Nestings and Intersections between Partitional Complexes. Gentil-Nunes, P. MusMat - Brazilian Journal of Music and Mathematics, I(2):93–108, 2017.
Nestings and Intersections between Partitional Complexes [pdf]Paper  abstract   bibtex   
The formalization of musical texture is the main objective of Partitional Analysis. Each integer partition corresponds to a specific textural configuration and is used as a tool to organize and systematize the work with textures through the compositional process. Partitional complexes, on the other hand, are sets of partitions, observed in the analysis of musical excerpts, that work in tune to create stable temporal domains where a referential partition projects, extends or presents itself as dominant. The number of partitions and complexes for a certain instrumental, vocal or electronic medium is finite and implies nestings and intersections that can provide important information about textural possibilities available to the composer. In the present work, the relationships establishedbetween distinct partitional complexes are discussed, as well as the characterization of an hierarchy related to the number of total choices that each complex offers to the composer.

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