International Workshop on Computational Music Analysis

Stephan Schaub
(Ircam / doctorant à Paris IV Sorbonne)
Les implications de la formalisation mathématique dans les pratiques compositionnelles
de Milton Babbitt et de Iannis Xenakis à travers deux études analytiques
Samedi 5 avril 2008, de 10h à 12h30
ENS, Salle Weil
45, rue d’Ulm 75005 Paris
(Entrée libre dans la mesure des places disponibles)
Mon intervention sera centrée autour des implications de la formalisation mathématique dans deux démarches de compositeurs de la seconde
moitié du XXe siècle : Milton Babbitt (1916) et Iannis Xenakis (1922-2001). Le terme d’« implication » sera ici entendu selon les deux sens qui lui
sont généralement attribués. Il s’agira en effet, à partir d’exemples précis, de cerner les modalités « opératoires » de la formalisation chez ces
deux compositeurs, la manière avec elle est, donc, impliquée dans les processus compositionnels. Dans un second temps, on s’interrogera sur
les implications, dans le sens logique cette fois-ci, que nos observations pourrait avoir sur l’interprétation analytique des œuvres concernées,
et sur celle des démarches plus générales de ces compositeurs.
International Workshop on Computational Music Analysis
(séance organisée par Chantal Buteau et Christina Anagnostopoulou)
Samedi 5 et dimanche 6 avril 2008
Ircam, Salle I. Stravinsky
1, place I. Stravinsky 75004 Paris
(Entrée libre dans la mesure des places disponibles)
Samedi 5
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14h30 - 14h40 Welcoming (Moreno Andreatta)
14h40 - 15h20 Christina Anagnostopoulou & Chantal Buteau : Computational Analysis Workshop Introduction: First movement of
Brahms' Op 51 No 1 and an Overview of the Proposed Computational Approaches
15h20 - 16h00 Fernando Gualda (Sonic Arts Research Centre - Queen's University of Belfast, UK) Structural Analysis and Motivic Pattern
Matching using Pitch-Class Categories and Dissimilarity Measurements
16h00 - 16h40 Olivier Lartillot (Finnish Centre of Excellence in Interdisciplinary Music Research, University of Jyväskylä, Finland) :
Automated motivic analysis of Brahms' String Quartet based on multi-dimensional closed pattern mining
17h20 - 18h00 Darrell Conklin : Mining for Distinctive Patterns in the First Movement of Brahms's String Quartet in C Minor
18h00 - 18h40 Philippe Cathé : Vecteurs harmoniques et analyse stylistique. Pourcentages et ratios nouveaux obtenus grâce au logiciel
"Charles" : l'exemple du premier mouvement du Quatuor à cordes opus 51-1 de Johannes Brahms.
Dimanche 6
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10h00 - 10h10 Introduction (Christina Anagnostopoulou & Chantal Buteau)
10h10 - 10h50 Yun Kang Ahn : Towards K-Nets in Quatuor n°1 of Brahms
10h50 - 11h30 Chantal Buteau : Topological Spaces of Motives of Brahms Op. 51 No1
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11h50 - 12h30 Atte Tenkanen (Department of Musicology, University of Turku, Finland) : Measuring Tonal Articulations in Compositions
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14h30 - 17h30 Discussion: Comparing Approaches and Analyses
Résumés :
Christina Anagnostopoulou and Chantal Buteau (Univ . of Athens, Greece & Dep. of Mathematics, Brock University, Canada) : Computational
Analysis Workshop Introduction: First movement of Brahms' Op 51 No 1 and an Overview of the Proposed Computational Approaches
We will briefly introduce of Brahms' Op.51 No1 through summarizing its analyses by Forte (1983), Lewin (1990), and Huron (2001) and will give
an overview of the common and different aspects of the computational approaches that will be presented during the workshop.
