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