Rhythmicon Relationships, Farey Sequences, and James Tenney’sSpectral CANON for CONLON Nancarrow(1974)
2012; Oxford University Press; Volume: 34; Issue: 2 Linguagem: Inglês
10.1525/mts.2012.34.2.48
ISSN1533-8339
Autores Tópico(s)Musicology and Musical Analysis
ResumoMulti-layered polyrhythms have appeared frequently in Western music of the past century. Such rhythmic combinations can display surprising, emergent forms of perceptible order. In this essay, I explore the objective and perceived characteristics of two such stratified rhythmic structures. The first of these, a divisive polyrhythmic array, superimposes “tuplets” of progressively higher order, each subdividing a common basic duration. In the second structure, a multiplicative polyrhythmic array, the inter-attack durations in successive rhythmic layers are progressively higher multiples of a common basic duration. Each of these array types exhibits characteristic composite features that are readily audible in performances and visible in scores, including patterns of attack coincidences and arpeggiations traversing multiple rhythmic layers. Mathematical modeling of the arrays elucidates such features. I conclude with a detailed analysis of a composition by James Tenney in which polyrhythmic arrays of both sorts supply fundamental musical material, and whose formal design involves a transition between the two array types. A detailed correspondence between pitch and rhythmic structures in that work is also examined.
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