Chantal Buteau (Department of Mathematics, Brock University, Canada) : Topological Spaces of Motives of Brahms Op. 51 No1
A topological computer-assisted analysis of Brahms' String Quartet, Op 51/No. 1, is presented. Our immanent approach, based on motif,
contour, gestalt, and motif similarity concepts, comprises neighborhoods of motives (bringing together motives of different cardinalities) that
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yield -topological spaces, called motivic spaces. In order to formalize germinal motives within motivic spaces, weight functions are introduced
and lead to 'Motivic Evolution Trees', a graphical representation of the overall motivic spectrum of a composition. The model implementation
(Java) constructs, given a music piece (midi) and (topological) analysis parameters, the motivic space of the piece, calculates the weight
function and motivic evolution tree, and exhibits (in OpenMusic and in Maple) diverse representations of the resulting motivic spaces.
Philippe Cathé (Université Paris-IV Sorbonne, France) : Vecteurs harmoniques et analyse stylistique. Pourcentages et ratios nouveaux obtenus
grâce au logiciel "Charles" : l'exemple du premier mouvement du Quatuor à cordes opus 51-1 de Johannes Brahms.
Au départ, le logiciel « Charles » a été conçu comme une automatisation des calculs issus de l'usage des vecteurs harmoniques de Nicolas
Meeùs, théorie s'intéressant aux progressions des fondamentales des accords. Les versions plus récentes offrent de nouvelles possibilités,
permettant d'inclure ou non les mouvements harmoniques pendulaires et donnant des statistiques détaillées sur les paires vectorielles, niveau
stylistiquement très important. Enfin, à rebours du projet initial, les dernières versions prennent en compte la nature des accords et visent à
valider expérimentalement certaines de mes hypothèses concernant les liens entre les dissonances et le comportement préférentiel de
certains accords. L'ensemble de ces questions sera évoqué et discuté à travers une analyse du premier mouvement du premier Quatuor à
cordes de Brahms.
First, « Charles » software has been conceived as an automation of the calculations consequent upon the use of Nicolas Meeùs's harmonic
vectors, a theory based on the classification of harmonic roots progressions. With new versions came new possibilities, allowing including or
not pendular harmonic motions and giving detailed statistics about the vectorial pairs, a very important stylistic level. Finally, unlike the
initial project, last versions take in account the nature of chords and try to confirm experimentally some of my hypothesis about the
connections between dissonances and the preferential moves of some chords. All these questions will be exposed and discussed through an
analysis of the first movement of Brahms first String Quartet.
Darrell Conklin (Department of Computing, City University London, UK) : Mining for Distinctive Patterns in the First Movement of Brahms's
String Quartet in C Minor
Motivic analysis can be viewed as a predictive data mining problem, with the goal of discovering general patterns that are distinctive:
occurring with significantly higher probability in an analysis corpus as compared to an anticorpus. Patterns are discovered by an algorithm that
explores a pattern specialization space using two refinement operators. The method was applied to the four instrumental sequences of the
first movement of Brahms's string quartet No. 1 in C Minor as an analysis corpus, with the string quartets Nos. 2 and 3 used as an anticorpus.
Several of the motives categories proposed by Forte (1983), including alpha, beta, epsilon, theta and lambda emerge as distinctive patterns.
In broad agreement with Huron's (2001) results, only the prime form of the alpha motive is found to be distinctive. The results indicate that
data mining can be useful for computational motivic analysis.
Fernando Gualda (Sonic Arts Research Centre - Queen's University of Belfast, UK) : Structural Analysis and Motivic Pattern Matching using PitchClass Categories and Dissimilarity Measurements
This research focus on three relationships: Structure x Motif, Equivalence x Dissimilarity, and Automation x Interaction; and suggests a
paradigm for computational analysis of music.
Structural analysis as a top-down, dissimilarity based approach, was used to partition the first movement of Brahms Op. 51 No. 1 to retrieve
its overall form. Motivic Pattern Matching (bottom-up) aims to find short arrays of notes that are either equivalent or exhibit small
dissimilarity.
