Génération automatique de mélodie par la programmation par contraintes

La programmation par contraintes est un type de programmation déclarative, un paradigme naturellement adapté au traitement de problèmes musicaux. En effet, la composition musicale s’apparente à un processus déclaratif pendant lequel le compositeur travaille pour créer de la musique qui respecte les règles générales de l’art et les critères plus spécifiques du style adopté tout en y incorporant ses propres contraintes. Le parallèle entre cet exercice et la résolution d’un problème de satisfaction de contraintes se fait donc instinctivement. La principale difficulté se trouve au niveau de la modélisation du problème. Une pièce musicale est composée de plusieurs dimensions entre lesquelles existent beaucoup d’interactions. Il est pratiquement impossible pour un système informatique de représenter précisément toutes ces dépendances. Les systèmes de contraintes conçus pour traiter de problèmes musicaux se concentrent alors sur des dimensions en particulier. Parmi ces problèmes, on retrouve la génération de mélodie qui concerne donc les hauteurs et les durées des notes d’une ligne mélodique accompagnée par une suite d’accords. La modélisation d’un tel problème se concentre sur une séquence de notes et ne présente donc aucun élément de polyphonie ou d’instrumentation par exemple, ce qui simplifie la situation. L’objectif de ce projet est de concevoir un système de génération automatique de mélodie selon une suite d’accords donnée qui utilise les informations d’un corpus pour guider la composition. Deux des principaux défis de ce type de problème sont l’organisation des variables et le contrôle de la structure globale de la mélodie générée. Pour relever le premier, nous avons émis l’hypothèse qu’un système structuré hiérarchiquement offrait le plus de flexibilité et permettrait donc d’exprimer les contraintes plus facilement. En ce qui concerne la structure du résultat, nous avons mis au point un algorithme de détection de patrons répétitifs basé sur des arbres des suffixes qui permet au système de répliquer les éléments de la structure d’une mélodie existante.----------ABSTRACT: Constraint programming belongs to the declarative programming paradigm which is naturally suited to tackle musical problems. Musical composition can be seen as a declarative process during which the composer works to create music respecting the general and specific rules of the chosen style and also adds his own touch. The connection between this process and resolving a constraint satisfaction problem is made instinctively. The main challenge of this field is modeling the problem because of all the different dimensions which interact together in a music piece. It is virtually impossible for a computer-based system to provide a view of the same quality a human composer would have. Thus, constraint systems designed to tackle musical problems usually focus on specific dimensions. One of these problems consists of generating a melody given a chord sequence, which only involves note durations and pitches, there is no concept of polyphony or instrumentation, for example. The goal of this project is to design and implement a system able to generate a melody given a chord sequence, using information from a corpus to guide composition. Two of the main challenges of this kind of problems are the variables arrangement and the control of the global structure of the melody. Regarding variables, we made the assumption that a hierarchical organization would improve the system’s flexibility which would make it easier to express constraints. For the structure, we designed an algorithm which uses suffix trees to detect repeating patterns in existing melodies and made the system able to replicate them in the result. Our system is made of hierarchically organized blocs. The melody is made of bars which contain chords under which are located the notes. Each block has a variable number of notes which needs to be fixed first in order to instantiate the corresponding variables. This means that the system has to work in two phases. The first one assigns a rhythm pattern to every bar, which decides both the number of notes and their durations. The second phase fixes the pitch of every note of the melody

Enforcing Meter in Finite-Length Markov Sequences

Markov processes are increasingly used to generate finite-length sequences that imitate a given style. However, Markov processes are notoriously difficult to control. Recently, Markov constraints have been introduced to give users some control on generated sequences. Markov constraints reformulate finite-length Markov sequence generation in the framework of constraint satisfaction (CSP). However, in practice, this approach is limited to local constraints and its performance is low for global constraints, such as cardinality or arithmetic constraints. This limitation prevents generated sequences to follow structural properties which are independent of the style, but inherent to the domain, such as meter. In this article, we introduce meter, a constraint that ensures a sequence is 1) Markovian with regards to a given corpus and 2) follows metrical rules expressed as cumulative cost functions. Additionally, meter can simultaneously enforce cardinality constraints. We propose a domain consistency algorithm whose complexity is pseudo-polynomial. This result is obtained thanks to a theorem on the growth of sumsets by Khovanskii. We illustrate our constraint on meter-constrained music generation problems that were so far not solvable by any other technique

Advances in Multiple Viewpoint Systems and Applications in Modelling Higher Order Musical Structure

PhDStatistical approaches are capable of underpinning strong models of musical structure, perception, and cognition. Multiple viewpoint systems are probabilistic models of sequential prediction that aim to capture the multidimensional aspects of a symbolic domain with predictions from multiple finite-context models combined in an information theoretically informed way. Information theory provides an important grounding for such models. In computational terms, information content is an empirical measure of compressibility for model evaluation, and entropy a powerful weighting system for combining predictions from multiple models. In perceptual terms, clear parallels can be drawn between information content and surprise, and entropy and certainty. In cognitive terms information theory underpins explanatory models of both musical representation and expectation. The thesis makes two broad contributions to the field of statistical modelling of music cognition: firstly, advancing the general understanding of multiple viewpoint systems, and, secondly, developing bottom-up, statistical learning methods capable of capturing higher order structure. In the first category, novel methods for predicting multiple basic attributes are empirically tested, significantly outperforming established methods, and refuting the assumption found in the literature that basic attributes are statistically independent from one another. Additionally, novel techniques for improving the prediction of derived viewpoints (viewpoints that abstract information away from whatever musical surface is under consideration) are introduced and analysed, and their relation with cognitive representations explored. Finally, the performance and suitability of an established algorithm that automatically constructs locally optimal multiple viewpoint systems is tested. In the second category, the current research brings together a number of existing statistical methods for segmentation and modelling musical surfaces with the aim of representing higher-order structure. A comprehensive review and empirical evaluation of these information theoretic segmentation methods is presented. Methods for labelling higher order segments, akin to layers of abstraction in a representation, are empirically evaluated and the cognitive implications explored. The architecture and performance of the models are assessed from cognitive and musicological perspectives.Media and Arts Technology programme, EPSRC Doctoral Training Centre EP/G03723X/1