance and prevalence;144
15.5;Conclusion;145
15.6;References;146
16;Calculating Tonal Fusion by the Generalized Coincidence Function
;150
16.1;1 Background;150
16.1.1;1.1 Tonal Fusion and Roughness;150
16.1.2;1.2 Interspike Interval Distributions, Pitch Estimates and Harmony;151
16.1.2.1;1.2.1 Neuronal Code and Pitch;151
16.1.2.2;1.2.2 Interspike Intervals;152
16.1.2.3;1.2.3 Coinciding Periodicity Patterns for Intervals;152
16.1.3;1.2 Autocorrelation;153
16.1.3.1;1.2.1 Autocorrelation versus Fourier-Analysis;153
16.1.3.2;1.2.2 Hearing Theories and Autocorrelation;153
16.1.4;1.3 Langner’s Neuronal Correlator;153
16.2;2 Mathematical Model of Generalized Coincidence;154
16.2.1;2.1 Correlation Functions;154
16.2.2;2.2 Sequence Representation of a Tone;155
16.2.3;2.3 Sequence Representation of an Interval;156
16.2.4;2.4 Autocorrelation Function of an Interval;158
16.2.5;2.5 Definition of the Generalized Coincidence Function;158
16.3;3 Application of the Model to Rectangular Pulse Sequences;158
16.3.1;3.1 Correlation Functions of Rectangular Pulses;158
16.3.1.1;3.1.1 Autocorrelation Function of the Rectangular Pulse;158
16.3.1.2;3.1.2 Cross Correlation Function of the Rectangular Pulse;159
16.3.1.3;3.1.3 Autocorrelation Function of an Interval Represented by Rectangular Sequences
;161
16.3.2;3.2 Calculation of the Generalized Coincidence Function;162
16.4;4 Conclusion;163
16.5;References;163
17;Predicting Music Therapy Clients’ Type of Mental Disorder Using Computational Feature Extraction and Statistical Modelling Techniques
;166
17.1;1 Introduction;166
17.2;2 Previous Music Therapy Research;167
17.3;3 Computational Music Analysis;168
17.4;4 Method;169
17.5;5 Quantifying the Client-Therapist Interaction;172
17.6;6 Results;174
17.7;7 Discussion;175
17.8;References;176
18;Nonlinear Dynamics, the Missing Fundamental, and Harmony
;178
18.1;1 Pitch Perception;178
18.2;2 Residue Behaviour;179
18.3;3 Nonlinear Dynamics of Forced Oscillators;181
18.3.1;3.1 n = 1;181
18.3.1.1;3.1.1 Synchronization;181
18.3.1.2;3.1.2 Quasiperiodicity;182
18.3.2;3.2 n = 2;183
18.3.2.1;3.2.1 Synchronization;183
18.3.2.2;3.2.2 Three-Frequency Resonances;183
18.4;4 A Nonlinear Theory for the Residue;184
18.5;5 The Golden Mean in Art and Science;186
18.6;6 The Need for Musical Scales;188
18.7;7 The Golden Scales;189
18.8;8 Playing and Transposing with Golden Scales in Equal Temperament
;192
18.9;9 Can Our Senses Be Viewed as Generic Nonlinear Systems?;194
18.10;References;196
19;Dynamic Excitation Impulse Modification as a Foundation of a Synthesis and Analysis System for Wind Instrument Sounds
;199
19.1;1 Introduction;199
19.2;2 Cyclical Spectra;200
19.3;3 Synthesis and Analysis Framework;203
19.3.1;3.1 The Digital Variophon;203
19.3.2;3.2 Formalisation;204
19.3.3;3.3 The Pulse Width Function;205
19.3.4;3.4 Application of the System;206
19.4;4 Discussion;206
19.5;Acknowledgement;207
19.6;References;207
20;Non-linear Circles and the Triple Harp: Creating a Microtonal Harp
;208
20.1;1 Introduction;208
20.2;2 The Triple Harp;209
20.3;3 Non-linear Tuning Systems;209
20.4;4 Microtonal Triple Harp;210
20.5;5 Notation;211
20.6;6 Composing for Microtonal Triple Harp;211
20.7;7 Conclusion;213
20.8;References;213
