Compositional Planning of Trivium for Helder Alto Recorder

Abstract

This article describes the compositional planning of Trivium, for Helder alto recorder, by articulating three referential frameworks associated with Trivium: Grammar, Rhetoric, and Logic. In the first movement, two Python programs implement a Type-3 Chomskyan grammar to generate strings of pitch classes, which are subjected to selection, application, complementation, and compositional polishing. In the second movement, a compositional system transforms an initial motive through rhetorical figures, using heuristic feedback. In the third movement, Boolean operations derived from the planning of Xenakis’s Herma are recontextualized to produce pitch-class sets organized into contrasting formal sections. The study proposes an applied articulation of these frameworks within a documented compositional process. Its main contribution is methodological: it demonstrates how distinct formal models can be converted into operational procedures, subjected to compositional curation, and filtered through concrete conditions of instrumental writing. In addition, the article provides resources for the teaching and practice of compositional planning.