Representing Melodic Patterns as Networks of Elaborations

Abstract

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.