21;Applying Inner Metric Analysis to 20th Century Compositions
;214
21.1;1 Inner Metric Analysis;214
21.2;2 Analytic Results;215
21.2.1;2.1 Skrjabin’s op. 65 No. 3;215
21.2.2;2.2 Webern’s Op. 27, 2nd Movement;216
21.2.3;2.3 Xenakis’ Keren;217
21.2.4;2.4 Comparison of the Results;220
21.3;References;220
22;Tracking Features with Comparison Sets in Scriabin’s Study op. 65/3
;221
22.1;1 Comparison Set Analysis;221
22.2;2 About the Tail Segmentation and Similarity Measures Used in the Analyses
;223
22.3;3 The Occurrences of the ’Mystic Chord’ among Scriabin’s Piano Pieces
;224
22.4;4 Detecting Op. 65/3 with Comparison Sets;225
22.5;5 Conclusions;228
22.6;References;229
23;Computer Aided Analysis of Xenakis-Keren;230
23.1;1 Introduction;230
23.2;2 Xenakis – Keren;231
23.3;References;239
24;Automated Extraction of Motivic Patterns and Application to the Analysis of Debussy’s Syrinx
;240
24.1;1 General Framework;240
24.1.1;1.1 Motivic Pattern Extraction;240
24.1.2;1.2 Musical Dimensions;241
24.1.3;1.3 Matching Strategy;241
24.1.4;1.4 Analysis of Debussy’s Syrinx;242
24.2;2 Controlling the Combinatorial Redundancy;242
24.2.1;2.1 Maximal Patterns and Closed Patterns;242
24.2.2;2.2 Multidimensionality of Music;244
24.2.3;2.3 Formal Concept – Representation of Patterns;245
24.2.4;2.4 Specificity Relations;246
24.2.5;2.5 Cyclic Patterns;247
24.3;3 From Monody to Polyphony;248
24.4;References;248
25;Pitch Symmetry and Invariants in Webern's Sehr Schnell from Variations Op.27
;250
25.1;1 Introduction;250
25.2;2 w = One Eighth Note;251
25.3;3 w = Two Eighth Notes;253
25.4;4 w = Three Eighth Notes;254
25.5;5 Center on A;255
25.6;Acknowledgements;256
25.7;References;256
26;Computational AnalysisWorkshop: Comparing Four Approaches to Melodic Analysis
;257
26.1;1 Comparing Four Approaches to Melodic Analysis;257
26.2;References;259
27;Computer-Aided Investigation of Chord Vocabularies: Statistical Fingerprints of Mozart and Schubert
;260
27.1;Presentation;260
27.2;References;266
28;The Irrelative System in Tonal Harmony;267
28.1;1 Introduction;267
28.2;2 Algorithm Enabling Classification of Chords;267
28.3;3 Chords;270
28.4;4 Metrical Units;272
28.5;5 Record Table;273
28.6;Acknowledgement;275
28.7;References;275
29;Mathematics and the Twelve-Tone System: Past, Present, and Future*
;276
29.1;1 Introduction;276
29.2;2 The Introduction of Math into Twelve-Tone Music Research;277
29.3;3 Important Results and Trends;283
29.4;4 Present State of Research;293
29.5;5 Future;294
29.6;6 Conclusion;295
29.7;References;295
30;Approaching Musical Actions*;299
30.1;References;311
31;A Transformational Space for Elliott Carter's Recent Complement-Union Music*
;313
31.1;References;320
32;Networks;321
33;From Mathematica to Live Performance: Mapping Simple Programs to Music
;328
33.1;1 Background;328
33.2;2 Data Gathering;330
33.3;3 Large Scale Piece;331
33.3.1;3.1 Choice of a Rule;331
33.3.2;3.2 Partitioning;331
33.4;4 Initial Conditions;332
33.5;5 Choice of Musical Parameters;332
33.6;6 The Outcome;332
33.7;7 Generative Pitch Collections and Rhythmic Grouping;333
33.8;8 Mapping;333
33.8.1;8.1 Rule 90;334
33.8.2;8.2 Rule 30;335
33.8.3;8.3 Rule 110;336
33.9;9 New Ground;338
33.10;Acknowledgements;338
33.11;References;338
34;Nonlinear Dynamics of Networks: Applications to Mathematical Music Theory
