Lecture Notes in Artificial Intelligence 7937 Subseries of Lecture Notes in Computer Science LNAI Series Editors Randy Goebel University of Alberta, Edmonton, Canada Yuzuru Tanaka Hokkaido University, Sapporo, Japan Wolfgang Wahlster DFKI and Saarland University, Saarbrücken, Germany LNAI Founding Series Editor Joerg Siekmann DFKI and Saarland University, Saarbrücken, Germany
Jason Yust Jonathan Wild John Ashley Burgoyne (Eds.) Mathematics and Computation in Music 4th International Conference, MCM 2013 Montreal, QC, Canada, June 12 14, 2013 Proceedings 13
Volume Editors Jason Yust Boston University, MA, USA E-mail: jason.yust@gmail.com Jonathan Wild McGill University, Montreal, QC, Canada E-mail: wild@music.mcgill.ca John Ashley Burgoyne University of Amsterdam, The Netherlands E-mail: j.a.burgoyne@uva.nl ISSN 0302-9743 e-issn 1611-3349 ISBN 978-3-642-39356-3 e-isbn 978-3-642-39357-0 DOI 10.1007/978-3-642-39357-0 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2013941478 CR Subject Classification (1998): H.5.5, J.5, I.1, I.6, G.2 LNCS Sublibrary: SL 7 Artificial Intelligence Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface The disciplines of mathematics and music share an intertwined history stretching back more than two and a half millennia. More recently, informatics has made possible new approaches to music research, often with transformative effect. The Society for Mathematics and Computation in Music promotes the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition, and other related fields, to further our understanding of a wide range of musical phenomena. The 4 th International Conference on Mathematics and Computation in Music (MCM 2013) continued the pattern, initiated in 2007 at the first MCM meeting, of biennial international conferences held on alternating sides of the Atlantic: Berlin in 2007, New Haven in 2009, and Paris in 2011. The 2013 edition saw the conference come to Montreal, Canada, sponsored by the Schulich School of Music of McGill University, and by CIRMMT, the Centre for Interdisciplinary Research in Music Media and Technology. The conference was accompanied by a concert presented by the live@cirmmt series the last concert of the series 2012 2013 season and the last official event of the Schulich School of Music Year of Contemporary Music. Events took place in Tanna Schulich Hall, in the New Music Building. The conference took place over three days in June, and as well as regular papers included poster sessions and a panel discussion. Papers for the conference were accepted from among the submissions after peer review by a large program advisory board, with multiple reviewers reading each submission and reporting back to the Program Committee. Participants attended from over a dozen countries across the world; they presented research that proceeded in novel directions, as well as research that continued themes present in previous editions of the conference. The breadth of mathematical applications in music research, the ways in which the new research documented here builds upon existing research, the skill of the researchers represented here, and the variety in their backgrounds all indicate a healthy field indeed. April 2013 Jonathan Wild
Organization The 4 th International Conference on Mathematics and Computation in Music (MCM 2013) was hosted by the Schulich School of Music at McGill University and the Centre for Interdisciplinary Research in Music Media and Technology (CIRMMT). Executive Committee Conference Chair Jonathan Wild Program Committee Jason Yust Jonathan Wild Concert Organization Fabrice Marandola Local Advisory Board Ichiro Fujinaga Chistoph Neidhöfer McGill University, Canada Boston University, USA (Chair) McGill University, Canada McGill University, Canada McGill University, Canada McGill University, Canada Review Board Emmanuel Amiot Christina Anagnostopoulou Moreno Andreatta Jean Bresson Chantal Buteau Clifton Callender Norman Carey Carmine Emanuele Cella Elaine Chew David Clampitt Darrell Conklin Classes Préparatoire aux Grandes Ecoles, Perpignan, France University of Athens, Greece IRCAM / CNRS / UPMC, France IRCAM / CNRS / UPMC, France Brock University, Canada Florida State University, USA CUNY Graduate Center, USA IRCAM, France Queen Mary, University of London, UK Ohio State University, USA Universidad del País Vasco UPV/EHU, Spain
VIII Organization Arshia Cont Michael Cuthbert Johanna Devaney Morwaread Farbood Thomas Fiore Harald Fripertinger Ichiro Fujinaga Aline Honingh Ozgur Izmirli Catherine Losada Guerino Mazzola Teresa Marrin Nakra Thomas Noll Panayotis Mavromatis Angelo Orcalli Robert Peck Richard Plotkin Ian Quinn Richard Randall Martin Rohrmeier William Sethares Anja Volk Geraint Wiggins Marek Žabka IRCAM, France Massachusetts Institute of Technology, USA Ohio State University, USA New York University, USA University of Michigan-Dearborn, USA Karl-Franzens-Universität Graz, Austria McGill University, Canada University of Amsterdam, The Netherlands Connecticut College, USA University of Cincinnati, USA University of Minnesota, USA The College of New Jersey, USA ESMuC Barcelona, Spain New York University, USA Università di Udine, Italy Louisiana State Univesity, USA University at Buffalo, SUNY, USA Yale University, USA Carnegie Mellon University, USA Massachusetts Institute of Technology, USA University of Wisconsin, USA Utrecht University, The Netherlands Queen Mary, University of London, UK Netherlands Institute for Advanced Study in the Humanities and Social Sciences, The Netherlands Society for Mathematics and Computation in Music President Guerino Mazzola University of Minnesota, USA Vice President Moreno Andreatta IRCAM / CNRS / UPMC, France Secretary Johanna Devaney Ohio State University, USA Treasurer David Clampitt Ohio State University, USA
