Computational creation and morphing of multi-level rhythms by control of evenness

We present an algorithm, instantiated in a freeware application called MeanTimes, that permits the parameterized production and transformation of a hierarchy of well-formed rhythms. Each “higher” rhythmic level fills in the gaps of all “lower” levels, and up to six such levels can be simultaneously sounded. MeanTimes has a slider enabling continuous variation of the ratios of the intervals between the beats (onsets) of the lowest level. This consequently changes—in a straightforward manner—the evenness of this level; it also changes—in a more complex, but still highly patterned manner—the evennesses of all higher levels. This specific parameter, and others used in MeanTimes, are novel: we describe their mathematical formulation, demonstrate their utility for generating rhythms, and show how they differ from those typically used for pitch-based scales. Some of the compositional possibilities continue the tradition of Cowell and Nancarrow, proceeding further into meta-human performance, and have perceptual and cognitive implications that deserve further attention