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.