Background
The normalized Pairwise Variability Index (nPVI) has become one of the go-to measures of rhythmic variability in speech, music, and, more recently, animal vocalizations. Despite its successes, the nPVI has been criticized. Condit-Schultz (2019) highlights unintuitive aspects of the measure, identifies problems with applications to symbolic data, and argues for more concrete descriptions of rhythmic features.
Aim
This study aims to develop a general approach to measuring rhythmic features based on rhythmic motifs. Specifically, it introduces a measure of isochronicity that can replace the nPVI.
Main contribution
We reformulate the nPVI in terms of rhythmic motifs and then propose a generalization. A rhythmic motif, such as 1 : 1 : 2, describes the ratios between successive inter-onset intervals. Motifs of length 3 form a triangle (Desain & Honing, 2003) with the isochronous motif 1 : 1 : 1 in the center and the most anisochronous (non-isochronous) motifs close to the corners. This suggests measuring the anisochrony of a motif as the normalized L1-distance from the isochronous motif, with isochrony defined as its complement. The nPVI of a dataset can then be shown to be proportional to the average anisochrony of all motifs of length 2. Importantly, increasing the motif length strengthens the measure of isochrony, since higher isochrony scores then require longer sequences of nearly identical intervals. We use the proposed measure to analyze rhythm in recorded music, but also in animal vocalizations, where the measure, for example, highlight the extreme isochronicity in echolocation click trains of sperm whales (Burchardt & Knörnschild, 2020).
Discussion and conclusion
This study proposes a measure of isochrony that generalizes the nPVI. Moreover, it advocates for analyzing distributions of rhythmical motifs directly, rather than relying on a single aggregate measure like the nPVI. Framing rhythm in terms of distances between rhythmic motifs may also help tailor measures towards particular research questions. The distance to small-integer ratios, to name just one example, could well be used to study such rhythmic categories in music—or indeed in vocalizations of other species.
The normalized Pairwise Variability Index (nPVI) has become one of the go-to measures of rhythmic variability in speech, music, and, more recently, animal vocalizations. Despite its successes, the nPVI has been criticized. Condit-Schultz (2019) highlights unintuitive aspects of the measure, identifies problems with applications to symbolic data, and argues for more concrete descriptions of rhythmic features.
Aim
This study aims to develop a general approach to measuring rhythmic features based on rhythmic motifs. Specifically, it introduces a measure of isochronicity that can replace the nPVI.
Main contribution
We reformulate the nPVI in terms of rhythmic motifs and then propose a generalization. A rhythmic motif, such as 1 : 1 : 2, describes the ratios between successive inter-onset intervals. Motifs of length 3 form a triangle (Desain & Honing, 2003) with the isochronous motif 1 : 1 : 1 in the center and the most anisochronous (non-isochronous) motifs close to the corners. This suggests measuring the anisochrony of a motif as the normalized L1-distance from the isochronous motif, with isochrony defined as its complement. The nPVI of a dataset can then be shown to be proportional to the average anisochrony of all motifs of length 2. Importantly, increasing the motif length strengthens the measure of isochrony, since higher isochrony scores then require longer sequences of nearly identical intervals. We use the proposed measure to analyze rhythm in recorded music, but also in animal vocalizations, where the measure, for example, highlight the extreme isochronicity in echolocation click trains of sperm whales (Burchardt & Knörnschild, 2020).
Discussion and conclusion
This study proposes a measure of isochrony that generalizes the nPVI. Moreover, it advocates for analyzing distributions of rhythmical motifs directly, rather than relying on a single aggregate measure like the nPVI. Framing rhythm in terms of distances between rhythmic motifs may also help tailor measures towards particular research questions. The distance to small-integer ratios, to name just one example, could well be used to study such rhythmic categories in music—or indeed in vocalizations of other species.
- Supplementary files
