Hemiola, maximal evenness, and metric ambiguity in late Ligeti

Classical hemiola, three regular pulses in the time of two (3:2), can be generalized to any ratio, such as 4:3, 5:6, 11:13, and so on. Maximally even rhythms, by contrast, distribute a set of onsets as evenly as possible against a background lattice. Polyrhythms in Ligeti's late music typically fall into two categories: those which superimpose two or more different pulse streams, and those which draw from sub-Saharan African rhythms. These two devices can be compared from the perspective of maximal evenness. Although hemiola-derived rhythms are less even, some sub-Saharan rhythms combine elements of both hemiola and maximal evenness. This paper looks at rhythm in Ligeti's late music and compares it with the music of the Aka Pygmies, as well as work on metric ambiguity by Simha Arom and Godfried Toussaint, to explore this synthesis of hemiola and maximal evenness.