Analytical Approaches to World Musics
ISSN 2158-5296
2013, Volume 2, No. 2
AAWM JOURNAL Volume 2, No. 2 (2013)
Volume 2, No. 2 (2013)
The Pairwise Variability Index as a Measure of Rhythm Complexity
Godfried T. Toussaint
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.
Tuning Procedures in Ancient Iraq
Sam Mirelman
A manual for tuning a lyre/harp from ancient Iraq (or “Mesopotamia”), dating to the early second millenium BCE, uses a cyclical procedure of tuning pairs of strings (dichords). It is the earliest known example of music theory, predating anything comparable from other cultures by approximately one millenium. This manual enables a lyre/harp player to use a diagnostic method of determining the current mode or tuning of the lyre; it directs the musician to transform the instrument from one mode to another, through a series of tightening or loosening dichords (pairs of open strings). The tuning procedure, which may more accurately be called a modulation procedure, is clearly cyclical. The text employs a complex and precise terminology for strings, dichords and modes. This paper presents a step by step analysis of the tuning procedure as described in this ancient text, which has recently been supplemented by the identification of a new manuscript. In addition, it attempts to outline the basic characteristics of the Mesopotamian tuning system as revealed by the tuning text.
Preliminary Remarks on a Helical Representation of Time
Andrew McGraw
In this article I describe a system for representing musical timing as a helix, enabling the three-dimensional visualization and printing of both micro- and piece-length temporality. Examples from the Balinese gamelan repertoire serve as the principal examples. I describe the functionality of Mathematica code developed to produce the visualizations, providing publically accessible links to the code, data, and output files. Rather than a study presenting extensive findings, this article outlines a method and describes preliminary examples. The model represented here aspires neither to a mathematical formulism—a computational approach to model composers’ processes—nor to a cognitive psychology, which would attempt to reveal ostensibly universal mental representations of musical time. This study combines ethnography with music theory to suggest one possible musical imagination—the helix as a spatial heuristic for listening.
Reflections on composing for Balinese gendér wayang: “The Birth of Kala”
Nicholas Gray
This paper discusses aspects of composing for a specific type of Balinese gamelan ensemble known as gendér wayang, a quartet of metallophones that accompanies shadow puppet plays and life-cycle rituals. The author is a composer and ethnomusicologist who spent many years studying this tradition and has conducted research on traditional compositional methods for the ensemble. He also teaches and leads a gendér wayang ensemble in London. The instrument’s technical difficulty and the highly complex, rhythmically ambiguous nature of the traditional repertoire make this a particularly challenging ensemble to compose for. The paper explores connections between certain ritual pieces in the traditional repertoire, legends surrounding these pieces, and the author’s own composition “The Birth of Kala” which formed part of a collaborative project with actor, storyteller and movement artist Tim Jones in 2012. The starting point of the concert was the instrument itself, with the music and storytelling a kind of meditation on it. The concert had three interwoven strands: firstly Balinese stories surrounding the origins of gendér including the birth of the demonic Kala, secondly traditional pieces, and thirdly the newly composed music. The latter took up most of the second half of the concert as a kind of abstraction of issues raised in the more narrative first half. This article presents a description and analysis together with score in cipher notation and references to the online video of the first performance. It then discusses some issues arising from the work, and from the analysis of it, locating the whole within the context of new gamelan composition.
Toward a New Comparative Musicology
Patrick E. Savage and Steven Brown
We propose a return to the forgotten agenda of comparative musicology, one that is updated with the paradigms of modern evolutionary theory and scientific methodology. Ever since the field of comparative musicology was redefined as ethnomusicology in the mid-twentieth century, musicologists have all but abandoned many features of its original research agenda, not least the overarching goal of cross-cultural musical comparison. We outline here five major themes that underlie the re-establishment of comparative musicology: (1) classification, (2) cultural evolution, (3) human history, (4) universals, and (5) biological evolution. Throughout the article, we clarify key ideological, methodological and terminological objections that have been levied against musical comparison. Ultimately, we argue for an inclusive, constructive, and multidisciplinary field that analyzes the world’s musical diversity, from the broadest of generalities to the most culture-specific particulars, with the aim of synthesizing the full range of theoretical perspectives and research methodologies available.