Abstract
This paper integrates a broad research about the pragmatic modelling of compositional process, and some mathematical abstractions that arises from the relations between textural configurations. As the available choices for textural organization are limited, it is possible to provide a global map of all possible configurations for a given number of sources (exhaustive taxonomy) and assess all the kinship and metrics between them (topology). The graphic called Partitiogram, in fact, constitutes this phase space, where three basic nets of parsimonious relations are drawn: mnet, vnet and tnet. Each net deals with a different kind of textural transformation. This framework is part of Partitional Analysis (PA) — an original proposal of mediation between mathematical abstractions derived from the Theory of Integer Partitions and compositional theories and practices. The main goal of the theory is the study of compositional games. It has been used in the pedagogy of composition and in the creation of new pieces.
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Notes
- 1.
The symbol \( \preceq \) means “is precedent”.
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Gentil-Nunes, P. (2017). Partitiogram, Mnet, Vnet and Tnet: Embedded Abstractions Inside Compositional Games. In: Pareyon, G., Pina-Romero, S., Agustín-Aquino, O., Lluis-Puebla, E. (eds) The Musical-Mathematical Mind. Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-319-47337-6_12
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DOI: https://doi.org/10.1007/978-3-319-47337-6_12
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