Previous discussions of musical pattern haveunderlined difficulties in seeking pattern as asequence of pitches, or of intervals or of other localand atomic features. This paper describes a manner ofrepresenting melodies through a hierarchical structureof elaboration, derived from concepts common in musictheory (in particular, the concept of reduction foundin the work of Schenker and of Lerdahl & Jackendoff).The fundamental structure is a planar directed acyclicgraph, each node of which represents a musical note(not necessarily as it is present in the actualmelody) and an elaboration which generates that noteon the basis of two parents. These graph structurescan be converted to trees, aiding processing andcomparison, in two ways. Firstly, any graph can betransformed into a set of binary trees in which eachnode represents an interval between two notes and anelaboration of that interval. Secondly, in the planargraph, the link of a node to one of its parents oftenprovides no useful information and can be disregarded,resulting in a reduction of the graph tending towardsa set of trees. From this arises a new approach to thequestion of melodic segmentation. Examples of melodicfragments represented in this manner demonstrate howthe representation makes explicit similarities betweenfragments which would not be found by an approachusing sequences of features.
This article is contained in a special issue on the subject of musical pattern processing arising from a symposium on Musical Creativity at a convention of the Society for the Study of Artificial Intelligence and the Simulation of Behaviour. Mechanisms for the description of musical patterns and for their discovery have become very important topics in the interdisciplinary field of Music Information Retrieval (with potential applications in the digital music industry). This article presents a formal system for representing melodies with the objective of making explicit the patterns of harmonic-contrapuntal structure in a piece, so facilitating their automatic discovery and processes based on patterns. Among musical grammars and representation systems, it is the one most closely based on Schenkerian theory. It is also the only one extended to a fully computable representation system, providing a basis for software systems which operate in a musically intelligent manner. This has been demonstrated in melody-generation and editing software written by the author, entitled Novagen, which may be seen online. This software was used together with the Eyesweb system of the Infomus musical informatics laboratory at the University of Genoa as the basis for a program to generate melodies in response to the movements of a dancer. The representation system allows control of high-level characteristics of the melody, such as the regularity of its structure, according to data extracted from the dancer's movements. The melody-generation project was supported by a grant from the AHRC and presented at the COST287-ConGAS Symposium on Gesture Interfaces for Multimedia Systems, University of Leeds, 2004. RAE_import_type : Journal article RAE_uoa_type : LICA