A Tool for the Quantitative Anthropology of Music: Use of the nPVI Equation to Analyze Rhythmic Variability within Long-term Historical Patterns in Music

Abstract

The development of musical style across time and geography is of particular interest to historians and musicologists, yet quantitative evidence to support these trends has been lacking. This paper illustrates a novel application of the nPVI ('normalized pairwise variability index') equation to probe and quantify the rhythmic components of music over time. The nPVI equation quantifies the average difference between adjacent events in a sequence (e.g. musical notes in a melody, successive vowels in a spoken sentence). Building upon an earlier finding that German/Austrian composer nPVI values increased steadily from 1600 to 1950 (while Italian composers showed no such increase), the nPVI 'distribution' of themes from individual composers was quantitatively explored. Interestingly, the proportion of 'low nPVI' or 'Italianate' themes decreases rapidly with time while 'high nPVI' (more Germanic) themes concomitantly increase in frequency. 'Middle range nPVIs' exhibit a constant incidence, arguing for a replacement of 'low nPVIs' (Italianate) with 'high nPVIs' over a short time instead of a more modest, long-term progressive shift. Thus, the precise rhythmic components of complex stylistic shifts in music can be quantitatively extracted from music and support the historical record and theory.

The War of the Romantics: An Alternate Hypothesis Using nPVI for the Quantitative Anthropology of Music

“…First, as discussed in London (2013), the Barlow and Morgenstern Dictionary for Musical Themes, which is the source for the data for both Daniele and Patel (2013) and Daniele (2016), is not necessarily a representative corpus. Of particular concern to this study is the under-representation of the German Baroque and the overrepresentation of Romantic composers of questionable historical significance.…”

“…However, the remainder of this response will use the same data set, criteria, and methodology as the Daniele (2016) paper so as to make a direct comparison and illustrate an alternate interpretation of the data.…”

“…Daniele's explanation for this trend is the "Replacement Hypothesis," which is that music with low rhythmic variability is being replaced by music with high rhythmic variability through this time period, which he claims supports the "waning influence" theory. Daniele (2016;reproduced). There is an error in the description of the "middle" bin in the legend of this chart; it should read "32.2 < nPVI < 43", to indicate that the nPVI value in that group is between 32.2 and 43.…”

“…[3] To add the data for these composers, the nPVI for each theme was calculated using the Humdrum toolkit and the standard nPVI command, and the themes were grouped into Daniele's (2016) "bins" as described in his Results section. Figure 3 combines the data from Table 2 with that from Daniele's (2016) Table 2 combined with the eleven from Daniele's (2016) …”

“…Since Daniele (2016) claims that the increase in the percentage of "high" nPVI themes is indicative of the waning influence of Italian music, it is instructive to isolate the data for that category. Figure 4 shows just the data for the percentage of "high" nPVI themes for each composer.…”