Arrays of notes presenting identical rhythmic patterns and identical pitches are equivalent. Sets of pitch-classes that are isomorphic under
certain tonal relationships were considered equivalent; dissimilarity was calculated using distance measurements depending on occurrences of
extra pitches, differences between rhythmic patterns, and overall variance.
New software application has been implemented, especially for demonstration at the Workshop. It offers two interfaces: an automatic
analysis,which is a type of unsupervised pattern recognition (clustering) based on an initial set of parameters; as well as a query based
interactive analysis,which allows users to decide what patterns to match. In both cases,the software lists equivalent and similar patterns,
according to their order and dissimilarity.
Yun Kang Ahn (IRCAM, Music Representation Team, France) : Towards K-Nets in Quatuor n°1 of Brahms
Considering the problem of musical motif, we intend to apply transformational theory to the Brahms'Quatuor. This leads us to think about
how important the motif is and we aim at emphasizing this view using Lewin's approach shown in his Klavierstucke analysis, where he targets a
covering of the musical score.
Olivier Lartillot (Finnish Centre of Excellence in Interdisciplinary Music Research, University of Jyväskylä, Finland) : Automated motivic analysis
of Brahms' String Quartet based on multi-dimensional closed pattern mining
A methodology for automated extraction of repeated patterns in discrete time series data is presented, dedicated to the discovery of
repeated motives in symbolic music representations. The principles of the approach are illustrated through an analysis of Brahms' String
Quartet, Op 51, No. 1, first movement (Allegro). The main idea consists in a search for closed patterns in a multi-dimensional parametric
space. A modeling of cyclic pattern enables an adapted filtering of combinatorial redundancy caused by successive repetitions of patterns. The
resulting algorithm offers compact but detailed analyses of the motivic content of the piece.
Atte Tenkanen (Department of Musicology, University of Turku, Finland) : Measuring Tonal Articulations in Compositions
In this presentation two algorithms for comparing pitch-class based distances between pitch-class sets are introduced. The main goal is to use
these distance functions with the so-called comparison set analysis (CSA), presented by Huovinen and Tenkanen (to appear in Music Analysis).
CSA is a method with which, for example, formal articulations of a musical composition can be perceived. In CSA musical units like pitch
classes in a composition are segmented into overlapping sets of the same cardinality and these segments are then compared with a selected
comparison set, constructed from similar units. The comparison set embodies a chosen musical property whose prevalence in a composition is
then evaluated in the analysis. The results can be presented in different types of graphs showing trend curves or mean points.
Two algorithms, mentioned in the beginning, are applied in solving such problems which are related to 'referential pitches' and tonalities in a
composition. The use of the latter function ('tonal distance') are exemplified by a specific problem: which are, with respect to tonality, the
most uncommon places on the surface level of a composition? The method makes possible interesting analytical approaches that concern the
musical form, harmonic trends, modulations and harmonic rhythm.
Quelques repères bibliographiques :
- A. Forte, "Motivic design and structural levels in the first movement of Brahms's String Quartet in C minor", The Musical Quarterly, Vol. 69
No 4, 1983.
- D. Huron, "What is a musical feature? Forte's analysis of Brahms's opus 51 no 1, revisited", MTO, Vol. 7 No 4, 2001.
- D. Lewin, "Brahms, his past, and modes of music theory". In G. Bozarth (Ed), Brahms Studies: Analytical and Historical Perspectives, 1990.
- M. Musgrave and R. Pascall, "The String Quartets op. 51 no 1 in C minor and no 2 in A minor: A preface". In Brahms 2, bibliographical,
documentary and analytical studies, Cambridge University Press, 1987
- A. Whittall, "Two of a kind? Brahms's op 51 finales". In Brahms 2, bibliographical, documentary and analytical studies, Cambridge University
Press, 1987.
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