The Pairwise Variability Index as a Tool in Musical Rhythm Analysis

The normalized pairwise variability index (nPVI) is a measure of the average variation of a set of distances (durations) that are obtained from successive ordered pairs of events. It was originally conceived for measuring the rhythmic differences between languages on the basis of vowel length. More recently, it has also been employed successfully to compare large-scale rhythm in speech and music. London & Jones (2011) suggested that the nPVI could become a useful general tool for musical rhythm analysis. One goal of this study is to determine how well the nPVI models various dimensions of musical rhythmic complexity, ranging from human performance and perceptual complexities, to mathematical measures of metric complexity and rhythm irregularity. A second goal is to determine to what extent the nPVI is capable of discriminating between short, symbolically notated, musical rhythms across meters, genres, and cultures. It is shown that the nPVI suffers from several shortcomings, when it comes to modeling metric complexity and rhythm complexity, in the context of short symbolic rhythmic patterns, such as Sub-Saharan African bell patterns, Arabic rhythms, Rumanian dance rhythms, and Indian talas. Nevertheless, comparisons with previous experimental results reveal that the nPVI correlates mildly, but significantly, with human performance complexity. It is also able to discriminate between most of the families of rhythms tested. However, no highly significant differences were found between the nPVI values of binary and ternary musical rhythms, partly mirroring the findings by Patel & Daniele (2003) for language rhythms.