Representing Trees with Constraints

Proceedings of the First International Conference on Computational Logic (CL2000)This paper presents a method for representing trees using constraint logic programming over finite domains. We describe a class of trees that is of particular interest to us and how we can represent the set of trees belonging to that class using constraints. The method enables the specification of a set of trees without having to generate all of the members of the set. This allows us to reason about sets of trees that would normally be too large to use. We present this research in the context of a system to generate expressive musical performances and, in particular, how this method can be used to represent musical structure

Towards a Computational Model of Musical Accompaniment: Disambiguation of Musical Analyses by Reference to Performance Data

Institute of Perception, Action and BehaviourA goal of Artificial Intelligence is to develop computational models of what would be considered intelligent behaviour in a human. One such task is that of musical performance. This research specifically focuses on aspects of performance related to the performance of musical duets. We present the research in the context of developing a cooperative performance system that would be capable of performing a piece of music expressively alongside a human musician. In particular, we concentrate on the relationship between musical structure and performance with the aim of creating a structural interpretation of a piece of music by analysing features of the score and performance. We provide a new implementation of Lerdahl and Jackendoff’s Grouping Structure analysis which makes use of feature-category weighting factors. The multiple structures that result from this analysis are represented using a new technique for representing hierarchical structures. The representation supports a refinement process which allows the structures to be disambiguated at a later stage. We also present a novel analysis technique, based on the principle of phrase-final lengthening, to identify structural features from performance data. These structural features are used to select from the multiple possible musical structures the structure that corresponds most closely to the analysed performance. The three main contributions of this research are:1- An implementation of Lerdahl and Jackendoff’s Grouping Structure which includes feature-category weighting factors; 2- A method of storing a set of ambiguous hierarchical structures which supports gradual improvements in specificity; An analysis technique which, when applied to a musical performance, succeeds 3- in providing information to aid the disambiguation of the final musical structure. The results indicate that the approach has promise and with the incorporation of further refinements could lead to a computer-based system that could aid both musical performers and those interested in the art of musical performance

Representing Trees with Constraints

This paper presents a method for representing trees using constraint logic programming over finite domains. We describe a class of trees that is of particular interest to us and how we can represent the set of trees belonging to that class using constraints. The method enables the specification of a set of trees without having to generate all of the members of the set. This allows us to reason about sets of trees that would normally be too large to use. We present this research in the context of a system to generate expressive musical performances and, in particular, how this method can be used to represent musical structure