Organization IX Journal of Mathematics and Music Editors-in-Chief Thomas Fiore Marek Žabka Reviews Editor Jonathan Wild University of Michigan-Dearborn, USA Netherlands Institute for Advanced Study in the Humanities and Social Sciences, The Netherlands McGill University, Canada Sponsoring Institutions Schulich School of Music, McGill University Centre for Interdisciplinary Research in Music Media and Technology
Poster Abstracts 1 Planet-4D Extensions: Hyperspheres for Musical Applications (Gilles Baroin, Emmanuel Amiot) The Planet-4D model, unveiled during Paris MCM 2011, is an original geometrical musical space based on graph theory [1] which grants each pitch class an equivalent physical position, involving more symmetries than any previous 3D model. On the 4D-hypersphere, we can now easily perceive visually all isometries in the Tonnetz as we interpret them as a product of two planar isometries [2]. To obtain the Hypersphere of Chords or Hypersphere of any set we project the generalized Tonnetz T[1,5] on the surface of the 4D-hypersphere of Tonnetze, in order to make the space fit with a specific piece of music [3]. The Hypersphere of Spectra associates any sound (sum of partials) to color and position within an animated Hypersphere [4]. Images and videos: planetes.info, mathemusic.net 1. Baroin, G.: The Planet-4D model: An original hypersymmetric music space. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J., eds.: Mathematics and Computation in Music: Third International Conference, MCM 2011. Lecture Notes in Artificial Intelligence, vol. 6726. Springer, Heidelberg (2011) 2. Amiot, E., Baroin, G.: New symmetries between pc-sets in the Planet-4D Model (forthcoming) 3. Bigo, L., Giavitto, J.L., Spicher, A.: Building topological spaces for musical objects. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J., eds.: Mathematics and Computation in Music: Third International Conference, MCM 2011. Lecture Notes in Artificial Intelligence, vol. 6726. Springer, Heidelberg (2011) 4. Baroin, G., de Gérando, S.: Sons, musique et représentation visuelle en hyperespace: L hypersphère des spectres. Les Cahiers de 3icar, Paris (2012) 2 Some Tools for Music Analysis: Graphs, Configuration Spaces and Fundamental Groups for Musical Modes (Mattia G. Bergomi) This research introduces some new mathematical tools for the analysis of modern (jazz) music. The first step is to build a fitting model to represent musical modes, where fitting means that it can be represented in at least three dimensions and
XII Poster Abstracts in agreement with the most common results of music theory. Our model is based on 2-dimensional graphs: modal structures are represented defining a product denoted by Q T where Q is the space of seventh chords and T is the space of triads. The notes of a modal scale are represented as nodes of a graph. Thanks to this representation, using the Seifert Van Kampen theorem, we compute the modal homotopy group of each kind of seventh chord, obtaining a classification in terms of degrees of freedom. Then we study the interaction between sonorities. This goal has been reached creating paths between graphs, the problem is that they are not easy to visualize, so we conclude introducing braids which make it easy to represent paths among sonorities and understand how a melodic line can be moved on a fixed harmonic structure. In conclusion, we use modal graphs to categorize sonorities, and braids to represent how a musician can use those sonorities when playing on an harmonic structure. In addition, thanks to the representation through braids we are able to recover information, one loses identifying octaves and consequently every chord and its inversions: to every inversion corresponds a non-trivial node of the braid strands. 3 Learning to Hear Transformational Pcset Networks (Yinan Cao, Jonathan Wild, Bennett Smith, Stephen McAdams) The present study investigates auditory learning of transformational patterns among pitch-class sets (pcsets) in a Stockhausen piano piece. We test how a sonority-based ear-training aid that uses contextual transformations could affect auditory plasticity in learning to perceive the functional interrelationships of salient pcsets as they appear in an analysis by David Lewin. Hypothesized behavioral distinctions in pitch-detection performance resulting from differences in atonal ear-training levels and a possible transfer of learning from the original Stockhausen piece to its globally transformed recomposition were observed in a behavioral experiment within the exposure-test framework. Results showed that behavioral plasticity was constantly shaped through cognitive bootstrapping, using working memory schemas that represent common-tone preservation, implicitly acquired during exposure in a pitch-detection trial. Some non-sensitivities to explicitly expressed transformational rule structures (specifically, statistical regularities in common-tone preserving rules) were quite pronounced in the outcomes. In the present experimental settings, auditory exposure to transformational patterns among pcsets triggered shallow, structural encoding of these patterns in an implicit fashion, rather than deep, semantic information processing in an explicit way.