;340
34.1;1 Introduction and Musical Motivation;340
34.2;2 Nonlinear Dynamics of Networks;341
34.3;3 Discussion and Applications;345
34.3.1;3.1 Nonlinear Dynamics and Musical Ontology;345
34.3.2;3.2 Applications to Algorithmic Composition;348
34.4;References;349
35;Form, Transformation and Climax in Ruth Crawford Seeger’s String Quartet, Mvmt. 3
;350
35.1;References;355
36;A Local Maximum Phrase Detection Method for Analyzing Phrasing Strategies in Expressive Performances
;357
36.1;1 Introduction;357
36.2;2 The Method;358
36.2.1;2.1 Data Extraction;358
36.2.2;2.2 The Case for Loudness;358
36.2.3;2.3 Local Maximum Phrase Detection;360
36.2.3.1;2.3.1 Phrase Strength and Volatility;360
36.2.3.2;2.3.2 Phrase Typicality;362
36.3;3 Conclusion and Discussion;362
36.4;Acknowledgements;363
36.5;References;363
37;Subgroup Relations among Pitch-Class Sets within Tetrachordal K-Families
;364
37.1;References;374
38;K-Net Recursion in Perlean Hierarchical Structure;375
38.1;1 Introduction;375
38.2;2 K-Nets and Perle Cycles;375
38.3;3 K-Nets, Arrays, and Axis-Dyad Chords;377
38.4;4 K-Nets and Array Relationships;378
38.5;5 K-Nets, Interval Systems, Modes, and Keys;379
38.6;6 K-Nets and Synoptic Arrays;380
38.7;7 K-Nets and Tonality;382
38.8;8 Summary;384
38.9;References;384
39;Webern’s Twelve-Tone Rows through the Medium of Klumpenhouwer Networks
;385
39.1;References;395
40;Isographies of Pitch-Class Sets and Set Classes;396
40.1;1 Introduction;396
40.2;2 Isography of Pitch-Class Sets and Set Classes;397
40.3;3 Tonality and Whole-Tone Scale Proportion;398
40.4;4 Relations of Set Classes;399
40.5;References;401
41;The Transmission of Pythagorean Arithmetic in the Context of the Ancient Musical Tradition from the Greek to the Latin Orbits During the Renaissance: A Computational Approach of Identifying and Analyzing the Formation of Scales in the De Harmonia Musicorum Instrumentorum Opus (Milan, 1518) of Franchino Gaffurio (1451–1522)*
;402
41.1;Bibliography;411
42;Combinatorial and Transformational Aspects of Euler's Speculum Musicum
;416
42.1;References;420
43;Structures Ia Pour Deux Pianos by Boulez: Towards Creative Analysis Using Open Musicand Rubato
;422
43.1;1 Introduction;422
43.2;2 Compositional Process in Structures Ia;423
43.2.1;2.1 Analysis of Constructional and Serial Principles: Decision and Automatism
;423
43.2.2;2.2 How to Create from an Analysis;423
43.3;3 An Implementation in OpenMusic: A Visual and Functional Environment
;424
43.3.1;3.1 Patches and Circularity;424
43.3.2;3.2 Composing Following the Model with the Benefit of a Graphical Composition Environment
;424
43.4;4 Rubato: A Higher Level of Abstraction with a Categorical View
;425
43.4.1;4.1 Different Perspectives Delivered by Rubato;425
43.4.2;4.2 Possibilities Brought by Rubato;426
43.4.3;4.3 Scheme of the Construction;426
43.5;5 Conclusion;427
43.6;References;427
44;The Sieves of Iannis Xenakis;429
44.1;1 Introduction;429
44.2;2 Types of Formulae;430
44.3;3 Symmetries/Periodicities;430
44.4;4 Inner-Periodic Formula;431
44.4.1;4.1 Inner Periodicities and Formulae Redundancy;431
44.4.2;4.2 Construction of the Inner-Periodic Simplified Formula;431
44.4.3;4.3 Analytical Algorithm: Early Stage;432
