Persistence and change: Local and global components of metre induction using Inner Metric Analysis

Abstract

This paper compares local and global perspectives on the metric structure of musical compositions using the computational model of Inner Metric Analysis. The comparison addresses different hierarchical levels of compositions with respect to metric stability and change. Inner Metric Analysis generates metric hierarchies that are persistent from the global perspective and sensitive to changes from the local perspective. While the global perspective indicates the predominant metric characteristic of a piece or fragment, the local perspective distinguishes between regions of different metric characteristics. Like studies of harmony that investigate tonality as a hierarchic web of relations between chords, phrases and large sections, this article suggests that the time organization of a piece consists of different hierarchical levels. The description of local and global metric characteristics of Webern's Op. 27 using Inner Metric Analysis complements and extends arguments given by David Lewin about a metrical problem observed in this piece.