Research question/background

There is one rhythmic phrase that is nearly ubiquitous across a large and diverse repertoire of Brazilian samba music. It consists of nine attacks in a cycle of sixteen. Theoretically, the rhythm can be conceptualized as a hyperdiatonic rhythm (cf. Clough 1991): it is both maximally even and prime-generated (c=16, d=9, g=7). If two attacks are removed from where the rhythm ‘clumps’, that is, if the ‘semi-tones’ of the hyperdiatonic rhythm are undone such that every interval is either 2 or 3 sixteenths, then a hyperpentatonic rhythm obtains: the complement of the original rhythm and also maximally even and prime-generated. This second rhythm can also be conceptualized as describing a non-isochronous meter, where the faster pulse stream consists of straight sixteenth notes, and the slow consists of a mixture of 5 eighths and 2 dotted eighths. The metric relationship between these two pulse layers can be described, for example, in one rotation, as 2232223. Music theorists are interested in these scales or rhythms—or even metric descriptions—because they feature unique properties. One of these is that they are just as stable (or just as unstable) in any of the other domains produced by even division of the aggregate (c=16). The ‘problem’ with c=16 is that there is only one domain where even division results: multiples of two, or 2-generation, or g=2. However, 3-generation will yield a maximally even rhythm, which like the hyperpentatonic, can also be interpreted as a meter between two pulses, one isochronous and the other non-isochronous.


The question: if theory suggests that a hyperdiatonic rhythm such as the one described will be multi-stabile (or unstable) across several meters due to its special properties, does this empirically appear to be the case? If, for example, the rhythm is played in various metric contexts (just pulses, for simplicity, and for starters), is the rhythm always just as clear, or more/less clear? Does the listener assume one to be more ‘natural’ or ‘simple’ or ‘obvious’ than the other? And so on.

-S P G

2 thoughts on “Research question/background

  1. This is a questions that I easily imagine being investigated through an experimental study (with exploratory and/or hypothesis-driven analysis). One aspect of the question that should drive the lit review is the concept of “multistability.” This is a phenomenon that has generated a sizable number of studies in the visual and linguistic domains, and there has also been several attempts at finding auditory analogs to these stimuli (e.g., Necker cube, “fly-life” perceptual shift, etc.).

    The other obvious body of research you will need to engage is the literature on nonisochronous beats/meters.

    While you embark on this task, think of the format you envision for the final product. Will this be mainly a literature review, a speculative paper, a detailed proposal for an experimental study, an analysis of representative examples informed by empirical findings, etc.?

  2. Briefly, I envision my work to be a theoretical development of a hypothesis (that will involve some small amount of lit. review) and an experimental proposal.

    I may need some clues on how to find the right literature pertaining to ‘multistability’….

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