Several operations on Euclidean rhythms based on musical motivations are defined. The operations defined are complementation, alternation, and decomposition. Some mathematical properties are proved for each and the conditions under which a given operation preserves the Euclidean property are examined. Finally, connections are shown to interlocking Euclidean rhythms and tiling canons, and tiling quasi-canons are introduced.
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Gómez et al. (2009) studied this question.
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