Cette thèse explore les rapports entre la formalisation mathématique, ses implications dans les pratiques compositionnelles et ses répercussions sur l’interprétation analytique. Elle se base sur l’étude de Semi-Simple Variations pour piano (1956) de Milton Babbitt, de Nomos Alpha pour violoncelle (1965-1966) de Iannis Xenakis (1921/22-2001), et d’une sélection de textes théoriques publiés par les compositeurs autour de ces deux œuvres.L’argumentaire est divisé en trois parties. La première étudie les textes théoriques afin d’en dégager les éléments formalisés (ou résultant de la formalisation) ainsi que les indices permettant d’en retracer les implications dans les pratiques compositionnelles. Ces éléments sont précisés dans la deuxième partie via la reconstitution des traces laissées par les composantes formalisées dans les textes musicaux (« modèles théoriques »). Ce travail est mené sur les deux œuvres proposées à l’analyse puis élargi à d’autres œuvres. Les modèles théoriques de deux d’entre elles étaient jusque-là restés inédits : Three Compositions for Piano de Babbitt (1947-1948) ; et Akrata de Xenakis pour 16 vents (1964-1965). La troisième partie soumet Semi-Simple Variations et Nomos Alpha à deux analyses : la première étudie les modèles théoriques, directement liés aux univers formels, alors que la seconde examine les surfaces sonores et comment elles articulent et/ou contredisent les éléments dégagés au niveau des modèles. Tout en soulignant le rôle fondamental, quoique très différent, joué par la formalisation dans les univers compositionnels de Babbitt et de Xenakis, la distance séparant les modèles théoriques des surfaces sonores amènent à considérer l’apport des premiers dans l’interprétation analytique comme étant de nature avant tout heuristique. En tant que traces de la pensée du compositeur, les modèles théoriques peuvent néanmoins suggérer de nouvelles pistes et méritent d’être intégrés à des recherches futures. / This thesis explores the links between mathematical formalization, its implications in compositional practices, and its repercussions on the analytical interpretation. It is based on the study of Milton Babbitt’s Semi-Simple Variations for piano (1956), on Iannis Xenakis’ Nomos Alpha for violoncello (1965-1966), and on a selection of theoretical texts published by the composers around these two works. The argumentation is divided in three parts. The first studies the theoretical texts with the aim of extracting from them the components that are formalized (or result form formalization) as well as the indices pointing towards their implications in the compositional practices. These are then put into sharper view in the second part, through the reconstruction of the traces left by these components in the musical texts (“theoretical models”). This reconstruction is first conducted on the two main works considered before other works are considered. The theoretical models of two of them had until now remained unknown: Three Compositions for Piano by Babbitt (1947-1948) ; and Akrata for 16 winds (1964-1965) by Xenakis. The third part submits Semi-Simple Variations and Nomos Alpha to two analyses: one is aimed at the theoretical models, directly linked to the formal universes, the second examines the musical surfaces and at the way they articulate and/or contradict the elements observed in the models. While underlining the fundamental - though very different - role played by mathematical formalization in Babbitt’s and Xenakis’ compositional universes, the distance that separates the theoretical models from the musical surfaces brings one to consider the role of the former within the analytical enterprise as essentially heuristic. As traces of the composer’s thinking, the theoretical models may however suggest new approaches and deserve to be fully integrated in future research.

Written in 1999, Concerto Piccolino is a part of the Composer's Guild of New Jersey Vibraphone Commission, which contains a collection of twelve soli written exclusively for vibraphone. Concerto Piccolino presents vibrant opportunities for both performer and listener to experience the compositional world of Milton Babbitt. With its limited register, ability to control duration and create extreme dynamics, the vibraphone serves as an appropriate vehicle for Babbitt's multi-dimensional style. The intent of this study is to first situate this work into Babbitt's compositional output as well as referencing Babbitt's other works for solo percussion. Next, an investigation into the background structure will provide a recommended analytical framework. Included is a performance guide for how these structures should be realized via surface materials throughout the interpretive and internalization stages of the work. Examining a recommended progression from analysis through performance will demonstrate Concerto Piccolino's significance and proper place in the standard repertoire of percussion. The study concludes with discussing connections to pedagogy and how the importance of Babbitt's work, as well as other composers of serious music, is vital to the forward progress of music performance.

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This dissertation discusses the potential of the snare drum as a solo concert instrument. Four pieces from a collection entitled The Noble Snare are used for demonstration ("Homily" by Milton Babbitt, "Composed Improvisation for Snare Drum" by John Cage, "Peeping Tom" by Dan Senn, and "The Noble Snare" by Stuart Saunders Smith). In the absence of many traditional musical devices (i.e. melody and harmony), alternative means of expression are used by the composer. Each piece is discussed with regard to its distinctive compositional approach and inherent performance issues. Information is also given pertaining to the background of the Noble Snare series. This includes: the inspiration for the project, editorial issues, and its influence on snare drum performance. Much of this research was completed through interviews by with author with Sylvia Smith, publisher of The Noble Snare and owner of Smith Publications.