Toussaint

AAWM JOURNAL VOL. 2 NO. 2 (2013)

The Pairwise Variability Index as a Measure of Rhythm Complexity

Godfried T. Toussaint

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Abstract:

The normalized pairwise variability index (nPVI) is a measure of the average variation (contrast) 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 and 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 correlates with various dimensions of musical and non-musical rhythm 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, styles, and cultures, as well as across non-musical rhythms such as the highly irregular mark patterns of Golomb rulers. It is shown that the nPVI suffers from several shortcomings 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 experimental results reveal that the nPVI correlates moderately, with human performance complexity. It is also able to discriminate between almost all the families of rhythms tested. However, no highly significant differences were found between the nPVI values of binary (duple) and ternary (triple) African syncopated rhythms, partly mirroring the findings by Patel and Daniele (2003) for language rhythms. In addition, a modification of the nPVI is proposed that incorporates knowledge of the underlying meter, and that correlates highly with two measures of human performance complexity, for rhythms that are syncopated.

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Contributor Information:

Godfried T. Toussaint is a Research Professor of Computer Science at New York University Abu Dhabi.

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