Poster Abstracts XIII 4 A Computational Model for a Morpho-Semantic Typology of Minimal Music Samples (Kaoutar El Ghali, Adil El Ghali, Charles Tijus) Minimal sound sample description usually concentrates on sound sources rather than perceived sound morphology that would explain the sound shape. We aim to determine categories of sound events, summarized by a small number of sonometric figures that are hierarchically organized and defined by the morphological properties of the sound stream; based on natural or taught procedures of segmentation, categorization of various sound events, formalization of sonometric figures and especially validation in terms of differentiation and composition of sonometric figures. Based on the work of Pierre Schaeffer on sound objects, the Laboratoire Musique et Informatique de Marseille has developed a typology of 19 music samples called Semiotic Temporal Units (UST, from French, Unités Sémiotiques Temporelles), that are considered as minimal meaningful units for music. These units are defined on the basis of morphological, kinetic and semantic criteria. We propose a computational description of the semantic criteria of this typology, namely energetic process, movement, and direction. Energetic process is the temporal evolution of matter and is described through sound spectral shape; movement describes the perceived overall movement within a UST and is modeled by instantaneous loudness; and direction informs of the time structure and is depicted as a minimal path in the self-similarity matrix. 5 Automatic Rock n Roll Accompaniment Using a Hidden Semi-Markov Model (Ryan Groves) Music has a specific underlying model which spans such fields as perception, cognition, physics, and more. Unsurprisingly, it is difficult to find an appropriate machine learning model to allow a machine to learn the latent structure of music. The continued expansion of the field of machine learning provides new perspectives and implementations of machine learning methods, which are a powerful tool set when approaching complex musical tasks. Similarly, accurate digital representations of popular songs have recently been created, designed specifically for machines to parse and analyse. Extended probabilistic models provide an inherently sequence-based representation of data, and new data sets provide enough information for machines to learn how to perform musical tasks. The work presented will explore the use of the Hidden Semi-Markov Model [1] to automatically discover Rock n Roll chord progressions using Temperley and de Clerq s Rock n Roll corpus [2]. 1. Yu, S.-Z.: Hidden semi-markov model. Artificial Intelligence 174(2) (2009) 215 243 2. Temperley, D., de Clerq, T.: A corpus analysis of rock harmony. Popular Music 30(1) (2011) 47 70
XIV Poster Abstracts 6 Toward Developing a Polyphonic Music Time-Span Tree Analyzer (Masatoshi Hamanaka, Keiji Hirata, Satoshi Tojo) We have been developing a music analysis system called a polyphonic music timespan tree analyzer (PTTA). A time-span tree assigns a hierarchy of structural importance to the notes of a piece of music on the basis of the Generative Theory of Tonal Music (GTTM). There is a big problem when analyzing polyphonic music by using GTTM, because GTTM only accepts homophonic music. To solve this problem, we first record the composers processes for arranging from polyphony to homophony because the processes show how a musician reduces ornament notes. Using the recording of the arrangement process with the timespan tree of the homophony, we manually acquire a time-span tree of polyphony. Then we attempt to develop a PTTA that semi-automatically acquires a timespan tree of polyphony by implementing a novel rule for time-span analysis. Experimental results show that the PTTA using our proposed rules outperforms the baseline. 7 Coding Schenker: Case Studies in Cadence Detection (Brian Miller) Any attempt at computational music analysis faces the challenge of translating a musician s intuition into algorithmic form. Computer languages with musical toolkits provide a powerful platform for such analysis, but complex methodologies like Schenkerian theory resist straightforward computerization. Seeking to avoid the computational costs associated with full Schenkerian reduction, the algorithm presented here is designed to detect significant cadential figures based on a simplified set of Schenkerian criteria, particularly including dominant tonic bass progression and melodic motion with scale degree one as target. Factors ranging from availability and quality of digitized scores to instrumentationspecific analytical considerations complicate such an approach, but it is nonetheless capable of generating useful data much more quickly than a human theorist working by hand. In the first case study, the cadence detection algorithm facilitates corpus-wide analysis and confirms some basic assumptions about cadences in Schenkerian theory. Next, the algorithm is adjusted to detect instances of the rare ascending Urlinie as described by David Neumeyer. The second study produces promising results but also highlights and leaves unresolved many of the difficulties involved in computational tonal analysis. 8 Normalizing Musical Contour Theory (Rob Schultz) The numerical representation of contour pioneered by Friedmann (1985), Morris (1987), and Marvin and Laprade (1987) represents a genuine watershed in the
