Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)

Pages 399–402

Maximally-even (ME) rhythms, in which attacks (or the onsets of
notes) are distributed as evenly as possible over a given number
of pulses, are common in many cultures. One way to generate a ME
rhythm with *m* attacks per *n* pulses is to digitize
a line of slope *m*/*n*. If the slope is rational,
the resulting rhythm is periodic; irrational slopes yield Sturmian
sequences, which are balanced, almost periodic, self-similar and
hierarchical sequences that are highly relevant in the study of
musical objects possessing these same properties. Rhythmic tilings
are combinations of rhythms that yield one and only one onset per
pulse. Rhythmic tiling canons are tilings in which the component
rhythms are version of a single tile. Sturmian rhythms can be used
to create completely new kinds of aperiodic rhythmic tiling canons,
in which the relations of the component rhythms are determined by
the continued fraction of the slope.

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