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Mathematical and Computational models in Music

Apr 18, 2018 - Apr 18, 2018

9am - 6pm

University of Pavia


The workshop “Mathematical and Computational models in Music” will be held in Pavia on 18th April 2018. The day before an inaugural concert will take place at the Conservatory of Music “Vittadini” in Pavia.

The talks will be devoted to discuss and disseminate recent research results in Mathematical Music Theory, Computer aided musical analysis and applications in composition. The workshop is addressed to mathematicians, computer scientists, composers, music theorists, musicologists and anyone who has an interest in this interdisciplinary field of research.

The workshop is organized by the Department of Mathematics “F. Casorati” of the University of Pavia (Italy) and SMIR (Structural Music Information Research) with the financial support of Embassy of France in Italy, the Institut Français Italia and the USIAS (University of Strasbourg Institute for Advanced Study).

Participation is free. Register to the Workshop 


17th April

20:30 // Concert at the Conservatory of Music “Vittadini” of Pavia

18th April

Conferences will be held at the University of Pavia, in the Aula Scarpa of the Palazzo Centrale, Corso Strada Nuova n.65, Pavia.

9:15 – 10:15 // Moreno Andreatta: “Elements of contemporary ‘mathemusical’ research: a survey on algebraic, topological and categorical approaches”
In this introductory talk, we will offer a short survey on some of the most fascinating music-theoretical and compositional problems that have been tackled by the ‘mathemusical’ community in the last twenty years. In particular, we will propose a journey through some algebraic, topological and categorical approaches showing the nice interplay between mathematical formalization and computational modeling. Some of these problems are currently investigated within the SMIR Project, an interdisciplinary research project based at IRMA (the Institut de Recherche Mathématique Avancée of the University of Strasbourg) and aiming at reinforcing the structural component of Music Information Research via a collaboration between mathematicians, computer scientists, computational musicologists and composers.

10:45 – 11:45 // Louis Bigo: “Musical representations and transformations with chord complexes”
The notion of symbolic pitch/chord space, as the Tonnetz, is frequently used in musical theory, analysis and composition to grasp melodic and harmonic properties that elude traditional representation systems. We generalize this approach by reformulating from a spatial point of view different musical problems (style recognition, melodic and harmonic transformations, etc.). Musical spaces that are used are formulated as simplicial complexes. A simplicial complex allows the discrete representation of a set of elements through topological cells linked to each other by specific neighborhood relationships. Elementary musical objects (e. g. pitchs or chords) are represented by simplices, and complexes are built by organizing them according to a neighborhood relationship which translates a musical property, for example consonance. A musical sequence is represented in a complex by a trajectory. The aspect of the trajectory reveals information about the style of the piece and the composition strategies that have been used. The application of geometrical operations on trajectories leads to musical transformations on the represented piece. These transformations are applied to pieces of different styles (classical, jazz, pop,…). We will present the software HexaChord dedicated to the use of this type of musical space for analysis, composition and pedagogy.

11:45 – 12:45 // Emmanuel Amiot: “Rhythmic canons and other fascinating tilings problems in music”
The topic of rhythmic canons — making a mosaic with copies of some rhythmic motif — is of interest both for mathematicians, being connected to actively studied conjectures, and for composers, providing quality material for a wide variety of music styles. The present talk will endeavour to show the state of the art on rhythmics canons by translation and also evoke some more general tilings, with unexpected journeys into high algebra, Galois theory or combinatorics.

14:30 – 15:30 // Giovanni Albini: “Discoveries and constraints: my mathematically informed aesthetics of music composition”
The aim of this lecture is to offer an individual, subjective answer to a broad, old question: how can mathematics participate informing an aesthetic theory of music composition? I’ll answer it through the case study of techniques and scores I elaborated and composed in the context of my personal aesthetics, artistic purposes and beliefs, that are mathematically informed themselves. More specifically, I’ll propose the theoretical description of certain composition systems of mine that feature mathematics as a tool for discoveries and for setting constraints, along with some aesthetic implications I believe these systems can entail.

15:30 – 16:30 // Sonia Cannas and Ludovico Pernazza: “Generalized PLR-group and Chicken-wire Torus for seventh chords”
The main idea of transformational theory is to model musical transformations using algebraic structures. Starting from the well-known neo-Riemannian group PLR that describes parsimonious transformations between major and minor triads, we will present a generalization to the classical types of seventh chord (dominant, minor, half-diminished, major, diminished). We will also introduce the correspondent chord-based graph for sevenths, that is a generalized Chicken-wire Torus (dual of the famous note-based graph Tonnetz). As in the latter, our graph of sevenths offers to the computational musicologists new and promising analytical tools.

17:00 – 18:00 // Daniele Ghisi: “Music Across Music: Towards a Corpus-Based, Interactive Computer-Aided Composition”
The reworking of existing music in order to build new one is a quintessential characteristic of the Western musical tradition. This talk proposes and discusses my personal approach to the subject: the borrowing of music fragments from large-scale corpora (containing audio samples as well as symbolic scores) in order to build a low-level, descriptor-based palette of grains. Parameters are handled via digital hybrid scores, in order to equip corpus-based composition with the control of notational practices. This talk also presents the dada library, providing Max with the ability to organize, select and generate musical content via a set of graphical interfaces manifesting an exploratory approach towards music composition. Its modules address a range of scenarios, including, but not limited to, database visualization, score segmentation and analysis, concatenative synthesis, music generation via physical or geometrical modelling, wave terrain synthesis, graph exploration, cellular automata, swarm intelligence, and videogames. The library is open-source and it fosters a performative approach to computer-aided composition. Finally, this talk addresses the issue of whether classical representation of music, disentangled in the standard set of traditional parameters, is optimal. Two possible alternatives to orthogonal decompositions are presented: grain-based score representations, inheriting techniques from corpus-based composition, and unsupervised machine learning models, providing entangled, `agnostic’ representations of music.