44.4.4;4.4 The Condition of Inner Periodicity;433
44.4.5;4.5 Analytical Algorithm: Final Stage;433
44.4.6;4.6 The Condition of Inner Symmetry;434
44.4.7;4.7 Inner-Symmetric Analysis;435
44.4.8;4.8 Modules and Degree of Symmetry;438
44.5;References;439
45;Tonal, Atonal and Microtonal Pitch-Class Categories;440
45.1;1 Introduction;440
45.2;2 Applying Pitch-Class Set Theory on Sets with Cardinality (Pitch-Classes) Other Than 12
;441
45.3;3 Pitch-Class Set Theory within a Bit-Sequence;442
45.4;4 Pitch-Class Categories;444
45.5;5 Discussion and Future Work;446
45.6;6 Conclusion;447
45.7;References;447
45.8;Appendix;448
46;Using Mathematica to Compose Music and Analyze Music with Information Theory
;451
46.1;1 Composition of Music Using Mathematica;451
46.2;2 Nonlinear Time Series Analysis of Musical Compositions
;453
46.2.1;2.1 Creating Time Series from Sheet Music;453
46.2.2;2.2 Transfer Entropy and the Relationship between Physical Systems;455
46.2.3;2.3 The Application of the Transfer Entropy to a Symphony;455
46.3;3 Conclusions;458
46.4;References;458
47;A Diatonic Chord with Unusual Voice-Leading Capabilities
;459
47.1;References;469
48;Mathematical and Musical Properties of Pairwise Well-Formed Scales
;474
48.1;1 Pairwise Well-Formed and Well-Formed Scales;475
48.2;2 Some Properties of Pairwise Well-Formed Scales;476
48.3;3 Classification of Pairwise Well-Formed Scales;476
48.4;References;478
49;Eine Kleine Fourier Musik;479
49.1;Introduction;479
49.2;1 DFT of a pc Set
;479
49.3;2 Maximal Values;480
49.3.1;2.1 Regular Polygons;481
49.3.2;2.2 The General Case;481
49.3.3;2.3 Other Maximal Values;482
49.4;3 Minimal Values;483
49.5;4 MeanValue(s);484
49.6;5 Coda;485
49.7;References;486
50;WF Scales, ME Sets, and Christoffel Words;487
50.1;1 Well-Formed Scales;487
50.2;2 Christoffel Words;489
50.3;3 Well-Formed Classes and Christoffel Words, Duality;490
50.4;4 Christoffel Words, Maximally Even Sets and Musical Modes
;492
50.5;5 Christoffel Tree and the Monoid SL(2, N);494
50.6;6 Final Remarks
;496
50.7;References;497
51;Interval Preservation in Group- and Graph-Theoretical Music Theories: A Comparative Study
;499
51.1;References;502
52;Pseudo-diatonic Scales;503
52.1;1 Shuffled Stern-Brocot Tree;503
52.2;2 Construction of Pseudo-diatonic Scales;504
52.3;References;507
53;Affinity Spaces and Their Host Set Classes;509
53.1;1 Affinities in the Medieval Dasian Scale;509
53.2;2 The Dasian Space;511
53.3;3 Four Properties of the Dasian Space;513
53.4;4 Affinity Spaces;515
53.5;5 Three Properties of Host Set Classes;519
53.6;6 Generating Affinity Spaces;519
53.7;7 Conclusion;521
53.8;References;521
54;The Step-Class Automorphism Group in Tonal Analysis;522
54.1;Bibliography;530
55;A Linear Algebraic Approach to Pitch-Class Set Genera
;531
55.1;1 ‘Corner-Stone Set-Classes’;531
55.2;2 Applying Cosine Distance and the Determinant of a Matrix with Musical Set Classes
;532
55.3;3 Volume Tests with Interval-Class Vectors;533
55.4;4 ‘Strangest’ Hexachords;535
55.5;5 Principal Component Analysis: A Flexible Approach for Mapping ICV-Space
;536
55.6;6 Using Corner-Stone Vectors for Producing a System of Genera
;537
55.7;7 Harmonic Space in Composition;538
55.8;8 Conclusions;539
55.9;References;539
56;Author Index;541
57;Index;542