Poster Abstracts XV development of musical contour theory. Foremost among its virtues is its greater precision, which enabled the creation of sophisticated similarity measurements that strictly graphic notation cannot easily accommodate. The standard method of numerical contour notation maps pitches onto a subset of the non-negative integers from 0 to n 1(wheren = cardinality) according to their registral position. When approached from a transformational perspective, however, this methodology can in fact yield counterintuitive results. This poster thus advances a normalized contour notation that maps pitches onto evenly distributed subsets of the real numbers from 0 to 1 inclusive. Through brief analytical vignettes and juxtaposition of the two notational schemes, the poster highlights the advantages of the normalized contour system and advocates its widespread adoption in the literature. 9 Testing Cognitive Theories by Creating a Pattern-Based Probabilistic Algorithm for Melody and Rhythm in Jazz Improvisation (Jonathan Spencer, Mariana Montiel, and Martin Norgaard) Previous research by one of the authors suggests that jazz improvisers insert patterns stored in procedural memory into ongoing improvisations while performing. Based on these findings, the present work involves the development and implementation of a probabilistic model using patterns from a corpus of Charlie Parker solos. This pattern-based approach aligns with the theoretical framework suggested by Pressing (1988) but is less compatible with the position that learned procedures control improvisation (Johnson-Laird, 2002). In the previous work, the number of patterns in the Parker corpus was compared with artificial improvisations created using the same chords as the corpus. These artificial improvisations were carried out on software based on grammars and contours, very much in line with the cognitive position that emphasizes learned rule-based procedures in improvisation, as opposed to stored patterns. An analysis of the artificially created improvisations showed minimal use of patterns. The present pattern-based improvisations, using our model, have graphs that coincide significantly with the actual human improvisation. Our model initially created melodic and rhythmic patterns separately but in the current version these two components are joined together. Currently, we can generate authentic jazz improvisations without a dependence on an underlying chord structure. In the future, chords will be incorporated, but with a very different philosophy than found in the software whose improvisations are based on rules that depend entirely on the chords.
Table of Contents Papers The Torii of Phases... 1 Emmanuel Amiot Towards a Categorical Theory of Creativity for Music, Discourse, and Cognition... 19 Moreno Andreatta, Andrée Ehresmann, René Guitart,and Guerino Mazzola Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes... 38 Louis Bigo, Moreno Andreatta, Jean-Louis Giavitto, Olivier Michel, and Antoine Spicher Compositional Data Analysis of Harmonic Structures in Popular Music... 52 John Ashley Burgoyne, Jonathan Wild, and Ichiro Fujinaga Sturmian Canons... 64 Clifton Callender Conceptual and Experiential Representations of Tempo: Effects on Expressive Performance Comparisons... 76 Elaine Chew and Clifton Callender Maximal Translational Equivalence Classes of Musical Patterns in Point-Set Representations... 88 Tom Collins and David Meredith Incorporating Voice Permutations into the Theory of Neo-Riemannian Groups and Lewinian Duality... 100 Thomas M. Fiore, Thomas Noll, and Ramon Satyendra Key Induction and Key Mapping Using Pitch-Class Set Assertions... 115 Eliot Handelman and Andie Sigler The Structure of Z-Related Sets... 128 Franck Jedrzejewski and Tom Johnson Hypergesture Homology for Performance Stemmata with Lie Operators... 138 Guerino Mazzola
XVIII Table of Contents Glarean s Dodecachordon Revisited... 151 Thomas Noll and Mariana Montiel Effects of Temporal Position on Harmonic Succession in the Bach Chorale Corpus... 167 Mitchell Ohriner A Hypercube-Graph Model for n-tone Rows and Relations... 177 Robert W. Peck Using Formal Concept Analysis to Represent Chroma Systems... 189 Tobias Schlemmer and Moreno Andreatta An Alphabet-Reduction Algorithm for Chordal n-grams... 201 Christopher W.M. White Evaluation of n-gram-based Classification Approaches on Classical Music Corpora... 213 Jacek Wo lkowicz and Vlado Kešelj The Minkowski Geometry of Numbers Applied to the Theory of Tone Systems... 226 Marek Žabka Author Index... 241