## Mathematics and Computation in Music: First International Conference, MCM 2007, Berlin, Germany, May 18-20, 2007. Revised Selected PapersThis volume comprises a selection of papers presented at the first International C- ference on Mathematics and Computation in Music – mcm2007. The conference took place at the Staatliches Institut für Musikforschung PK – National Institute for Music Research in Berlin during May 18–20, 2007 and was jointly organized by the National Institute for Music Research Berlin and the Society of Mathematics and Computation in Music. The papers were selected for the conference by the program committee and classfied into talks and posters. All papers underwent further selection, revision and elaboration for this book publication. The articles cover a research field which is heterogeneous with respect to content, scientific language and methodology. On one hand, this reflects the heterogeneity and richness of the musical subject domain itself. On the other hand, it exemplifies a t- sion which has been explicitly intended by both the organizers and the founders of the society, namely to support the integration of mathematical and computational - proaches to music theory, composition, analysis and performance. The subdivision into three parts reflects the original structure of the program. These parts are opened by invited papers and followed by talks and posters. |

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### Contents

Rhythm and Transforms Perception and Mathematics | 1 |

Visible Humour Seeing PDQ Bachs Musical Humour Devices in The ShortTempered Clavier on the Spiral Array Space | 11 |

CategoryTheoretic Consequences of Denotators as a Universal Data Format | 19 |

A Reevaluation and Reintegration | 25 |

A Model of Musical Motifs | 52 |

Visualization in OpenMusic and Application to Schumanns Traumerei | 59 |

Topological Features of the TwoVoice Inventions | 67 |

Comparing Computational Approaches to Rhythmic and Melodic Similarity in Folksong Research | 78 |

A Transformational Space for Elliott Carters Recent ComplementUnion Music | 303 |

Networks | 311 |

Mapping Simple Programs to Music | 318 |

Applications to Mathematical Music Theory | 330 |

Form Transformation and Climax in Ruth Crawford Seegers String Quartet Mvmt 3 | 340 |

A Local Maximum Phrase Detection Method for Analyzing Phrasing Strategies in Expressive Performances | 347 |

Subgroup Relations among PitchClass Sets within Tetrachordal KFamilies | 354 |

KNet Recursion in Perlean Hierarchical Structure | 365 |

Automatic Modulation Finding Using Convex Sets of Notes | 88 |

On Pitch and Chord Stability in Folk Song Variation Retrieval | 97 |

Bayesian Model Selection for Harmonic Labelling | 107 |

The Flow of Harmony as a Dynamical System | 117 |

Tonal Implications of Harmonic and Melodic TnTypes | 124 |

Calculating Tonal Fusion by the Generalized Coincidence Function | 140 |

Predicting Music Therapy Clients Type of Mental Disorder Using Computational Feature Extraction and Statistical Modelling Techniques | 156 |

Nonlinear Dynamics the Missing Fundamental and Harmony | 168 |

Dynamic Excitation Impulse Modification as a Foundation of a Synthesis and Analysis System for Wind Instrument Sounds | 189 |

Creating a Microtonal Harp | 198 |

Applying Inner Metric Analysis to 20th Century Compositions | 204 |

Tracking Features with Comparison Sets in Scriabins Study op 653 | 211 |

Computer Aided Analysis of XenakisKeren | 220 |

Automated Extraction of Motivic Patterns and Application to the Analysis of Debussys Syrinx | 230 |

Pitch Symmetry and Invariants in Weberns Sehr Schnell from Variations Op27 | 240 |

Comparing Four Approaches to Melodic Analysis | 247 |

Statistical Fingerprints of Mozart and Schubert | 250 |

The Irrelative System in Tonal Harmony | 257 |

Past Present and Future | 266 |

Approaching Musical Actions | 289 |

Weberns TwelveTone Rows through the Medium of Klumpenhouwer Networks | 375 |

Isographies of PitchClass Sets and Set Classes | 386 |

A Computational Approach of Identifying and Analyzing the Formation of Scales in the De Harmonia Musicorum Instrumentorum Opus Milan 1518... | 392 |

Combinatorial and Transformational Aspects of Eulers Speculum Musicum | 406 |

Towards Creative Analysis Using Open Musicand Rubato | 412 |

The Sieves of Iannis Xenakis | 419 |

Tonal Atonal and Microtonal PitchClass Categories | 430 |

Using Mathematica to Compose Music and Analyze Music with Information Theory | 441 |

A Diatonic Chord with Unusual VoiceLeading Capabilities | 449 |

Mathematical and Musical Properties of Pairwise WellFormed Scales | 464 |

Eine Kleine Fourier Musik | 469 |

WF Scales ME Sets and Christoffel Words | 477 |

A Comparative Study | 489 |

Pseudodiatonic Scales | 493 |

Affinity Spaces and Their Host Set Classes | 499 |

The StepClass Automorphism Group in Tonal Analysis | 512 |

A Linear Algebraic Approach to PitchClass Set Genera | 521 |

531 | |

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### Common terms and phrases

affinity spaces algorithm analysis array bars Berlin Heidelberg 2009 calculated cardinality CCIS 37 Christoﬀel chromatic CINT1 composer composition computational corresponding cyclic permutation David Lewin deﬁned deﬁnition diatonic diatonic scale diﬀerent dyads dynamical equal temperament equivalence Example ﬁgure ﬁrst ﬁxed Franchino Gaffurio frequency function Gaffurio graph harmonic hexachords INT1 integer interval classes inversion inversional isography K-class K-nets Klouche Klumpenhouwer Lewin major major third mapping mathematical melodic segments melody modules motif motives multisets Music Theory Noll Eds normal form notes octave onset pairs parameters Parncutt pattern pc-sets perception perfect fifth perimeter interval period Perle cycles phrase piece pitch pitch-class set pulse relationships representation represented rhythmic semitones sequence set classes sieve similarity space Springer-Verlag Berlin Heidelberg step structure subset symmetry tetrachords Tn-type tonal tones Tonnetz transformations transposition trichords triple harp twelve-tone values vectors well-formed scales Xenakis