Musical Rhythm: A Formal Model for Determining Local Boundaries, Accents and Metre in a Melodic Surface

In this paper a general theory will be introduced that allows the description of a melodic surface i.e. a score-like representation of a melody in terms of local grouping, accentuation and metrical structures. Firstly, a formal model will be proposed that detects points of maximum local change that allow a listener to identify local perceptual boundaries in a melodic surface. The Local Botmdary Detection Model (LBDM) is based on rules that are relating to the Gestalt principles of proximity and similarity. Then, it will be shown that the accentuation structure of a melody may automatically be inferred from the local boundary grouping structure. This is based on the assumption that the phenomenal accents of two contiguous musical events are closely related to the degree by which a local boundary is likely to be perceived between them. Finally, the metrical structure is revealed by matching a hierarchical metrical template onto the accentuation structure. It is suggested that the Local Boundary Detection Model presents a more effective method for low-level segmentation in relation to other existing models and it may be incorporated as a supplementary module to more general grouping structure theories. The rhythmic analyses obtained by the methods described herein are tentative, and complementary to higher-level organizational theories. 1 I n t r o d u c t i o n Many contemporary theories of rhy thm (Cooper & Meyer, 1960; Epstein, 1995; Kramer, 1988; Lerdahl ~; Jackendoff, 1983; Yeston, 1976) consider rhy thm to be the organizat ion/structuring of musical sounds into groups (grouping structure) of more or less salient elements (accentuation structure) tha t are in constant interplay/interaction with a hierarchy of beats (metrical structure). Metre receives somewhat different t rea tment in each of these theories and is to a varying extent integrated into the ways rhy thm is defined (Moelants, 1997, this book). For instance, Lerdahl and Jackendoff 's definition of rhy thm is based on two kinds of structures: namely grouping structure that "expresses a hierarchical segmentat ion of a piece into motives, phrases and sections" and metr i cal structure tha t "expresses the intuition tha t the events of a piece are related to a regular alternation of strong and weak beats at a number of hierarchical levels" (Lerdahl ~ Jackendoff, 1983, p.8). They define three kinds of musical accents: phenomenal accents which are due to local intensification such as